This paper brings to fruition recently found \cite{migdal2023exact} exact reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the \textbf{quantum} statistical theory of $N$ fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the turbulent limit $N\to \infty, \nu \to 0$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without approximations or fitted parameters. The energy spectrum decays as $k^{-\frac{7}{2}}$. We compute resulting integrals in \Mathematica{} and present effective index $n(t) = -t\partial_t \log E $ for the energy decay as a function of time Fig.\ref{fig::NPlot}. The asymptotic value of the effective index in energy decay $n(\infty) = \frac{5}{4}$, but the universal function $n(t)$ is neither constant nor linear.

Due to the retrognathic mandible, an orthodontist frequently observes skeletal class II malocclusion in growing patients. The preferred technique for analyzing and monitoring the temporomandibular joint alterations caused by the functional device is magnetic resonance imaging [MRI]. The study aimed to assess and compare changes in the articular disc's dimension and location before and following the use of various class II correctors to correct the class II molar relation using MRI technology. Methods: 39 adolescent patients aged 15-23 years old [24 girls and 15 boys] who were diagnosed with skeletal Class II division 1 malocclusion based on clearly defined criteria underwent treatment with either the power scope II [PS], Sabbagh Advanced Repositioning Appliance [SARA] and or Dynaflex [DF] with fixed appliances. For fixed functional treatment, the average length of treatment was 5-7 months. The changes in the articular disc dimension and position and condylar position were assessed. The study was done at the Department of Orthodontics at the College of Dentistry, Hawler Medical University in Erbil City. Results: Group DF has a significant effect on the condylar position index and posterior joint space on the closed mouth and disc length on both open and close mouth techniques, and in the group SARA, disc position, and condylar position index on closed mouth technique have shown that significant differences were observed. Conclusion: Class II malocclusions can be effectively corrected by fixed functional appliances. The statistical significance forward movement of the condyle in the glenoid fossa and the posterior movement of the articular disc concerning the condylar head was observed. The mechanism of action of functional appliances appears to include the forward migration of the C-GF complex.

Pulverized coal pyrolysis based on solid heat carrier has a huge advantage in high tar yield. In this study, pyrolysis experiments of pulverized coal were conducted in a lab-scale fluidized bed reactor at 650 ℃, utilizing char as the solid heat carrier. The influence of mass ratio of char to coal (RATIO) was investigated. Results show that the incorporation of solid heat carrier of char significantly enhanced the initial reaction in coal pyrolysis, resulting in increasing yields of tar and gas but reducing one of char. The yield of tar maximally reached 148.80-262.22% of the Gray-King analysis value at the RATIO of 14.52 g/g. As the RATIO increased, the tar contained more light component content, indicating that incorporating solid heat carriers improved the tar quality. These findings offer significant insights for the design of fluidized bed pyrolysis unit utilizing char as solid heat carrier.

This paper presents the results of investigations into the pyrolysis of waste polypropylene in a laboratory fixed-bed batch reactor. The experiments were designed and verified in such a way as to allow the application of the Response Surface Methodology (RSM) in the development of an empirical mathematical model that quantifies the impacts mentioned above. The influence of the mass of the raw material (50, 100 and 150 g), together with the reactor temperature (450, 475 and 500 °C) and the reaction time (45, 50 and 75 min) was examined. It has been shown that the mass of the raw material, i.e. the filling volume of the reactor, has a significant influence on the pyrolysis oil yield. This influence exceeds the influence of reactor temperature and reaction time. This was explained by observing the temperature change inside the reactor at three different spots at the bottom, middle and top of the reactor. Recorded temperature diagrams show that with greater masses of feedstock, local overheating occurs in the middle part of the reactor, which leads to overcracking of vapor products, and from there to an increased formation of non-condensable gases, i.e. reduced yield of pyrolytic oil.

Chromium (Cr) metal has garnered significant attention in alloy systems owing to its exceptional properties, such as high melting point, low density, and superior oxidation and corrosion resistance. However, its processing capabilities are hindered by the high Ductile-Brittle Transition Temperature (DBTT). Recently, powder bed fusion-laser beam for metals (PBF-LB/M) has emerged as a promising technique, offering the fabrication of net shapes and precise control over crystallographic texture. Nevertheless, research investigating the mechanism underlying crystallographic texture development in pure Cr via PBF-LB/M still needs to be conducted. This study explores the impact of scan speed on relative density and crystallographic texture. At the optimal scan speed, an increase in grain size attributed to epitaxial growth was observed, resulting in the formation of cubic texture. Consequently, a reduction in High Angle Grain Boundaries (HAGB) was achieved, suppressing defects such as cracks and enhancing relative density up to 98.1%. Furthermore, with increasing densification, Vickers hardness also exhibited a corresponding increase. These findings underscore the efficacy of PBF-LB/M for processing metals with high DBTT properties.

This study explored the feasibility of fluoride removal from simulated semiconductor industry wastewater and its recovery as calcium fluoride using fluidized bed crystallization. The continuous reactor showed best performance (>90% fluoride removal and >95% crystallization efficiency) at a calcium to fluoride ratio of 0.6 within first 40 days of continuous operation. The resulting particle size increased by more than double during this time along with a 36% increase in the seed bed height indicating deposition of CaF2 onto the silica seed. The SEM-EDX analysis showed the size and shape of the crystals formed along with high amount of Ca-F ions presence. The purity of the CaF2 crystals were determined to be 91.1% though ICP-OES analysis. Following the continuous experiment, different process improvement strategies are explored. The addition of excess amount of calcium resulted in an additional 6% fluoride removal, however, compared to this single stage process, a two-stage approach was found to be better strategy to achieve a low effluent fluoride concentration. The fluoride removal reached 94% with this two-stage approach under optimum condition of 4 + 1 h HRT combinations and a [Ca2+]/[F-] ratio of 0.55 and 0.7 for the two reactors, respectively. CFD simulation showed the impact of inlet diameter, bottom-angle shape and width and height ratio of the reactor on mixing inside reactor and possibility of further improvement in reactor performance by optimizing the FBR configuration.

The fine chemical and pharmaceutical sectors are starting to advocate the use of flow chemistry due to reasons such as EHS, environmental, efficiency, cost saving and regulatory compliance. The use of trickle bed or fixed bed system could replace a batch autoclave typically used for hydrogenation reactions. However, there are few studies which detail the process from laboratory proof of concept through design to commercial realization. This study, using the production of 1,3-cyclohexanedione from catalytic hydrogenation of resorcinol as a case study demonstrates how the laboratory-scale recycle trickle bed can be used for catalyst screening and selection. Further, design data are generated by operation over a range of design superficial velocities and operating pressure that are used to derive a design correlation that is then used to specify a single stream plant at a level of definition consistent with a Preliminary Design for capital cost estimation. Finally, the further actions required in terms of data generation to increase the level of definition and confidence to a Sanction Grade or Final Design are discussed.

Existing implants used with Total Knee Arthroplasty (TKA), Total Hip Arthroplasty (THA), and other joint reconstruction treatments, have displayed premature failures and frequent needs for revision surgery in recent years, particularly with young active patients who represent more than 55% of all joint reconstruction patients. Bone cement and stress shielding have been identified as the major reasons for premature joint failures. A breakdown of the cement may happen, and revision surgery may be needed because of the aseptic loosening. The significant mismatch of stiffness properties of patient trabecular bones and metallic implant materials in joint reconstruction surgery results in the stress shielding phenomenon. This could lead to significant bone resorption and increased risk of bone fracture and the aseptic loosening of implants. The present project introduces an approach for development of customized cellular structures to match the mechanical properties and architecture of human trabecular bone. It consists of four modules:1- characterization of geometry, microarchitecture, and stiffness properties of patient’s bones; 2- developing customized lattice structures tailored to mimic properties established in module 1; 3 - integration of developed lattice structure into full scale implant design and manufacturing; 4- implementation of the developed technology for use in implants that would overcome most of the issues related to aseptic loosening phenomenon. The present work aims at fulfilling the objectives of module 2 by exploring new designs of customized lattice structures and texture tailored to mimic closely patients’ bone anisotropic properties and that can incorporate an engineered biological press-fit fixation technique. The effects of various lattice design variables on mechanical performance of the structure are examined through systematic experimental plan using statistical design of experiments technique and analysis of variance method. All tested lattice designs were explored under realistic geometrical, biological, and manufacturing constraints. Of the four design factors examined in this study, strut thickness was found to have the highest percent contribution (41%) regarding the structure stiffness, followed by unit cell type, and cell size. Srut shape was found to have the lowest effect with only 11% contribution. The introduced solution offers lattice structure designs that can be adjusted to match bone stiffness distribution and promote bone ingrowth and hence eliminating the phenomenon of stress shielding while incorporating biological press-fit fixation technique.

Ozonated oil has several benefits for humans, as it contributes to numerous interventions, maintaining the quality of life and the well-being of individuals. Being a natural product, it has few or almost no side effects. Thus, the study aimed to verify the sensitivity and/or resistance of fixed o “Ozonated” and “Non-Ozonated” oils from Mauritia flexuosa (Buriti), Carapa guaianensis (Andiroba) and essential “Ozonated” oils from Menta piperita (Mint), Eugenia caryophyllus (Clove) in different concentrations, against internationally known bacteria from the American Type Culture Collection – ATCC, comparing with the “Non-Ozonated” versions of the respective oils, using the Agar diffusion technique. Thus, it is evident that the ozonation of the fixed oils of Buriti and Andiroba, as well as the essential oils of Mint and Clove, provided significant results, although they were statistically different. The Buriti and Andiroba oil were ineffective in inhibiting microorganisms. On the other hand, the essential oil of Mint and Clove obtained similar activity of inhibition of microorganisms. With regard to Ozonation, the Essential Oil of “Ozonated” Clove provided greater activity than the “Non-Ozonated” one, which inhibited only one tested microorganism, in addition to producing changes in its chemical composition, requiring individualized studies for the ozonation of each essential oil.

Electromobility promises to efficiently mitigate consequences of increasing traffic volume and its accompanied greenhouse gas emissions. On an individual level, electrified bikes allow emission free electrified mobility at moderate costs and consequently their stock has increased significantly in recent years. This simultaneously increases the demand for spare parts, which are often manufacturer or application-specific, and due to many variants, challenging to provide for the market. This article evaluates powder-based and extrusion-based metal additive manufacturing of a typical electrified bike component to demonstrate an alternative spare parts supply. The investigation demonstrates how these parts can be additively manufactured function equivalent and with sufficient mechanical properties, also taking economical aspects into account. Furthermore, the needed resources and related environmental consequences for metal-based additive manufacturing spare-part production are compared for both process routes. The results show that both routes are capable of producing spare-parts at comparatively same mechanical performance and resource costs, while needed resources such as energy, gases and manufacturing time are significantly lower for powder-based, respectively machine costs for extrusion-based additive manufacturing. Therefore, additive manufacturing offers a promising opportunity to produce parts in small quantities resource efficient and rapidly.

Efficient fixed crane position analysis is critical in precast buildings construction to maximize lifting efficiency for precast elements. The primary objective is to minimize the travel distances of fixed cranes, thereby enhancing operational efficiency and cost control. This involves strategically reducing the distances between the transport truck parking, where elements are stored, the fixed crane, and the construction installation point. Despite its significance, existing studies often overlook the dynamic movement efficiency of transport trucks, particularly when dealing with multiple transport trucks and various models of fixed cranes, rendering the opti-mization of this scenario a challenging NP-hard problem susceptible to combinatorial explosion. This study presents a novel mathematical model leveraging the Genetic Algorithm (GA). The model aims to solve optimal model and position of fixed cranes, along with identifying ideal positions for transport truck parking. The study's methodology is validated and demonstrated through a project case study. Comparative analyses between the proposed model and the original planning underscore a noteworthy 6% reduction in both duration and costs when lifting elements directly from transport trucks, as opposed to establishing an on-site stock yard. Furthermore, the developed GA exhibits a substantial improvement in final solutions, achieving a remarkable 30% reduction in both operational duration and costs. This research contributes valuable insights into fixed crane position analysis of precast building construction, providing foundation for enhanced operational efficiency and cost-effectiveness in the industry.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

This paper investigates the effect of Fe contamination on the microstructure and mechanical properties of Al-7Si-0.7Mg-Fe2.5 alloy processed by Laser Powder Bed Fusion (LPBF) and heat treated in two different conditions: (1) Solution Heat Treatment (SHT) at 520 °C, followed by artificial ageing at 160 °C (T6), and (2) Direct Artificial Ageing of the as-printed material at 160 °C (DAA). Microstructural characterization was carried out by Optical Microscopy (OM), X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), and Transmission Electron Microscope (TEM). Mechanical characterization was carried out by tensile tests at room temperature. The formation of fine AlSiFe phases such as α-AlFeSi, β-AlFeSi, and π-Al8Si6Mg3Fe had no deleterious effect on the mechanical properties compared to previous studies for AlSIMg alloys without Fe. However, compared to the as-printed condition, the T6 heat treatment decreased the ultimate tensile strain significantly, while the elongation to the fracture presented a slight improvement.

This paper presents laboratory devices on which experimental measurements were carried out to prove the validity of the assumption about the reduction of vibrations transmitted to the conveyor belt structure generated by the impact forces of falling material grains in the places of transfer or on the hoppers of conveyor belts. In order to limit damage to the conveyor belts caused by the impact of the sharp edges of material grains, conveyor belts are supported by impact rollers or impact rubber rods in the places of transfers and on the hoppers of belt conveyors. The flattened ends of the impact rollers are inserted into the grooves of steel brackets installed on the supports of the fixed conveyor idlers of a conventional design. In this paper, a special modification of the fixed conveyor idler is presented, which consists of inserting plastic brackets into the structurally modified roller axle holders of the fixed conveyor idler. Measurements were carried out on the first laboratory device, which showed that the specially modified fixed conveyor idler resulted in a higher damping of up to 15% of the impact forces of the falling weight on the rubberized hoop of the impact roller shell compared to the conventional fixed conveyor idler design. Measurements carried out on the second laboratory device show that the effective vibration velocity values detected at the points where the impact roller axis fits into the fixed roller table holder, i.e. points B and D, are higher than when using plastic brackets, up to 6% for a 108 mm diameter roller, compared to steel impact roller brackets.

Photovoltaic shading devices (PVSDs) have the dual function of providing shade and generating electricity, which can reduce building energy consumption and improve indoor daylighting levels. This study adopts a parametric performance design method and establishes a one-click simulation process by using the Grasshopper platform and Ladybugtools. The research focuses on the effect of dynamic PVSDs on daylighting and energy consumption in an office building in Qingdao. Through simulation, the study calculates the monthly energy consumption and useful daylight illuminance (UDI) under different inclination angles and installation heights of PVSDs. And the optimal configuration of PVSDs for each month under three dynamic strategies (rotation, sliding, and hybrid) is determined. Additionally, different control strategies and fixed PVSDs are compared to clarify the impact of various control strategies on daylighting and energy consumption. The findings reveal that, compared to no shading, dynamic PVSDs in rotation strategy (with an installation height of 0 m), sliding strategy (with an inclination angle of 20°), and hybrid strategy can achieve energy savings of 32.13%, 47.22%, and 50.38%, respectively. They can increase the annual average UDI by 1.39%, 2.8%, and 3.1%, respectively.

The uncertainty in the secondary path of an Active Noise Control (ANC) headphone affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones, and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized by the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensures more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

Laser powder bed fusion can fabricate porous structure through lattices, but it remains a challenge to prepare micropores (

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

Monge-Ampere equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge-Ampere equations with two parameters is investigated based on Guo-Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our main results.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

Technical components should be produced sustainably and are subject to growing demands in terms of durability and reliability. To meet these expectations, the development of thermochemical processes is auspicious. Titanium alloys, which have a comparatively high gas solubility, allow temporary hydrogen (H) loading, often called thermo hydrogen treatment (THT). THT causes lattice deformation and reduces the β transformation temperature. These effects enable an adjustment of the microstructure, which improves the mechanical properties as compared to those produced conventionally. Furthermore, the process is applicable to complex geometries that cannot be surface hardened by mechanical surface treatment techniques. The investigation presented intends to realize a local microstructure gradient in additively via laser-powder bed fusion (L-PBF) manufactured cylindrical Ti–6Al–4V specimens by changing the distribution and morphology of strengthening precipitates as well as the β grain size depending on the distance to the surface, which should improve the material fatigue properties. To evaluate the mechanical properties of such THT-induced microstructure gradients, the resulting change in fatigue life in the LCF and HCF range was determined by stress-controlled cyclic deformation tests. Besides, the resulting microstructure was characterized by means of XRD and TEM. In addition to the additively manufactured and thermo hydrogen treated cylindrical specimens, conventionally produced tube-like specimens were thermo hydrogen treated and examined. For the THT-induced microstructure gradients, numerically simulated H concentration profiles as well as experimentally determined hardness profiles were used for the evaluation of the THT process. The study shows that H-loading at 500°C and H-degassing at 750°C, followed by aging at 550°C, allows the establishment of a microstructure gradient that shows an 8% improvement in fatigue properties compared to a reference condition without THT. The reason for this improvement is an increased volume fraction secondary alpha phase in the near-surface area of the specimens. Moreover, the results show that the process is applicable a tube-like specimen with varying wall thicknesses.

In this paper, a positive answer to the open question of Fabino et al. is given, and the concept of I\c sik type set valued contractions is introduced and fixed point theorem for such contractions is established. Examples to support main theorems are given, and an application to integral inclusion is given.

Vibro-fluidized dry coal beneficiation involves the unavoidable mixing of -1 mm coal dust into the fluidized bed, which compromises the stability and homogeneity of the bed density and reduces the effectiveness of fine-grained coal separation. In order to understand the features of coal powder separation and mixing (-1 mm) in a vibrating fluidized bed, as well as to achieve a uniform and stable bed density, a wide-grained dense medium consisting of -1 mm coal dust and 0.3-0.15 mm magnetite powder was homogeneously mixed in this work. The degree of density separation in the entire bed was examined, as well as the local mixing properties of the Wide-grained Dense Medium. It was discovered that when low vibrational energy was introduced at the same gas velocity, particle separation was enhanced in comparison to the usual fluidized bed. Little bubbles were found to ensnare fine coal dust and migrate upward, increasing density separation. The introduction of high vibrational energy leads to particle disorder within the bed and an increase in the level of particle mixing. The beneficial effects of vibration on the bed are diminished when the gas velocity is gradually increased under specified vibration circumstances. This causes big bubbles to develop more frequently, which increases particle mixing. Among them, the 1-0.5 mm fine-grained coal exhibits the best mixing state; it is less impacted by variations in air velocity and vibration levels, whereas the -0.5 mm coal dust is more affected by each of these variables. Furthermore, a wide range of air velocity regulation without a significant segregation state change was discovered to be achievable by the particle system under vibration circumstances of f=25Hz A=1mm and f=25Hz A=2mm.

Drying grains in a fixed bed can be an interesting alternative to prevent undesirable breaks and fractures of solids due to mechanical shocks, something that cannot be avoided when drying in moving beds. A disadvantage of fixed bed drying is that there can be significant gradients in the critical variables if the layer of particulate solids is thick. This work shows that periodically changing the direction of drying air flow is an effective technique to reduce differences within the bed and allow better uniformity of the product. Drying in a thick layer of 10 cm of sorghum grains was carried out at 50 and 60oC for air flow velocity of 2.1 m.s-1. The results showed that despite increasing the total drying time, the technique actually allowed a significant decrease in the temperature gradients and moisture content of the sorghum grains. The change in direction of the air flow caused the drying front to be displaced, sometimes towards the top, sometimes towards the base of the bed. At 50oC, drying lasted a total of 240 min, bringing the sorghum grains to an average overall moisture content of 0.13 on a dry basis.

This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We designed novel algorithms for simulation, which take a small amount of computer RAM so that only the CPU time grows linearly with the size of the system and its statistics. This algorithm allows us to simulate systems with billions of discontinuity points on our fractal curve, dual to the decaying turbulence. For the vorticity correlation function, we obtain \textbf{quantum fractal laws} with regime changes between universal discrete values of indexes. The traditional description of turbulence with fractal or multifractal scaling laws does not apply here. The measured conditional probabilities of fluctuating variables are smooth functions of the logarithm of scale, with statistical errors being negligible at our large number of random samples $T = 167,772,160$ with $N = 200,000,000$ points on a fractal curve. The quantum jumps arise from the analytical distribution of scaling variable $X = \frac{\cot^2(\pi p/q)}{q^2}$ where $\frac{p}{q}$ is a random fraction. This distribution is related to the totient summatory function and is a discontinuous function of $X$. In particular, the energy spectrum is a devil's staircase with tilted uneven steps with slopes between $-1$ and $-2.03$. The logarithmic derivative of energy decay $n(t)$ as a function of time is jumping down the stairs of universal levels between $1.50$ and $1.53$. The quantitative verification of this quantization would require more precise experimental data.

In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

To determine the fracture rate of ceramic crowns and causes of ceramic crown failure, this study used keywords—namely “endocrown,” “veneered fixed dental prosthesis,” “monolithic lithium disilicate (LS2),” and “all-ceramic single crown”—to search for articles published in English from 2005 to 2023 in the PubMed electronic database. Rather than using the Boolean logic algorithm between MESH terms and keywords, we accurately calculated the numbers of final clinically tracked cases with crown fractures from the contents of articles. The titles and abstracts of many related articles focused on implant or abutment fracture, while crown fracture was investigated and mentioned only in the main texts of the articles. Our studies included those crowns as well as having more complete data collection. Our search yielded 228, 93, 404, and 358 articles for the keywords “endocrown,” “veneered fixed dental prosthesis,” “monolithic lithium disilicate (LS2),” and “all-ceramic single crown,” respectively. We used the Newcastle–Ottawa Scale (NOS) to assess article quality, and our inclusion criteria were randomized controlled trials (RCT) and cohort study articles involving more than 3 years of follow-up and more than 20 cases. After reviewing, 16 high-quality articles were selected for analysis. The 4.4% crown fracture rate recommended on the basis of most clinical results was achieved in only 6 of the 16 articles. In these 6 articles, the researchers concluded the following reasons that may cause the crown fractures: the thickness of the veneer ceramic material; the connector dimensions; pontic span of the fixed prosthesis; the type of cement; the treatment of the ceramic surface before luting. Other articles inferred that the computer-aided design libraries that were insufficient for the creation of appropriate anatomically supported frameworks for prostheses with ceramic veneers; the thermal expansion coefficient and fracture toughness of the framework material did not match those of the veneer ceramic, resulting in an insufficient area supporting the ceramic veneer then leads to premature crown failure after a long period chewing. The future prospective for material developing could focus on solving those problems and have better clinical results.

With the continuous update of gene editing technology, great progress has been made in livestock breeding, researchers have produced gene edited pigs, cattle, sheep and other improved livestock. Gene editing technology is a genetic means to knock in, knock out, delete, inhibit, activate or replace specific bases of DNA or RNA sequences at the genome level to achieve accurate modification, and can edit genes at a fixed point without the need for DNA templates. In recent years, although regular clusters of interspaced short palindromic repeats (CRISPR)/Cas9 system mediated gene editing technology has been widely used in animal genetic breeding research, but so far, the system's precise insertion efficiency of foreign genes is not high enough, and there are certain off-target effects, and it is not enough to be used in genome editing of large livestock such as cashmere goats. In this paper, the development status, challenges, application prospects and look into the distance of CRISPR/ Cas9-mediated precisiongene editing technology in livestock breeding were reviewed, in order to provide theoretical reference for livestock gene function analysis, genetic improvement and livestock breeding with local economic characteristics.

Vit-106 is a promising zirconium-based alloy with high glass-forming ability and belongs to the so-called bulk metallic glasses (BMG). Workpieces with a size of around one centimeter in all three dimensions can be obtained from a BMG alloy by casting. However, further increasing the cast size decreases the cooling rate and thus induces crystallization. Selective laser melting (SLM) is a well-known technique to overcome the size limitations for BMGs because a workpiece is built by the addition of multiple melt portions where the cooling rate is kept above the critical one. Currently, BMG parts obtained by SLM suffer from partial crystallization. The present work studies the influence of SLM process parameters on partial crystallization of Vit-106 by metallography and the influence of the microstructure on mechanical properties by microhardness and wear resistance testing. Submicron crystalline inclusions are observed in an amorphous matrix of Vit-106 alloy obtained by SLM. The size and the concentration of the inclusions can be controlled by varying the laser scanning speed. It is shown that submicron crystalline inclusions formed in the amorphous matrix during SLM can favorably affect microhardness and wear resistance.

In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.

Bambara groundnut (BG) (Vigna subterranean L. verdc) is a highly nutritious and economically important leguminous crop of African origin that forms symbiotic relationships nitrogen fixing rhizobia, but it has a low yield. Currently, there is paucity of information on effective rhizobium inoculant, (to improve the yield), for BG which are cheaper and safer alternatives to chemical fertilizers. Indigenous rhizobia strains were trapped from 54 farm soils collected at three Nigerian states (Niger, Kaduna and Kano). Six selected rhizobium strains (Bradhyrhizobium spp) were identified using 16S rDNA sequencing, applied as inoculant in field experiment using completely randomized block design and compared with USDA110 strain (Bradhyrhizobim japonicum), urea fertilizer and un-inoculated plants on 2 selected BG varieties (TVSU1248 and TVSU 631). Nutrient utilization and nitrogen fixation in plants were determined at 6 weeks while leaf chlorophyll was determined forth-nightly. Seed yield was determined at maturity. The strains increased the %nitrogen (1.33±0.10 - ≥1.37±0.05), and %phosphorous (0.48±0.02 - ≥0.51±0.02), %nitrogen fixed (21.07±2.38 - ≥61.30±6.13), nodulation (72.50±21.075 - 154.00±23.79) and leaf chlorophyll were ≥49.74±1.47mg/L, ≥51.82±1.86mg/L and ≥49.65±1.56mg/L at 2nd, 4th and 6th week after planting respectively and the yield of BG (from average of 398.6 Kgha-1 to 1454.725 Kgha-1). Seed yield was highest (1869.85±273.68 Kgha-1) in BG variety TVSU1248 using BN5 strain. Indigenous Bambara-symbiotic strains significantly increased the seed yields, and plant nutrient, showing their potential as use for inoculant to improve the yield of Bambara groundnut.

Esters are versatile compounds with a wide range of applications in various industries due to their unique properties and pleasant aromas. Conventionally, the manufacture of these compounds has relied on the chemical route. Nevertheless, this technique employs high temperatures and inorganic catalysts, resulting in undesired additional steps to purify the final product by removing solvent residues, which decreases environmental sustainability and energy efficiency. In accordance with the principles of “Green Chemistry” and the search for more environmentally friendly methods, a new alternative, the enzymatic route, has been introduced. This technique uses low temperatures and does not require the use of solvents, resulting in more environmentally friendly final products. In spite of the large number of studies published on the biocatalytic synthesis of esters, little attention has been paid to the reactors used for it. Therefore, it is convenient to gather the scattered information regarding the type of reactor employed in these synthesis reactions, considering the industrial field in which the process is carried out. The comparison between the performance of the different reactor configurations will allow us to draw the appropriate conclusions regarding their suitability for each specific industrial application.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

This study explores the dynamics of liquid holdup in a lab-scale co-current two-phase upflow moving packed bed reactor, specifically examining how superficial gas velocity influences the line average external liquid holdup at a fixed superficial liquid velocity. Utilizing Gamma-ray Densitometry (GRD) for precise measurements, this research extends to determining line average internal porosity within catalyst particles and the overall external bed porosity. Conducted with an air-water system within a bed packed with 3 mm extrudate porous particles, the study presents a novel methodology to calculate liquid holdup, grounded in Beer–Lambert's law. Findings reveal a decrease in liquid holdup corresponding with increased superficial gas velocity across axial and radial locations, with a notable transition from bubbly to pulse flow regime at a critical velocity of 3.8 cm/sec. Additionally, the lower sections of the packed bed exhibited higher external liquid holdup compared to the middle sections at varied gas velocities. The liquid holdup distribution appeared uniform at lower flow rates, whereas higher flow rates favored the middle sections.

In this paper, we demonstrate that fixed-weight layers, generated from random distribution or logistic functions, can effectively extract significant features from input data, resulting in high accuracy on a variety of tasks, including Fisher’s iris, Wisconsin Breast Cancer, and MNIST datasets. We have observed that logistic functions yield high accuracy with less dispersion in results. We have also assessed the precision of our approach under conditions of minimizing spikes number generated in the network, it is a practically useful for reducing energy consumption in spiking neural networks. Our findings reveal that the proposed method demonstrates a highest accuracy on Fisher’s iris and MNIST datasets with logistic regression. Furthermore, they surpass the accuracy of the conventional (non-spiking) approach using logistic regression in the case of Wisconsin Breast Cancer. We have also investigated the impact of non-stochastic spike generation on accuracy.

In view of the problem of charging and hydrogen filling facilities construction in the transition from fuel vehicles to electric vehicles and hydrogen fuel cell vehicles, in order to meet the electric energy demand of electric vehicles and hydrogen energy demand of hydrogen fuel cell vehicles at the same time, this paper puts forward a method of siting and capacity determination of electric-hydrogen refueling integrated station (EHRIS) based on Voronoi diagram and particle swarm algorithm based on calculating the demand of charging and filling of hydrogen in vehicles. Firstly, OD pair(Origin-Destination) is used to represent the starting point and end point of the car to portray the travel demand of the car, and on the basis of the traffic network model, the shortest driving path of the new energy car is determined by Dijkstra algorithm, and Monte Carlo simulation is used to get the electric-hydrogen energy demand of the car; secondly, the Voronoi diagram is introduced to classify the service scope of the electric-hydrogen charging station to determine the equipment capacity of the electric-hydrogen charging station, while taking into account the electric-hydrogen charging and refueling capacity. Secondly, a Voronoi diagram is introduced to divide the service scope of the EHRIS, determine the capacity of the equipment in the EHRIS, and consider the distance constraints between the sites of EHRIS, so as to make the division of the site and service scope more reasonable. Finally, a dynamic optimal current model framework for distribution networks based on second-order cone relaxation is established, and each element of the active distribution network is planned, so that the distribution network can operate safely and stably after being connected to the EHRIS. With the objective of minimizing the total social cost of EHRIS and considering the constraints of the charging equipment and hydrogen production and injection equipment of the EHRIS, a siting and capacity model to meet the electric-hydrogen energy demand of electric and hydrogen fuel cell vehicles is developed, and solved by a particle swarm algorithm. Finally, the simulation planning is carried out with Sioux Falls city and IEEE33 network, which ensures the stable operation of the power grid while meeting the energy demand of automobiles, and the results verify the effectiveness and feasibility of the proposed method.

The Kuznetsk Basin (Kuzbass) is one of the largest coal basins in Siberia and a reference area for the ancient Angaraland continent. The proximity of the Kuzbass and Siberian platform caused their biotic similarities in the Late Palaeozoic. However, due to biota endemism, the Kuzbass Upper Palaeozoic does not correlate directly with the International Chronostratigraphic Chart (ICC). This paper discusses radioisotopic (CA-ID-TIMS) dating of zircons from a volcanic tuff located in the Starokuznetsk Formation. This level matches the interval of the Balakhonka/Kolchugino (B/K) floral change in Kuzbass, i.e. the gradual replacement of cordaitoid-dominated wet forests (Balakhonka flora) by more arid fern-pteridosperm-cordaitoid assemblages (Kolchugino flora). New age (276.9 ± 0.4 Ma) directly correlates the Starokuznetsk Fm with the Upper Kungurian of the ICS. We compared the Kuzbass data with data of the Western Verkhoyanie, where Middle Permian ammonoids (Sverdrupites assemblage) occur in strata recording the B/K floral change. Available (ICC) and new datings indicate the lag between the B/K floral change in low (Kuzbass) and high (Verkhoyanie) latitudes of Angaraland. The B/K floral change in the Kuzbass began in the early Late Kungurian and was completed by the end of this age. In contrast, the B/K floral change in Verkhoyanie began at the end of the Late Kungurian and was completed in the Late Wordian. The delay in the floral changes at different latitudes of Angaraland suggests that existing interregional correlations need further improvement.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

Laser scanning 3D imaging technology, because it can get accurate three-dimensional surface data, has been widely used in the search for wrecks and rescue operations, underwater resource development, and other fields. At present, the conventional underwater rotating laser scanning imaging system maintains a relatively fixed light window. However, in low-light situations underwater, the rotation of the scanning device causes some degree of water fluctuation, which warps the light strip data that the system sensor receives about the object's surface. To solve the problem, this research studies an underwater 3D scanning and imaging system that makes use of a fixed-light window and a spinning laser (FWLS). A refraction error compensation algorithm is investigated that is based on the fundamentals of linear laser scanning imaging and the dynamic refraction mathematical model is established by the motion of the imaging device. During the imaging process, the incident angle between the laser and the light window varies due to the scanning mode of the system. The experimental results show that the reconstruction radius error is reduced by 60% (from 2.5 mm to about 1 mm) when the measurement data for a standard sphere with a radius of 20 mm are compensated. Moreover, the compensated point cloud data exhibits a higher degree of correspondence with the model of the standard spherical point cloud. This study has a specific reference value for the refractive error analysis of an underwater laser scanning imaging system, and it provides certain research ideas for the subsequent refractive error analysis of various scanning imaging modalities.

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

Laser powder bed fusion (LPBF) is an additive manufacturing technique that is gaining popularity for producing metallic parts in various industries. However, parts produced by LPBF are prone to residual stress, deformation, cracks and other quality defects due to uneven temperature distribution during the LPBF process. To address this issue, in prior work, the authors have proposed SmartScan, a method for determining laser scan sequence in LPBF using a model-based and optimization-driven approach, rather than using heuristics, and applied it to simple 2D geometries. This paper presents a generalized SmartScan methodology that is applicable to arbitrary 3D geometries. This is achieved by: (1) expanding the thermal model and optimization approach used in SmartScan to multiple layers; (2) enabling SmartScan to process shapes with arbitrary contours and infill patterns within each layer and (3) providing SmartScan with global foresight to make it less myopic in its optimization. Sample 3D parts are printed using the proposed generalized SmartScan and compared to those printed using standard heuristic scan sequences. Reductions of up to 93% in temperature inhomogeneity, 87% in residual stress, and 26% in maximum deformation were observed, without significantly sacrificing print speed. However, SmartScan was found to cause minor (<5%) to significant (up to 20%) increases in surface roughness compared to the heuristic approaches, depending on the scan pattern used.

The aim of this paper is to deep into the dynamic study of the well known Chebyshev-Halley family of iterative methods for solving nonlinear equations. Our objetives are twofold: one the one hand, we are interested in characterize the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in study the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have a bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where this two situations happen simultaneously. That is, the rational map obtained by applying a method in the Chebyshev-Halley family to a polynomial has both super-attracting extraneous fixed point and super-attracting cycles different to the roots of the polynomial.

Currently, most plastic waste stems from packaging materials, with a large proportion of this waste either discarded or used to derive fuel. Accordingly, there is growing interest in the use of pyrolysis in the context of chemically recycling non-recyclable (i.e., via mechanical means) plastic waste into petrochemical feedstock. The aim of this study is to use kinetic analyses to elucidate the pyrolytic properties of solid recovered fuel (SRF) produced using two types of reactors, namely, fixed bed and fluidized bed reactors. From the kinetic analysis, the activation energy corresponding to the rate of pyrolysis reaction conversion was obtained. In conclusion, we found that the pyrolysis occurs more vigorously in fluidized bed reactors compared to fixed bed reactors.

Facing the charging difficulties of free-floating shared electric vehicle and the high cost of mobile charging for single demand, this article proposes a collaborative charging planning method based on the complementary advantages of fixed charging stations and mobile charging vehicles, which can charge shared electric vehicles more efficiently and reduce the charging cost at the same time. A bi-level programming model for fixed and mobile cooperative charging is constructed. The upper level of the model is the minimization model of system charging total cost, seeking the optimal charging scheme and the number of mobile charging vehicles. The lower model is a fixed and mobile cooperative charging path planning model, which calculates the optimal routes for mobile charging vehicles and the shared electric vehicles that need to be transferred to the fixed charging station. The example results show that the cost of the proposed fixed-mobile cooperative charging scheme is reduced by 12.6% compared with the pure fixed charging scheme and 14.9% compared with the pure mobile charging scheme

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

Delayed discharge for non-clinical reasons is defined as a period of stay that continues after a patient has been deemed medically fit to leave the hospital but is unable to do so for non-medical reasons. This circumstance overburdens the healthcare system and constitutes a major problem for healthcare systems and the patients themselves in this situation.The aim of this study was to evaluate the delay in effective discharge for non-medical reasons in patients admitted to acute care hospitals in Spain. A scoping review was conducted in order to revise and obtain an up-to-date review. The initial search strategy identified a total of 123 references, which were successively screened to a final selection of 13 studies. To conclude, delayed discharge from hospital for non-clinical reasons is a multifactorial problem. It may be due to factors internal or external to the hospital, as well as personal factors. The main causes of the delay are similar among the studies found, as are the clinical characteristics of the patients, most of whom are elderly, frail, and more dependent due to declining functional capacities. Further studies addressing the socio-familial characteristics of the patients and the perspective of the patient and families would be necessary.

Polyamide 11 (PA11) is a plant-based nylon made from castor beans. Powder bed fusion laser sintering (PBF-LS) is an additive manufacturing process used for PA11 which allows the reuse of the unsintered powder. The unsintered powder is mixed with virgin powders at different refresh rates which has been studied extensively for most semi-crystalline polyamides. However, there is lack of information on the effect of using 100% reused PA11 powder and the number of times it is reused on its own during powder bed fusion laser sintering. This paper investigates the effect of reusing PA11 powder in PBF-LS and number of times it is reused on the dimensional accuracy, density, thermal and tensile properties. From 100% virgin powder to 3rd use of the powder, there is a decrease in powder wastage, decrease in crystallinity and tensile strength. These was associated with the polymerisation and cross-linking process of polymer chains, upon exposure to high temperature. This results in a higher molecular weight and hence density. From the 4th use to 10th reuse, the opposite was observed which was associated to an increase in high-viscosity and un-molten particles which resulted in defects in the PBF-LS parts.

Based upon 30-years of research by the author a new approach to hospital bed planning and international benchmarking is proposed. The number of hospital beds per 1000 population is commonly used to compare international bed numbers. This method is flawed because it does not consider population age structure or the effect of nearness-to-death on hospital utilization. Deaths are also serving as a proxy for wider bed demand arising from undetected outbreaks of 3000 species of human pathogens. To remedy this problem a new approach to bed modelling has been developed which plots beds per 1000 deaths against deaths per 1000 population. Lines of equivalence can be drawn on the plot to delineate countries with higher or lower bed supply. This method is extended to attempt to define the optimum region for bed supply in an effective health care system. England is used as an example of a health system descending into operational chaos due to too few beds and manpower. The former Soviet bloc countries represent a health system overly dependent on hospital beds. Several countries also show evidence for over-utilization of hospital beds. The new method is used to define a potential range for bed supply and manpower where the current most effective health systems currently reside. The method is applied to total curative beds, medical beds, psychiatric beds, critical care, geriatric care, etc., and can also be used to compare different types of healthcare staff, i.e., nurses, physicians, surgeons. Issues surrounding the optimum hospital size and the optimum average occupancy will also be discussed. The role of poor policy in the English NHS is used to show how the NHS has been led into a bed crisis. The method is also extended beyond international benchmarking to illustrate how it can be applied at a local or regional level in the process of long-term bed planning. Issues regarding the volatility in hospital admissions are also addressed to explain the need for surge capacity and why an adequate average bed occupancy margin is required for an optimally functioning hospital.

Calcium and magnesium are important not only for human health, but also for reducing problems related to the corrosive and aggressive effects of soft water on drinking water distribution materials. Experimental and mathematical modeling of the recarbonization process aimed at increasing the content of these biogenic elements in water was carried out using the novelty of a continuous laboratory and pilot scale fluidized bed reactors. Water remineralization using half-calcined dolomite (HCD) and carbon dioxide was used. The influence of operating conditions Q(CO2), freshwater inflow and HCD dose on quality indicators of treated drinking water (c(Ca2+), c(Mg2+), c(Ca2++Mg2+) and Ca/Mg) was studied. The results show that the concentration of Mg2+ is more significantly affected by the amount of HCD in the system and the flow of CO2. The influence of freshwater inflow on the Mg2+content is to a lesser extent. At a constant CO2 flow, therefore, as the tap water inflow increases, the Ca2+ content decreases and the Mg2+ content increases, which has results in a decrease in the Ca/Mg molar ratio. However, the Ca/Mg ratio can be effectively controlled by adding an appropriate amount of HCD at certain time intervals. Overproduction of ions is easily controlled by CO2 flow.

This paper presents the results of investigations on the pyrolysis of tyres waste in a laboratory fixed bed batch reactor. The results regarding the influence of either the reaction temperature (425, 450, 475, and 500 °C) and the flow of the inert gas (0, 100, 300, and 500 mL/min) on products yield (referred to pyrolysis of waste tyres) are also considered and discussed. On the basis of the above mentioned findings, the most appropriate experimental conditions were selected to contribute to a higher yield of pyrolysis oil. The sample of pyrolysis oil obtained from the experiments carried out in the selected optimal conditions (reaction time 120 min, temperature 450 °C and the inert gas flow of 100 mL/min) was subjected to a calorimetric and infrared spectroscopy analysis. The results of IR spectroscopy analysis on this oil sample showed the following content in percentages (by mass): 32.59 % of aromatics, 51.06 % of paraffins and 16.35 % of naphthenes. The pyrolysis oil so obtained has a high calorific value (42 MJ/kg) and a low sulfur content (0.41 % by mass), which makes it an excellent raw material for energy production. The solid product, i.e. pyrolysis char or carbon black, has the potential to be used as an adsorbent or catalyst support after an activation process, which changes its irregular pore structure to a more voluminous one, making the overall structure more crystalline and symmetrical. Pyrolysis coal has a fairly high calorific value of 31 MJ/kg, when compared to typical solid fuels, so it can be used in energy production or as a feedstock for the gasification process.

Recently, Li et al [1] investigated the nonlinear Langevin equations existence including two fractional orders with infinite-point boundary conditions. It has shown that the outcomes given it does count on the solution form for which it has boundary values. It means that their solution needs more to be in the final step. In current work, we will have discussion about the existence and uniqueness for the same boundary conditions by investigating the closely explicit solution form that has no boundary values. Numerical example is supported to have more vision to compare the between new and previous results. It turns out that our results are superior.

In this research, a design method for the graded triply periodic minimal surface (TPMS) structures with lightweight, high-strength, and high sound absorption properties is proposed. The graded TPMS structures are controlled by linear, quadratic, and sine functions. Uniform TPMS and graded TPMS were manufactured by laser powder bed fusion (LPBF) with AlSi7Mg powder, and an acoustic impedance tube test, compression test, and digital image correlation (DIC) test were ap-plied to obtain the sound absorption and compression properties. The sound absorption coefficient of a uniform Gyroid increases as the number of layers and surface thickness increase, and it in-creases as element size decreases. The sound absorption peak shifts to low frequencies as the number of layers increases. The sound absorption property of Type-Ⅰ graded TPMS is superior to the Type-Ⅱ, and the G-LinearⅠ has the highest sound absorption properties among the three functions. It reveals that the graded TPMS has superior sound absorption performance at low and medium frequencies. The compression and DIC results of graded TPMS also show excellent mechanical properties and energy absorption characteristics.

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\mathbb C^d$ with random steps parametrized by $N$ Ising variables $\sigma_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number $r$, related by $\sum \sigma_i = q r$. This equivalence provides a \textbf{dual} theory describing a strong turbulent phase of the Navier-Stokes flow in $\mathbb R_d$ space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a \textbf{quantum} statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size $N \rightarrow \infty$ or its chemical potential $\mu \rightarrow 0$. The system with fixed $N$ has different asymptotics at odd and even $N\rightarrow \infty$, but the limit $\mu \rightarrow 0$ is well defined. The energy dissipation rate is analytically calculated as a function of $\mu$ using methods of number theory. It grows as $\nu/\mu^2$ in the continuum limit $\mu \rightarrow 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu} \to 0$. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda}$, where the anomalous dimensions $\lambda$ satisfy the spectral equation \eqref{spectralEq}. The spectrum becomes a continuum in the statistical limit $N \to \infty$, presumably leading to multifractal phenomena.

The impacts of COVID-19 (Novel Coronavirus) epidemic cannot have been more severe, with the globe experiencing both economic and health crises. This study examines the trends and correlations in number of COVID-19-related deaths and number of COVID-19-infected patients in all 37 regions of Tamil Nadu state, India, in the month of August 2020 on the basis of panel regression model,

Abstract Aims: In recent years, electro kinetic (EK) remediation has become more popular as a novel method for removing chromium contamination from soil. This approach, however, is ineffective since it uses both cationic and anionic forms of chromium. In this work, a membrane –based technique was employed to increase the efficiency of the electro kinetic removal of chromium. Methods: Chromium removal from polluted sludge was studied in four bench-scale experiments, two of which used distilled water (EK-1, EK2 & Membrane) and two of which used acetic acid as a catholyte (EK-3, EK4 &Membrane). Results: The pH, total chromium, and fractionation of chromium in the sludge were measured after remediation. In the EK-1, EK-2 & Membrane and EK-3, EK-4 & Membrane trials, the average removal efficiency of total chromium was 47.6%, 58.6%, and 74.4%, 79.6%, respectively. Conclusion: In contrast to the electro kinetic remediation strategy, which left approximately 80% of the sludge neutral or alkaline after treatment, the use of the membrane created acidic soil conditions throughout the sludge. For example, the high field intensity used in the membrane tests may have helped to facilitate chromium desorption, dissolution and separation from the sludge, as well as enhance chromium mobility. The findings show that the membrane can improve the effectiveness of chromium removal from sludge when utilized in the EK remediation process.

How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is done by matching the Fermi-liquid xed (FLFP) point theory to the "Extreme Single Particle (shell) Model" (acronym ESPM) in superallowed Gamow-Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1-qssb) ≠0 - that one might identify as "fundamental quenching (FQ)" - in certain experiments seems to be alarmingly signicant. I present arguments how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to conrm or refute this observation is discussed in terms of the superallowed Gamow-Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In.

Breakthrough curves for the adsorption of H2S using a metal-oxides mixture were predicted using the Bohart-Adams model of fixed bed adsorption. This mixture (ZnMn2O4+ZnO+Mn2O3) came from the processing of an urban waste as spent alkaline batteries were. The H2S adsorption experiments were carried out in a fixed-bed column at 20º C, and under various experimental conditions: gas flow rate, inlet H2S concentration and adsorbent dosage. Curves predicted by the model matched well with experimental data, providing data for the possible scale-up of the system. At the various experimental variables, the efficiency of the column, were also provided in the work. This investigation demonstrated the usefulness of a waste material, like spent alkaline batteries, to provide an adsorbent material to mitigate the problem of the presence of this harmful gas.

In this work, a systematic study was conducted on the fabrication of multi-material components obtained employing Laser-Powder Bed Fusion (L-PBF) technology. The idea of making multi-material components is a winning capability of additive technologies because it allows the fabrication of Functionally Graded Materials (FGMs) with the customization of parts according to different required properties. The transition from one material to another was achieved gradually and continuously within the same layer using ad-hoc equipment designed for L-PBF systems with a powder spreading technique based on coaters or rollers. The influence of the relative position of the different materials within the powder chamber and the geometry of the developed equipment on the metallurgical and mechanical properties of the manufactured samples was evaluated. The performed tests involved the use of two materials, a nickel-based superalloy, and a stainless steel, having different chemical, physical and mechanical properties to obtain gradual properties variation in the manufactured samples. Based on the results of post-process characterization obtained through metallographic, chemical, and mechanical analysis, the relative positions of the materials and the geometry of the developed equipment have a limited effect on the sample’s manufactured properties. The characteristics of the FGM zone depend on the nature of the employed powders, and its extent coincides with that defined during the design of the divider.

Most of the literature on the optimization problem of transportation in supply chain networks (SCN) considered fixed costs (FC). However, in the practical applications of this problem it is important to study the effect of FC. This paper examines the impact of fixed cost increase as well as the variable cost on the optimization of a Two-Stage SCN. To do so, two mathematical models for mixed-integer nonlinear programming are developed. The first model optimizes fixed and variable costs in addition to the opening cost, whereas the second model only optimizes variable and opening costs. To evaluate the effect of considering FC on the optimization supply chain problem, four groups of instances are randomly generated, and solved using Lingo. The results of the two models are compared utilizing the average percentage deviation. In addition, sensitivity analysis is performed to determine the impact of changes in opening and variable costs on the considered optimization problem. The computational results and the sensitivity analysis show that the first model with minimized FC outperforms the second model, which does not consider the FC in minimization and FC affect the optimization.

This study analyzes the effect of economic growth and income distribution on health inequality using data from the Organization for Economic Cooperation and Development (OECD). A panel analysis was conducted by combining 21 years of data (from 2000 to 2020) from 38 OECD countries. Life expectancy and avoidable mortality were set as the dependent variables; gross domestic product and poverty gap were set as the independent variables; body mass index, consumption, smoking rate, healthcare personnel, number of beds in health service facilities, national medical expenses, and unemployment were set as control variables. First, economic growth and poverty gap significantly affect life expectancy and avoidable mortality. It has been confirmed that to resolve health inequality, growth during growth and distribution must be prioritized. Second, it has been confirmed that as the poverty gap increases, life expectancy increases and the avoidable mortality rate decreases. A mechanism different from the existence of a medical security system targeting the lowest class or an increase in the welfare of society worked. In conclusion, as a policy proposal to alleviate health inequality, this study suggests that policy intervention is necessary to block or alleviate the negative impact of income inequality in health care policies.

Pathological aseptic calcification is the most common form of structural valvular degeneration (SVD), leading to premature failure of heart valve bioprostheses (BHVs). The processing methods used to obtain GA-fixed pericardium-based biomaterials determine the hemodynamic characteristics and durability of BHVs. This article presents a comparative study of the effects of several processing methods on the degree of damage to the ECM of GA-fixed pericardium-based biomaterials as well as on their biostability, biocompatibility, and resistance to calcification. Based on the assumption that preservation of the native ECM structure will enable the creation of calcinosis-resistant materials, this study provides a soft biomimetic approach for the manufacture of GA-fixed biomaterials using gentle decellularization and washing methods. It has been shown that the use of soft methods for preimplantation processing of materials, ensuring maximum preservation of the intactness of the pericardial ECM, radically increases the resistance of biomaterials to calcification. The data obtained are of interest for the development of new calcinosis-resistant biomaterials for the manufacture of BHVs.

In recent years discrete element method (DEM) has gradually been applied to the traditional fluidization simulation of fine particles in micro fluidized bed (MFB). The application of DEM in simulating fast fluidization of fine particles in MFB has not yet received attention. This article presents a drag model that relies on the surrounding environment of particles, namely particle circumstance-dependent drag modle or PCDD model. Fast fluidization in MFB of fine particles is simulated using DEM based on the PCDD model. It is found that the gas-solid two-phase flow in MFB meets the common law of fast fluidization in circulating fluidized bed (CFB) to a certain extent, and also presents a special law that is significantly different from that in CFB. Simulations indicate that the local structure in MFB exhibits particle aggregation which is a natural property of fast fluidized, forming a structure where continuous dilute phase and dispersed concentrated phase coexist. The formation and fragmentation of particle clusters in different local regions of the bed have time synchronization. There exists strong effect of solid back-mixing in MFB, leading to relatively low outlet solid flux. The gas back-mixing effect is, however, not so distinct. The axial porosity shows a monotonically increasing distribution with the bed height, but does not strictly follow the single exponential distribution. The solid volume fraction at the bottom of the bed is significantly lower than the correlated value in CFB. The axial heterogeneous distribution of the cross-sectional average porosity in the lower half of the bed is also weakened. The radial porosity shows a distribution pattern of higher in the central region and lower in the sidewall region. Compared with the correlation results in CFB, the porosity near the central region in MFB is relatively low, while the porosity near the sidewall region is relatively high. The geometric size of the container, especially the radial size, is much smaller than that of a CFB. The relative area of contact between the MFB wall and particles is larger, and the wall friction factor becomes more significant. This may be the main reason for the time synchronization of particle agglomeration, severe particle back-mixing, low outlet solid flux, monotonically increasing axial porosity and weak core-annular structure of radial porosity.

Computer and Smart Device-assisted Learning (CSDL) has gained increasing attention from educational researchers and practitioners in recent years. However, it remains controversial whether student can benefit from CSDL and what moderator could affect the impact of CSDL. Within the specific context of Korea, where the interest in digital education is steadily increasing, the number of empirical studies exploring the causal effect of CSDL remains relatively scarce. The primary objective of this empirical study was to investigate the impact of CSDL on students' academic achievement in Korea. To achieve this objective, a two-way fixed effect model was employed, utilizing a panel dataset spanning three years derived from the 'Korean Education Longitudinal Study 2013'. The findings revealed a significant positive impact of CSDL on students’ Mathematics achievement. Notably, higher income levels, increased availability of computer resources provided by schools, and the implementation of more individualized education were identified as factors that moderate the effect of CSDL on students' achievement levels in Korean and English subjects. These findings underscore the need for an approach that optimizes the educational benefits of CSDL by considering subject-specific characteristics. Furthermore, this study highlights the importance of allocating educational resources, such as computers and smart devices, and integrating individualized educational activities within the classroom environment.

In estimating logistic regression models, convergence of the maximization algorithm is critical, however, this may fail. Numerous bias correction methods for maximum likelihood estimates of the parameters have been conducted for cases of complete data sets and also longitudinal models. For binary response fixed effects panel data model, the conditional logit estimator is consistent for balanced data. When faced with missing covariates problem, researchers opt for various imputation techniques to make the data complete and without loss of generality consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique which yields the best estimates with minimum variance is still elusive. The main aim of this paper is to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector which will make the Newton-Raphson algorithm to converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through partitioning of the covariate matrix. We also confirm from the moduli of the Hessian matrices that the log likelihood of a panel data logistic model has a global maximum as the parameter estimates. Simulation results reveal that model based simulation perform better than classical imputation techniques yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models with single fixed effects.

Progesterone receptor (PGR) expression level determines biological characteristics of the serous ovarian carcinoma, and low PGR expression appears to be associated with chemoresistance and worse outcome. In this study, we aimed to find relationships between tumor progesterone receptor level and RNA-profile (miRNAs, piwiRNAs, and mRNAs), determining its biological characteristics and behavior. For this purpose, we applied next generation sequencing of small noncoding RNAs, quantitative RT-PCR, and immunohistochemistry to analyze FFPE and frozen tumor samples as well as blood plasma from patients with benign cystadenoma (BSC), serous borderline tumour (SBT), low-grade and high-grade serous ovarian carcinoma (LGSOC and HGSOC, respectively). We found significant upregulation of MMP7 and MUC16 and downregulation of PGR in LGSOC and HGSOC in comparison with BSC. The tissue content of miR-199a-5p, miR-214-3p, miR-424-3p, miR-424-5p, miR-125b-5p significantly inversely correlated with the expression level of MUC16 and blood serum CA125 concentration, and significantly directly correlated with the PGR expression level in tumor tissue. On the contrary, the tissue content of miR-16-5p, miR-17-5p, miR-20a-5p, miR-93-5p, responsible for epithelial-mesenchymal transition (EMT) of the cell, significantly directly correlated with the blood serum CA125 concentration and significantly inversely correlated with the PGR expression level in the tumor tissue. Levels of the EMT-associated miRNAs significantly directly correlated with the content of hsa_piR_022437, hsa_piR_009295, hsa_piR_020813, hsa_piR_004307, hsa_piR_019914 in tumor tissues. Among them, expression level of hsa_piR_004307 significantly inversly correlated with the PGR expression level in the tumor. Two optimal logistic regression models were developed based on the quantitation of hsa_piR_020813, miR-16-5p, hsa_piR_022437 or hsa_piR_004307, hsa_piR_019914, miR-93-5p in the tumor tissue, both of which significantly diagnose PGR-negative tumor phenotype with 93% sensitivity. According to FunRich3.1.3 functional enrichment analysis tool, 72 gene-targets of miRNA and piRNA identified here as markers of PGR-negative ovarian tumor phenotype were proven to be mutated in different cancers such as ovarian, breast, colorectal, liver, stomach, lung, endometrial, thyroid cancer. Among them, the blood plasma levels of miR-16-5p and hsa_piR_022437 can be used to diagnose PGR-negative tumor phenotype with 86% sensitivity before surgery and chemotherapy to choose the treatment strategy for this most aggressive type of ovarian cancer (for instance, neoadjuvant chemotherapy followed by cytoreduction in combination with hyperthermic intraperitoneal chemotherapy) to increase the effectiveness of treatment and longevity of the patient.

Background - Mandibular flexion (MF) is a complex biomechanical phenomenon, which involves a deformation of the mandible, due mainly to the contraction of the masticatory muscles, and can have numerous clinical effects. The main aim of the current systematic review is to highlight the different factors that can increase MF, to help clinicians, identify patients to whom they should pay more attention. As a secondary outcome, we wanted to analyze the preventive measures and suitable techniques to be adopted to minimize the negative effects of this phenomenon on oral fixed rehabilitations. Methods - The review, which was carried out in accordance with the “Preferred Reporting Items for Systematic reviews and Meta-Analyses” (PRISMA) flowchart, was recorded in the “International Prospective Register of Systematic Reviews” (PROSPERO). As research questions, “Patient/Population, Intervention, Comparison and Outcomes” (PICO) questions were employed. Using the ROBINS-I technique, the risk of bias in non-randomized clinical studies was evaluated. Results - The initial electronic search identified over 1300 potential articles, of which 54 studies were included in this systematic review. Information regarding the relationship between MF and individual factors, mandibular movements, impression-taking and fixed rehabilitations were obtained. Conclusions – The studies included in this systematic review showed that MF is greater during protrusive movements, in the posterior areas of the lower jaw, and in patients with brachial facial type, greater jaw length, small gonial angle and less density, length and bone surface of the symphysis. The biomechanical effects of mandibular flexion on fixed restorations are debated. Prospective clinical and radiological observational studies should be conducted to evaluate the potential short-, medium- and long-term consequences of MF.

We develop a quantitative microscopic theory of decaying Turbulence by studying the dimensional reduction of the Navier-Stokes loop equation for the velocity circulation. We have found an infinite dimensional manifold of solutions of the Navier-Stokes loop equation\cite{M93, M23PR} for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This family of solutions corresponds to a fractal curve in complex space $\mathbb C^d$, described by an algebraic equation between consecutive positions plus a nonlinear periodicity condition. We derive the constrained SDE for the evolution of the fractal curve at a fixed moment of physical time as a function of an auxiliary stochastic time. We expect this stochastic process to cover our fixed manifold of the solutions of the decaying Turbulence. The energy density of the fluid decays as $\mathcal E_0/t$, where $\mathcal E_0$ is an initial dissipation rate. Presumably, we have found a new phase of extreme Turbulence yet to be observed in real or numerical experiments.

In this paper, the experimental study of heating in 2 h lunch mode of air-conditioned bed system is carried out. The results show that the power consumption of heat conduction heating is only 0.34 kW·h, and the average heat dissipation is 81.3 W, while the power consumption of convection heating is 1.43 kW·h, with an average heat dissipation of 748.7 W. Regardless of power consumption or heat dissipation, convection heating is significantly higher than heat conduction heating, resulting in the room air temperature of the former increased from 12.3 °C to 17.3 °C, while the latter only increased from 14.4 °C to 15.2 °C. The study found that the water temperature of heat conduction heating can meet the thermal comfort needs of the human body in the range of 38~40 °C, while convection heating requires a higher temperature range, In contrast, the grade of hot water required for heat conduction heating is lower. Through the experiment, it is also found that the temperature of convection heating rises fast, but it is easy to appear dry feeling after a long time, while heat conductive heating has a slow temperature rise. there is a cool feeling within 20 min after the heating starts, and then the thermal comfort is better. The air conditioning system in this paper is used for the heating experiment in the winter lunch break mode, compared with convection heating, the overall thermal comfort of heat conduction heating is better and more energy efficient. it is suggested to adopt heat conduction heating mode in the winter heating of this system.

Significant design efforts were undertaken during the Pre-Concept Design (PCD) phase of the European DEMO programme to optimize the Helium Cooled Pebble Bed (HCPB) breeding blanket. A gate review was conducted for the entire European DEMO programme at the conclusion of the PCD phase. This article presents a summary of the design evolution and the rationale behind the HCPB breeding blanket concept for the European DEMO. The main performance metrics, including nuclear, thermal hydraulics, thermal mechanical, and tritium permeation behaviors, are reported. These figures demonstrate that the HCPB breeding blanket is a highly effective tritium-breeding and robust driver blanket concept for the European DEMO. In addition, three alternative concepts of interest were explored. Furthermore, this article outlines the upcoming design and R&D activities for the HCPB breeding blanket during the Concept Design phase (2021-2027).

Humankind has entered a new era wherein a main characteristic is the convergence of various technologies providing services exerting major impact upon all aspects of human activity, be it social interactions as well as interactions with the natural environment. Fixed networks are about to play a major role in this convergence, since they form, along with mobile networks, the backbone that provides access to a broad gamut of services, accessible from any point of the globe. It is for this reason that we introduce a forward-looking approach for fixed networks, particularly focused on Fixed 6th Generation (F6G) networks. First, we adopt a novel classification scheme for the main F6G services, comprising six categories. This classification is based on the key service requirements, namely latency, capacity and connectivity. F6G networks differ from those of previous generations (F1G-F5G) in that they concurrently support multiple key requirements. We then propose concrete steps towards transforming the main elements of fixed networks, such as optical transceivers, optical switches etc. such that they satisfy the new F6G service requirements. Our study categorizes the main networking paradigm of optical switching into two categories namely ultra-fast and ultra-high capacity switching, tailored to different service categories. With regard to the transceiver physical layer, we propose: a) use of all-optical processing to mitigate performance barriers of analog to digital and digital to analog converters (ADC/DAC); b) exploitation of optical multi-band transmission, space division-multiplexing and adoption of more efficient modulation formats.

The integration of spray drying and agglomeration offers significant advantages, such us continuous production with lower energy consumption. However, it is a knife-edge process with a narrow operating window and limited degrees of freedom that decide between successful agglomeration and fluidized bed blockage due to excessive moisture. In this contribution, factors influencing the spray-through agglomeration process of skim milk powder as a model system were investigated via a design of experiments. Three in-line monitoring methods were applied and tested to observe the most important parameters in the agglomeration process: product moisture and particle size distribution. Regarding the moisture content, a capacitive moisture sensor was calibrated with linear regression and a near-infrared sensor with partial least squares regression. Near-infrared spectroscopy was found to be the suitable method for determining moisture content, while the capacitive moisture sensor mainly provides information on the bulk density, the filling level or fluidization state in the fluidized bed. Additionally, particle size distribution data was extracted from the spectral data using in-line data of a spatial filter velocimetry probe in the fluidized bed. This opens the potential to monitor both parameters in real-time with a single non-invasive sensor.

Rivaroxaban and aspirin are commonly used antithrombotic agents that are used in combination for the prevention of coronary artery disease (CAD) and atherothrombotic events in adult patients after an acute coronary syndrome (ACS) with elevated cardiac biomarkers, or with coronary artery disease (CAD) or symptomatic peripheral artery disease (PAD) in high-risk patients. The recommended dosage is 2.5 mg Rivaroxaban twice daily with 75–100 mg aspirin daily. This study aimed to develop a fixed-dose combination tablet of rivaroxaban (2.5 mg) and aspirin (50 mg) to decrease the patient's pill burden and enhance medication adherence. The product formula was developed based on compatibility studies among the active ingredients and the active ingredients' compatibility studies. The formula and the manufacturing procedure were chosen based on the risk assessment for each active substance, wet granulation with both actives intragranular was found to have faster dissolution than direct mix formulae. Furthermore, a validated reverse-phase HPLC stability indicator method was developed to detect APIs and their possible degradants in the formula.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

Polymeric composites such as Poly-ether-ether-ketone (PEEK)/carbon fiber (CF) have been widely utilized due to outstanding performances such as high specific strength and specific modulus. The PEEK/CF components via powder-bed fusion additive manufacturing usually show brittle fracture behaviors induced by their poor interfacial affinity and inner voids. These defects are strongly associated with powder packing quality upon deposition. The particle dynamic model has been widely employed to study the interactions of particle motions. Powder property, bulk material property, and interfacial features of composite powders are key factors in the particle dynamic model. In this work, an efficient and systematic material evaluation is developed for composite powders to investigate their deposition mechanism. The discrete element method is utilized to simulate the dynamic behaviors of PEEK/CF composite powders. The powder properties, bulk material properties, and interfacial features of powders are calibrated and justified by experimental measurement, numerical simulation, and design of experiments. The particle dynamic model can well explain the powder flow behaviors and interactions. It reveals that the addition of short CF particles can assist the flow of PEEK powders and improve the packing quality of the composite powders.

Remote sensing plays a central role in the assessment of environmental phenomena and has increasingly become a powerful tool for monitoring shorelines, rivers morphology, flood waves delineation and floods assessment. Optical based monitoring and characterization of river evolution at long time scales is a key tool in fluvial geomorphology. However, the evolution occurring during extreme events is crucial for the understanding of the river dynamics under severe flow conditions and requires the processing of data from active sensors to overcome cloud obstructions. This work proposes a cloud-based unsupervised algorithm for the intra-event monitoring of river dynamics during extreme flow conditions based on time series of Sentinel-1 SAR data. The method allows the extraction of multi-temporal series of spatially explicit geometric parameters at high time and spatial resolutions, linking them to the hydrometric levels acquired by reference gauge stations. Intra-event reconstruction of inundation dynamics has led to the estimation of the relationship between hydrometric level and wet area extension and the assessment of bank erosion phenomena. Time series of SAR acquisitions, provided by Copernicus Sentinel-1 satellites, were analyzed to quantify changes in the wet area of a reach of the Tagliamento river under different flow conditions. The algorithm, developed within the Python-API of GEE, first empowers the Sentinel-1 images with the hydrometric level, then involves radiometric slope correction and speckle noise filtering. The Otsu method is then used for image segmentation leading to a water and dry land binary classification. Results support many types of analysis about river dynamics, including morphological changes, floods monitoring and relief efforts and bio-physical habitat dynamics. The results encourage future advancements and applications of the algorithm, specifically exploring SAR data from ICEYE and Capella Space constellations, which offer significantly higher spatial and temporal resolutions compared to Sentinel-1 data.

In the present work, a comparative evaluation of an MBBR unit performance was carried out for the following cases: when adding 3D-printed biocarriers fabricated with 13X and bentonite, when using K1 commercial biocarriers and when not adding biocarriers at all. For the evaluation of the MBBR efficiency, various physicochemical parameters were measured, while static light scattering and optical microscopy observations were additionally used. Finally, biofilm extracted from the biocarriers was evaluated. The findings suggest that there is an optimal biodegradation of the organic load in all MBBR units. The nitrification and denitrification process were improved at the 3D MBBR as compared to the control MBBR and MBBR K1. The dry mass of the biofilm in the 3D-printed biocarriers was two orders of magnitude larger than the one in the K1 biocarriers. What is more, in the K1 biocarriers the mass of the biofilm varied in relation to time, due to the fact that it could not be kept inside the holes, something that was not observed to happen with the 3D-printed biocarriers. Finally, it was observed, mostly in the 3D MBBR and less in the K1 MBBR, that the growth of nitrifying bacteria and heterotrophs inside the units increased the biomass production in the form of SMP, which in turn favored the adhesion of biomass on the surface of biocarriers.

The combination of non-steroidal anti-inflammatory drugs (NSAIDs) with non-opioid analgesics is common in clinical practice for the treatment of acute pain conditions like post-operative and post-traumatic pain. Besides that, and despite the very satisfactory results achieved by oral analgesics, parenteral analgesia is a key tool in the treatment of painful conditions when the enteral routes are not convenient. The parenteral ready-to-use fixed-dose combinations of NSAIDs with non-opioid analgesics like paracetamol or metamizole could play a central role in the treatment of painful conditions since they are able to gather into only one formulation the advantages of multimodal and parenteral analgesia. Surprisingly, only very recently a parenteral ready-to-use fixed-dose combination of Ibuprofen/Paracetamol was launched to the market. This review aims to review the current availability of NSAID-based Parenteral Fixed-dose combinations with paracetamol and metamizole in the European and American markets, and how the combination of such drugs could play a central role in a multimodal analgesia strategy. Also, it is explored how the parenteral formulations of NSAIDs, paracetamol, and metamizole could serve as starting elements for the development of new parenteral ready-to-use fixed-dose combinations. With this review, we concluded that, despite the well-recognized utility of combining NSAIDs with non-opioid analgesics, there are in the literature several randomized clinical trial studies unable to demonstrate clear advantages concerning their efficacy and safety. In the future, it is deemed necessary to perform clinical trials specifically designed to assess the efficacy and safety of these fixed-dose formulations to generate solid evidence of their clinical advantages.

Liability to prevent consequences of an unhealthy situation due to accumulating toxic and hazardous emissions caused by open dumping of municipal solid waste with increasing urbanization has necessitated a renewed thinking on waste disposal. Grate fired incineration systems were adopted by urban managements in past and present but with criticisms due to formation of air borne emissions. Improved combustion methods like fluidized bed are now propagated because of current requirements like efficient energy recovery potential, stricter emission norms, adaptability with urban growth, adaptability to co-firing with other waste like biomass, edible oil wastes or industrial effluent and integration with conventional energy generation. Such a comprehensive and futuristic approach is more sustainable for the community. Multi-criteria decision-making tool is used to identify the best technology option among grate combustion and fluidized bed combustion for disposing and energy recovery from waste. Ten different collection and disposal options involving two combustion methods, namely, grate combustion and fluidized bed method are considered. Utilization of the energy is done for three end uses, namely, power generation, water distillation and district cooling. Two different regions in Saudi Arabia are considered for this study under two types of scenario, namely with recycling and without recycling. The different options are prioritized based on their overall ranking using five major performance factors.

Aim of the study: To draw inferences from a retrospective evaluation of PSMA PET CT scans performed for the evaluation of biochemical recurrence. Material and Methods: Retrospective analysis of 295 PSMA PET CT scans spanning 3 years between 2020 and 2022 was undertaken. Results: Of 295 PET CT scans, 179 were positive, 66 negative and 50 had indeterminate findings. In positive group, 67 had radical prostatectomy and PSMA avid lesions were seen most commonly in pelvic lymph nodes. Remaining 112 positive scans, in non-radical prostatectomy group; 25 had recurrence only in prostate, 17 had recurrence involving prostate bed; 28 had no recurrence in prostate gland, while 42 had recurrence in prostate as well as extra prostatic sites. Overall, in non-prostatectomy group, 75 % population was harbouring a PSMA avid lesion in prostate gland while in remaining 25% population recurrence did not involve prostate gland. Majority of indeterminate findings were seen in small pelvic or retroperitoneal lymph nodes or skeletal regions (ribs/others) and in 9 patients indeterminate focus was seen in the prostate bed only. Follow up PSMA PET CT was helpful in prior indeterminate findings and unexplained PSA rise. Conclusion: A higher recurrence in prostate bed while evaluating biochemical recurrence prompts us to think; whether prostatectomy should be offered more proactively? Follow up PSMA PET CT is helpful for indeterminate findings; a PSA rise of 0.7 ng/ml in 6 months can result in positive PSMA PET CT while negative scan can be seen upto 2ng/ml PSA rise in 6 months.

This study seeks to determine how economic policy uncertainty (EPU) influences investment decisions and the market value of the Pakistan Stock Exchange. The study examines investment and operational data from 249 energy and petroleum companies between 2015 and 2020, in addition to macroeconomic variables such as EPU. This study investigates the moderating effects of EPU on investments in fixed and intangible assets, as well as its effect on Tobin's Q and the market price per share. The outcomes demonstrate that EPU reduces the costs of both tangible and intangible assets for businesses. In addition, companies with a greater Tobin's Q and market price per share are more impacted by uncertain corporate investment policies. However, financial leverage is found to be negatively correlated with share price and positively correlated with earnings per share and earnings per unit. Tobin's Q is positively correlated with financial leverage, indicating that firms that raise capital through debt are more likely to create value for investors. The research indicates that market-dependent enterprises are more susceptible to the unpredictability of monetary policy. Eventually, the findings suggest that consistent and transparent economic policies may increase the efficiency of corporate investment.

The main issues of accounting reporting regarding goodwill are whether a firm’s management reliably conveys their private information about future earnings, and whether they disclose value-relevant and useful information to accounting users. In the current International Financial Reporting Standards (IFRS) regulations, the goodwill impairment test is based on management’s discretionary assessments. This study examines how goodwill impairment is reported under IFRS considering company- and industry-specific economic factors, proxies for earnings management, and macroeconomic crisis years. We extend previous research using Tobit and Logit regression, by employing a fixed-effects model. This approach is possible because of a panel data set comprising 449 of 600 active companies sampled from the STOXX Europe 600 index from 2005 to 2018. We find that goodwill impairments are largely concentrated in certain companies, industries, and years. The regression models show a significant negative correlation between companies’ return on total assets and goodwill impairments. Moreover, we discover that goodwill impairments have a significant positive correlation with goodwill intensity, debt ratio, and the proxy for reporting a one-off big bath charge. In addition, we find that the global financial crisis in 2008-2009 and the European debt crisis in 2011 differ significantly from other fiscal years

The increased demand for resources and energy that is developing with rising global consumption represents a key challenge for our generation. Biogas production can contribute to sustainable energy production and closing nutrient cycles using organic residues or as part of a utilization cascade in the case of energy crops. Compared to hydrogen (H2), biogas with a high methane (CH4) content can be fed into the gas grid without restrictions. For this purpose, the CH4 content of the biogas must be increased from 52 to 60 % after anaerobic digestion to more than 96 %. In this study, biological hydrogen methanation (BHM) in trickling-bed reactors (TBR) is used to upgrade biogas. Design of experiments (DoE) is used to determine the optimal process parameters. The performance of the reactors is stable under all given conditions, reaching a “low” gas grid quality of over 90 %. The highest CH4 content of 95.626 ± 0.563 % is achieved at 55 °C and 4 bar, with a methane formation rate (MFR) of 5.111 ± 0.167 m³/(m³·d). The process performance is highly dependent on the H2:CO2 ratio in the educts, which should be as close as possible to the stochiometric ratio of 4. In conclusion, BHM is a viable approach to upgrade biogas to biomethane quality and can contribute to a sustainable energy grid.

The diamagnetic levitation technique can be applied to non-destructive testing for identifying cracks and defects in magnetic materials. Pyrolytic graphite is a material that can be leveraged in micromachines due to its no-power diamagnetic levitation on a permanent magnet (PM) array. However, the damping force applied to pyrolytic graphite prevents it from maintaining con-tinuous motion along the PM array. This paper investigates the in-plane motion and damping characteristics of pyrolytic graphite sheets on the PM array. The centroid of pyrolytic graphite will maintain a stable levitation when positioned on the intersecting point of the PM array. Fur-thermore, the in-plane motion of two different pyrolytic graphite sizes - PG10 (10×10×0.5mm3) and PG20 (20×20×0.5mm3) - has revealed that the in-plane forces applied to them are approximately 61.4μN and 28.2μN, respectively. The smaller sheet has a shorter oscillation time while oscillating before it stabilizes. The damping ratio of the oscillation was between 0.1-0.2. The in-plane force and the stable time of pyrolytic graphite are related to its size ratio in comparison with the PM. This relationship is believed to promote stability, as the force acting on the graphite sheet will be distributed over a larger area when the sheet size increases. During the fixed-axis rotation process, the study found that the friction coefficient and friction force decreased as the rotational speed decreased. The diamagnetic levitation of pyrolytic diamagnetic levitation is also unable to maintain long-term axial rotation. Finally, friction force was tested using PG10 during fixed-axis rotation above a circular PM array. The results showed that the order of the friction coefficient is 10-3, and the friction force is about 0.8μN, decreasing with graphite rotation speed. We hope this technique will be used in crack detection, magnetic detection and other micromachine.

Increasing green total factor productivity is the key to achieving green development in agriculture. This study measured the green total factor productivity of Jiangxi’s agriculture, and its regional and temporal evolution characteristics were examined. The fixed-effects model was then used to investigate the model’s fundamental components empirically. The study’s findings reveal the following: During the period under review, technical change was the primary element driving the rise in the green total factor productivity of agriculture. A rising “U”-shaped trend with notable regional variances characterizes the spatial and temporal evolution. The primary factors that affect changes in green total factor productivity in agriculture include the ease of transportation, the per capita disposable income of rural residents, the level of agricultural mechanization, the degree of urbanization, the level of financial support for agriculture, and the percentage of workers in secondary industries. As a result, it is suggested that, in order to substantially increase agricultural green total factor productivity, agricultural green technological support should be strengthened, more fully developed, and promoted in a multi-pronged approach.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

Considering rotation-induced centrifugal stiffening, spin softening, and Coriolis effects, the three-dimensional finite element model of a rotating blade with a dovetail structure is built through the contact dynamics theory. The fixed-interface component mode synthesis method is then adopted to reduce the model for high computational efficiency and adequate model accuracy. The effects of the number of normal modes on the first-six-order modal characteristics of the model varying with the rotating speed are studied between the reduced and full models. Next, the influence of rotating speed and friction factor on the nonlinear dynamic characteristics of the model under the action of aerodynamic force are elaborately discussed. The results show that: (1) tenon-mortise joint contact-induced nonlinearity under low rotating speeds results in the intermittent interference of contact surfaces and frequency multiplications of aerodynamic excitation frequency in the spectrum cascades, while that under high rotating speeds causes the continuous interface contact and asynchronous excitation at the tenon-mortise joint; (2) the increase of friction factor results in a lower contact pressure distribution and the right shift of the resonance peak (i.e., hard nonlinearity).

This study utilized panel data from 31 Chinese provinces over a period of nine years to investigate the impact of green finance on the upgrading of the agricultural industrial structure. A fixed-effect model was employed, and the findings indicate that green financing has a positive effect on the growth of China's agricultural industry. However, regional disparities exist, particularly in the uneven distribution of green financing across the eastern, central, and western regions. Moreover, it emphasizes the need to consider regional differences and tailor development strategies accordingly. To promote further development and transformation of China's agricultural industrial structure, the study recommends innovative green financial products, improved regulations and policies, and the integration of digital technologies.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

The last decade was characterized by the reduction of hospital beds throughout Europe. When facing Covid pandemic, this has been an issue of major importance as hospitals were seriously overloaded with an unexpected growth in demand. The dichotomy formed by the scarcity of beds and the need for acute care was handled by the Bed Management (BM) function. This study explores how BM was able to help the solidness of the healthcare system, managing hospital beds at best and recruiting others in different set-tings as intermediate care, in a large Local Health Authority (LHA) in central Italy. Ad-ministrative data show how the provision of appropriate care was achieved recruiting approximately 500 beds belonging to private healthcare facilities affiliated with the re-gional healthcare system and exercising at best the BM function. The ability of the system to absorb the extra demand caused by Covid was made possible using intermediate care beds, which allowed to stretch the logistic boundaries of the hospitals, and by the promptness of Bed Management in converting beds in Covid beds and reconverting them and timely managing internal patient logistic, thus creating space according to the healthcare demand.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

Serial femtosecond crystallography (SFX) using an X-ray free-electron laser (XFEL) enables determination of room-temperature structures without causing radiation damage. Using an optical pump-probe or mix-and-injection, SFX enables the intermediate state visualization of a molecular reaction. In SFX experiments, serial and stable microcrystal delivery to the X-ray interaction point is vital for reasonable data collection and efficient beam time. The Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL) facility established SFX instruments at a nanocrystallography and coherent imaging (NCI) experimental station. Various sample delivery methods, including injection, fixed-target scanning, and hybrid methods, have been developed and applied to collect XFEL diffraction data. Herein, we review the currently available sample delivery methods for SFX at the NCI experimental station at the PAL-XFEL. This article will help PAL-XFEL users access the SFX system for their experiments.

Biochar is an inexpensive and effective carbon sequestration technology produced by slow and fast pyrolysis of biomass feedstock at elevated temperatures in inert conditions producing large quantities of solid residue (i.e., biochar), condensable liquids (bio-oil) and hydrocarbon gases. Biochar have shown excellent adsorption capabilities. Biochar has shown excellent adsorption capabilities for short-chain PFAS and short chain PFAS. This paper suggests optimal pyrolysis reaction conditions to adsorb PFAS to maximum allowable concentrations in wastewater up to Environmental Protection Agency (EPA) is 70 ng/L. The paper highlights the operation conditions and influential reaction conditions to control the microporous structures in Biochar. The paper also aims to summarize the fundamentals of production of Biochar from biomass slow pyrolysis as well as optimal conditions for extraction of PFAS from wastewater streams and destruction of PFAS in biosolids. The scientific contributions for production of Biochar from biomass pyrolysis are highlighted. The paper also highlights the advantages of biochar over activated carbon in terms of low manufacturing costs and higher adsorption rates.

The importance of both recycling and additive manufacturing (AM) is increasing, however there has been a limited focus on development of AM alloys that are recyclably compatible with the larger scrap loops of wrought 5xxx, 6xxx and cast 3xx aluminium alloys. In this work the powder bed fusion (PBF) printability of AlMgSi alloys in the interval of 0-30wt%Mg and 0-4wt%Si is screened experimentally with a high throughput method. This method produces PBF mimicked material by PVD co-sputtering followed by laser remelting. Strong evidence was found for AlMgSi alloys being printable in two different composition ranges; Si+Mg<0.7wt% or for Si+2/3Mg>4wt% when Mg < 3wt% and Si > 3wt%. Increasing the amount of Mg and Si influence the grain structure by introducing fine columnar grains at the melt pool boundary, although the melt pool interior was unaffected. Hardness in as-built state increased with both Mg and Si, alt-hough Si had neglectable effect at low levels of Mg. Both evaporative loss of Mg and the amount of Mg in solid solution increased linearly with the amount of Mg.

Additive manufacturing (AM) technologies show potential for the development of functionally integrated lightweight designs, biomimetic structures and material savings. Typically, as-built surfaces show powder particle agglomerations and re-entrant features, leading to rough surfaces, which are associated with poor fatigue performance. To benefit from the full range of advantages with special focus on aerospace applications, critical features for crack initiation when subjected to fatigue loading need to be identified and mitigated. A first step toward achieving this goal is the surface texture characterisation based on the quantification of surface features. In this paper, selected areal height, functional and feature parameters from ISO 25178-2:2022 are generated and process-specific features are examined for as-built AlSi7Mg0.6 from laser powder bed fusion (PBF-LB). A connection with the particle size distribution of the used powder is demonstrated. It is shown that surface feature analysis opens up opportunities to use physically meaningful surface characteristics in future quality assurance and part qualification processes.

Selective Paste Intrusion (SPI) is an additive manufacturing (AM) process in which thin layers of aggregates are selectively bonded by cement paste only where the structure is to be produced. In this way, concrete elements with complex geometries and structures can be created. Reinforcement is required to increase the flexural strength of the concrete elements and, thus, enable their applicability in practice. Integrating the reinforcement is a difficult task, particularly in the case of SPI due to the layer-wise printing method. Especially with respect to possible complex structures, the production of the reinforcement needs to be adapted to SPI, thereby offering a high degree of freedom. One concept for a reinforcement integration is combining the two additive manufacturing processes SPI and Wire and Arc Additive Manufacturing (WAAM). However, since the two processes serve different fields of application, their compatibility is not necessarily given. Ongoing investigations show that the temperatures caused by WAAM adversely affect both, the cement paste rheology required for sufficient paste penetration into the particle bed and the overall concrete strength. This paper provides an overview of ongoing research focusing on different cooling strategies and their effects on the compressive strength of SPI-printed concrete parts.

The Selective Paste Intrusion (SPI) method is a layer-by-layer additive manufacturing technique that allows for the production of complex geometries in concrete elements by selectively bonding aggregates with cement paste in a particle bed. To create reinforced concrete, the Wire and Arc Additive Manufacturing (WAAM) process shall be integrated into SPI. This technique allows the production of almost free-formed reinforcement and thus complements the advantage of SPI to produce free-formed structures of almost any geometry. However, integration of WAAM into SPI poses a considerable challenge, as high temperatures are generated during the welding process. These temperatures can negatively affect the rheological properties of the cement paste, in turn the penetration behavior of the paste in the particle bed and, subsequently, the mechanical properties of the hardened concrete. A possible passive cooling strategy is to increase the protruding length of the reinforcement bars out of the particle-bed. This requires that the distance of the print nozzle to the particle bed is as well increased, since it must be possible to move it across the reinforcement. The objective was thus to investigate the effect of that distance on print quality and to quantify a maximum allowable distance for an adequate print quality (for the printer setting used) in terms of shape accuracy and concrete strength. Compressive and flexural strength tests as well as geometrical measurements using a 3D scanning method were performed on specimen, printed with varying print nozzle to particle bed distances. It can be stated that for the used SPI print-heads, nozzle-types and parameter settings, the distance between the nozzle and the particle bed should not exceed 50 mm to ensure sufficient print quality in both shape accuracy and mechanical strength.

Surfaces of additively manufactured metal parts from powder-based processes typically show powder particle agglomerations and other features, resulting in high surface roughness. Proper characterization of those surfaces is necessary in order to assess part quality with respect to coatability, mechanical performance or corrosion resistance for use in aerospace, automotive, medical and more industrial applications. Optical surface texture measurement allows for collection of areal surface data, while the established contact stylus method only captures line profile data. When applying optical methods for surface topography measurements, proper data acquisition and post-processing in order to assess surface texture may be complex. A number of variables can be adjusted, such as different measurement settings, approaches to outlier removal, evaluated area size or form removal. This work shows the influence of selected z-range prior to measurement and the influence of choosing pre-defined outlier removal settings in MountainsMap 9.2 on selected ISO 25178-2:2022 parameters calculated from data obtained from confocal microscopy for as-built Ti6Al4V from laser powder bed fusion. The aim is to show the influence of variation in measurement and post-processing on calculated surface texture parameters and stress the importance of proper documentation in order to achieve reproducibility of data for quality management.

Metal additive manufacturing technologies have large potential for future use in load bearing aerospace applications, requiring a deeper understanding of mechanical performance and influencing factors. The objective of this study is to manufacture fatigue specimens by laser powder bed fusion with comparable bulk and different as-built surface quality (without post-processing). This goal was pursued by using identical bulk/hatch scan parameters while varying contour scan parameters. The bulk quality was evaluated by density measurements according to Archimedes’ principle and tensile testing. The surfaces were investigated using the optical fringe projection method and surface quality was assessed by the areal surface texture parameters Sa (arithmetic mean height) and Sk (core height, derived from material ratio curve). The resulting mean values of max (ultimate tensile strength) were between 375 and 405 MPa, which is a variation of roughly 8%, for seven different surface conditions. It could be confirmed that the influence of contour scan variation on bulk quality is insignificant for the assessed samples.

About 50% of colorectal cancer patients develop liver metastases. Patients with metastatic colorectal cancer have 5-year survival rates below 20% despite new therapeutic regimens. Tumor heterogeneity has been linked with poor treatment response and clinical outcome, but was so far mainly studied via bulk genomic analyses. In this study we performed spatial proteomics via MALDI mass spectrometry imaging on six patient-matched CRC primary tumor and liver metastases to characterize interpatient, intertumor and intratumor hetereogeneity. We found several peptide features that were enriched in vital tumor areas of primary tumors and liver metastasis and tentatively derived from tumor cell specific proteins such as annexin A4 and prelamin A/C. Liver metastases of colorectal cancer showed higher heterogeneity between patients than primary tumors while within patients both entities show similar intratumor heterogeneity sometimes organized in zonal pattern. Together our findings give new insights into the spatial proteomic heterogeneity of primary CRC and patient-matched liver metastases.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.