We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

This study aims to categorize the morphological changes during cabbage (B. oleracea ssp. capitata) development: seedling, rosette, folding, and heading and to elucidate the cellular mechanisms of leaf curvature, essential for the formation of the leafy head. We followed the growth of two cabbage morphotypes with distinct head shapes (round and pointed); we phenotyped the size and volume of the whole-plant as well as the size, shape, and curvature of the leaves during growth. By integrating these phenotypic data, we determined the four vegetative stages for both cabbages. Cytological phenotypes of microtome sections from five distinct leaf positions of the rosette, folding, and heading leaves at two timepoints during leaf growth were quantified and revealed variations in cellular parameters among leaf types, between leaf positions, and between the adaxial and abaxial sides. We identified two synergistic cellular mechanisms contributing to the curvature of heading leaves: differential growth across the leaf blade, with increased growth at the leaf's centre relative to the margins; and increased expansion of the spongy parenchyma layer compared to the palisade parenchyma layer, resulting in the direction of the curvature, which is inwards. These two processes together contribute to the typical leafy heads of cabbages.

A wide variety of renal neoplasms can have cystic areas. It happens for different reasons: some tumors have an intrinsic cystic architecture, others have a pseudocystic degeneration of necrotic foci or they have cystically dilated renal tubules constrained by stromal neoplastic cells. Clear cell renal cell carcinoma (CCRCC), either solid or cystic, is the most frequent type of renal cancer. While pseudocysts are found in high-grade aggressive CCRCC, cystic growth is associated to low-grade indolent cases. The latter also form through a cyst-dependent molecular pathway and they are more frequent in patients suffering from VHL disease. The differential diagnosis with multilocular cystic renal neoplasm of low malignant potential and clear cell papillary renal cell tumor can be especially hard and it requires a focused macroscopical and microscopical pathological analysis. As every class of renal tumors include cystic forms, a knowledge of criteria for a differential diagnosis is mandatory.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

The structure and phenomena arising from charge transfer in cold field emission modus in a single closed carbon nanotube under cold field emission conditions were studied. By studying microphotographs in various microscopes - AFM, SEM, TEM it was found inhomogeneities in the form of two types of superlattices. The conductivity of the emitter section of a nanodiode circuit with an emitter made of an individual closed carbon nanotube (CNT) and arrays of closed CNTs was studied. High values of cold field emission were observed, as well as nonlinearity and anomalies of the current-voltage characteristic (I-V characteristics), which manifested themselves in the form of peaks at low and high current values. Peaks in the CVC have distinct areas of negative differential conductivity. It is argued, that the anomalously high currents in the I–V characteristics of cold field emission of electrons from a nanoemitter made of closed CNTs can be associated with a sharp increase in the density of electron states at energies near the van Hove singularity.

This study investigates the effect of Re addition on the microstructure evolution and oxidation resistance of Co-Cr-Ta-Ti-C alloys. The alloys tested in this study consist of a Co-rich matrix with mixed HCP and FCC phases, together with TaTiC2 and Ti-based carbides. The addition of Re promotes the precipitation and growth of a CoCr-rich σ phase. Differential thermal analysis (DTA) showed that the melting temperatures did not change drastically up to 10 at% Re addition, whereas 15 at% Re addition significantly increased the melting temperature of the alloys. Oxidation tests in air at 1200°C showed that excessive Re content could lead to deterioration in oxidation resistance, mainly due to the accelerated formation of volatile Re oxides.

Pea (Pisum sativum L.), like most legumes, forms mutualistic symbioses with nodule bacteria and arbuscular mycorrhizal (AM) fungi. The positive effect of inoculation is partially determined by the plant genotype, thus, pea varieties with high and low symbiotic responsivity have been described, but the molecular genetic basis of this trait remains unknown. Here, we compare the symbiotically responsive breeding line ‘Triumph’ of grain pea with its parental cultivars ‘Vendevil’ (a donor of high symbiotic responsivity) and ‘Classic’ (a donor of agriculturally valuable traits) using genome and transcriptome sequencing. We show that ‘Triumph’ inherited one-fourth of its genome from ‘Vendevil’, including the genes related to AM and nodule formation, and reveal that under combined inoculation with nodule bacteria and AM fungi, ‘Triumph’ and ‘Vendevil’, in contrast to ‘Classic’, demonstrate similar up-regulation of the genes related to solute transport, hormonal regulation and flavonoid biosynthesis in their roots. We also identify the gene PsGLP2, whose expression pattern distinguishing ‘Triumph’ and ‘Vendevil’ from ‘Classic’ correlates with difference within the promoter region sequence, making it a promising marker for the symbiotic responsivity trait. The results of the study may be helpful for future molecular breeding programs aimed at creation of symbiotically responsive cultivars of pea.

Alzheimer’s disease (AD) is the leading cause of dementia, characterised by beta-amyloid plaques, neurofibrillary tangles, and oxidative stress. Iron is suspected to enhance disease progression, and chelation may be a potential treatment. We propose that Aloysia citrodora Paláu (AC), a plant in the Verbenaceae family, can act as a moderate chelator of iron. It may reduce the effect of iron on beta-amyloid 1-42 (Aβ1-42) aggregation. Cyclic voltammetry (CV) and differential pulse voltammetry (DPV) were used to demonstrate that AC can interact with iron (II) and iron (III), the two most abundant forms of iron within the body. DPV was also used to characterise Aβ1-42 aggregation, and two main features were obtained. The first is the tyrosine peak (~0.6 V) decreased in magnitude over time, which is a sign of aggregation and folding. The other is a conglomerate of peaks at ~0 V, whose identity is unknown. Furthermore, iron (II) increased the rate of tyrosine peak depreciation, and the addition of AC negated this induced effect. This implied that iron (II) increases Aβ1-42 aggregation into higher order, and AC may be an effective countermeasure.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

In this study, a design of Morlet wavelet neural networks (MWNNs) is presented to solve the prediction differential model (PDM) using the global approximation capability of genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS), i.e., MWNN-GAIPAS. The famous PDM is known as a variant of functional differential system that works as an opposite of the historical delay differential models. A fitness function is optimized using the mean square error by applying the GA-IPAS for solving the PDM. Three PDM examples have been presented numerically to check the authenticity of the MWNN-GAIPAS. For the perfection of the designed MWNN-GAIPAS, the comparability of the obtained results and exact results is performed. Moreover, the neuron analysis is performed by taking the 3, 10 and 20 number of neurons. The statistical observations have been performed to authenticate the reliability of the MWNN-GAIPAS for solving the PDM.

This paper describes methods for evaluating the thermal properties of textile materials, clothing composites, and clothing using an integrated measurement system that includes a hot plate, a multi-purpose differential conductometer, a thermal manikin, a temperature gradient measurement device, and a device for measuring the physiological parameters of the human body during the exact evaluation of garment thermal comfort. In practice, measurements were taken on four types of materials widely used in the production of conventional and protective clothing. The measurements were carried out using a hot plate and a multi-purpose differential conductometer, determining the thermal resistances of the material in its uncompressed form and a force that was ten times greater than that needed to determine its thickness. Using a hot plate and a multi-purpose differential conductometer, thermal resistances of textile materials were assessed at different levels of material compression. On hot plates, both conduction and convection had an impact on thermal resistance, but in multi-purpose differential conductometer, only conduction did. Moreover, the reduction of thermal resistance was observed while compressing textile materials.

Tandemly organized rRNA genes are the typical example of a multigene family, where individual members evolve coordinately within but independently between species due to gene conversion and unequal crossing over. More frequently, in eukaryotic species with an inter-species hybrid origin, expression of unhomogenized rRNA genes from one progenitor is epigenetically silenced because of nucleolus dominance, and distinct rRNA genes may lose functionality and evolve faster. Interestingly, we obtained unusual ribosomal gene sequences from Oryza species that showed great diversity and did not appear in the present rice genomic sequence. The diversity of rDNA sequences indicated that the homogenization in rice is incomplete and explains the introgression of distinct rRNA gene families into ancestral rice genome before speciation and continent separation. The divergent large subunit (LSU) ribosomal genes are expressed, some of them differentially, depending on the N-fertilization of plants. Detection of differential transcripts of the rRNA genes suggested that rRNA gene families are not functionally equivalent. Phylogenetic analysis assigned Oryza species branching order to monocots, and monocot lineages probably have the same ecological origin by molecular clock calculation. Therefore, our results suggested that the geographical distances of continents separation cause barriers to the gene flow and homogenization among Oryza species which requires further explanation,

In this paper, we derive Jeffreys divergence, generalized Fisher divergence and corresponding De Bruijn identities on space-time random field. First, we determine the relation between Fisher information on the space-time random field in one of the space-time points and the ratio of Jeffreys divergence on a space-time random field at distinct space-time positions to the square of coordinate difference. In addition, we also find identities between the partial derivative of the Jeffreys divergence and the generalized Fisher divergence with respect to space-time variables, i.e. the De Bruijn identities, between two space-time random fields obtained by different parameters under the same Fokker-Planck equations. At the end of this paper, we present three examples of the Fokker-Planck equations on space-time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and accompanying De Bruijn identities.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black-Scholes-Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath-Jarrow-Morton model and adapting the Hull-White interest rate model to fit BMM. The study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.

The morphology of virgin reactor powder (RP) of high-density polyethylene HDPE with MW = 160,000 g/mol was investigated with the help of DSC, SEM, SAXS and WAXS methods. The morphological SEM analysis showed, that the main morphological units of RP are macro- and micro-shish kebab structures with significantly different geometric dimensions, as well as individual lamellae of folded chain crystals. Quantitative analysis of an asymmetric SAXS reflection made it possible to reveal the presence of several periodic morphoses in the RP with long periods from 20 nm to 60 nm and to correlate them with the observed powder morphology. According to the DSC crystallinity data, the thickness of the lamellae in each long period was estimated. Their surface energy was calculated in the framework of the Gibbs-Thompson theory. The presence of regular and irregular folds on the surface of the different shish-kebab lamellae is discussed. The percentage of identified morphoses in the RP was calculated. It has been suggested that the specific structure of HDPE RP is due to the peculiarity of polymer crystallization during suspension synthesis in a quasi-stationary regime, in which local overheating and inhomogeneous distribution of shear stresses in a chemical reactor are possible.

This work assesses the dietary use of two insect meals of Tenebrio molitor (TM) larvae reared in conventional (TM-10) or MAPs-enriched substrates (MAP-TM-10) as fish meal replacements (10%) in the diets of gilthead seabream (Sparus aurata). Fish (n=4,500; 207.19 ± 1.47 g) were divided into three groups with triplicates: Control (fed conventional diet), TM-10 and MAP-TM-10 groups.The fish were reared in floating cages for 12 weeks and The dietary effects on white blood cell ac-tivation, heat shock proteins, MAPKs, and apoptosis of the fish were evaluated. The MAP-TM-10 group exhibited the highest eosinophilic induction and plasma cells. Phosphorylated levels of p38 MAPK; p44/42 MAPK; HSP70 and HSP90 increased in the TM-10 and MAP-TM-10. In terms of apoptosis, Bax levels were lower in the TM groups compared to the Control, and the MAP-TM-10 group showed even lower levels than the TM-10 group. Bcl-2 levels increased in the TM-10 compared to the Control, and further increased in the MAP-TM-10 group. The Bax/Bcl-2 ratio, an apoptosis indicator, decreased in the TM groups, with the MAP-TM-10 group showing a further decrease compared to TM-10. These findings suggest that insects breeding substrate enriched with MAPs modulated the effect of TM on cellular stress and apoptosis.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

Novolac phenol-formaldehyde resins have gained extensive commercial utilization across diverse applications due to their exceptional mechanical, thermal, and chemical resistance properties. In this investigation, we successfully synthesized a traditional novolac, and a biobased novolac phenol-formaldehyde resin by partially substituting phenol with a bio-oil obtained from the organic phase resulting from the fast pyrolysis of pinewood biomass. Despite extensive investigations into the curing behavior of novolac resins crosslinked with hexamethylenetetramine (HMTA) through numerous model-fitting cure kinetic studies, a comprehensive model for predicting the crosslinking of bio-based phenol-formaldehyde resins in the presence of HMTA has not yet been studied. The primary objective of this research was to compare and apply several commonly used kinetic models to predict the degree of curing and cure rate of the synthesized resins, using DSC dynamic measurements. Our results demonstrated that the autocatalytic model exhibited excellent fitting for the traditional novolac resin and HMTA mixture, while the Kamal model showed better fitting with the experimental data obtained for the bio-based phenol-formaldehyde resin and HMTA system. In addition, the results evidenced a significant drop in the curing temperature by partially replacing phenol with bio-oil. Additionally, the results revealed a notable reduction in curing temperature when phenol was partially substituted with bio-oil. This substitution not only offers environmental benefits but also promotes energy efficiency and enhances production safety. The data collected in this study is pivotal for our subsequent research endeavors, which aim to develop environmentally sustainable materials optimized for use in 3D printing manufacturing processes.

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

The National Institute of Justice reported that current methods for processing sexual assault samples have a high failure rate, with 60 to 80 percent of tested kits unable to produce usable DNA profiles. Even when samples test positive for male DNA, 34 percent of sexual assault kits (SAK) do not yield recovered male DNA after differential extraction. Less than 30% recovery of available sperm DNA contributes to this low success rate. The SpermX™ method (SX) has been shown to recover 80 percent or more of sperm DNA from sexual assault samples. An interlaboratory evaluation compared SX to standard differential extraction (DE) protocols. Mock samples with known ratios of female epithelial cells and sperm cells were processed using both methods. Results revealed that SX consistently provided CODIS up-loadable DNA profiles, even with as few as 25 sperm cells, whereas DE failed to produce usable results. On average, SX yielded a seven-fold increase in the recovery of unshared male alleles compared to DE. In conclusion, SX outperformed DE in recovering higher quantities of male DNA with minimal female carryover in sexual assault-type samples. This improved success rate in obtaining usable DNA profiles can significantly aid in solving sexual assault cases. Keywords: Differential extraction, Sexual Assault Kit (SAK), Sperm DNA, STRmix™, Combined DNA Index System (CODIS), Forensic DNA analysis, Low Sperm Samples, DNA Mixtures, Autosomal STR Analysis, SpermX.

Background: By using outcome prediction scores, it is possible to distinguish between good and poor performers with cochlear implants (CI) after CI implantation. The reasons for poor performance, despite good basic conditions, can be manifold. On the one hand, the postoperative fitting may be inadequate; on the other, neurophysiological disease processes may impair speech understanding with a CI. These disease processes are not yet fully understood. In acoustics, it is known that the auditory brainstem responses (ABR) and their latencies and amplitudes allow differential diagnosis based on reference values for normal-hearing individuals. The aim of this study was to provide reference values for electrically evoked brainstem responses (EABRs) in terms of rate-dependent latencies and amplitudes. Methods: 20 experienced adult CI recipients with a predicted and measured good postoperative word recognition score were recruited from the clinic’s patient pool. In the same stimulation mode and intensity we measured latencies and interpeak-latencies of EABRs and electrically evoked compound action potentials (ECAPs). With a defined supra-threshold stimulation intensity above the individual ECAP threshold, we applied stimulation at several rates between 11 and 91 stimuli per second. Results: We found rate dependences for EABR latency t3 and t5 in the order of 0.19 ms and 0.37 ms respectively, while ECAP was not affected by rate. Correspondingly, the interpeak intervalls’ rate dependences for t5-t1, t5-t3 and t3-t1 were of the order of 0.37 ms, 0.18 ms and 0.19 ms. Comparing the EABR amplitudes between the stimulation rates 11/s and 81/s, we found that at 81/s the amplitudes were significantly reduced down: to 73% for A3 and 81% for A5. These rate dependences of latency and amplitude in EABR have characteristics comparable to those of acoustic ABR. Conclusions: These data may serve to provide reference values for EABR and ECAP latencies, interpeak intervals and amplitudes with respect to stimulation rate. Altered response patterns of ECAPs and EABRs to normalised stimulation modes could be used in the future to describe and classify neuropathological processes in a better-differentiated way.

In a power plant that uses seawater as a coolant, a debris filter is required to remove foreign substances from the seawater, and differential pressure leads to a decrease in the coolant flow rate, leading to a decrease in power generation efficiency. In this study, analysis was performed under different initial flow velocity conditions of 1.5m/s, 2.0m/s, and 2.5m/s for a debris filter used in a power plant to understand flow characteristics in CTCS. The flow and differential pressure characteristics of a CTCS with an installed debris filter were considered in a comparative analysis of velocity, pressure, and turbulent kinetic energy distribution. The results confirmed that a vortex was generated in the pipe with the debris filter, apparently due to the collision of the flow with the bracket of the debris filter. As the flow rate increased, the range of the vortex increased, causing a loss in flow.

Discrete distribution estimation is a fundamental statistical tool, which is widely used to perform data analysis tasks in various applications involving sensitive personal information. Due to privacy concerns, individuals may not always provide their raw information, which leads to unpredictable biases in the final results of estimated distribution. Local Differential Privacy (LDP) is an advanced technique for privacy protection of discrete distribution estimation. Currently, typical LDP mechanisms provide same protection for all items in the domain, which imposes unnecessary perturbation on less sensitive items and thus degrades the utility of final results. Although, several recent works try to alleviate this problem, the utility can be further improved. In this paper, we propose a novel notion called Item-Oriented Personalized LDP (IPLDP), which independently perturbs different items with different privacy budgets to achieve personalized privacy protection. Furthermore, to satisfy IPLDP, we propose the Item-Oriented Personalized Randomized Response (IPRR) based on the observation that the sensitivity of data shows an inverse relationship with the population size of respective individuals. Theoretical analysis and experimental results demonstrate that our method can provide fine-grained privacy protection and improve data utility simultaneously.

This paper presents a new low-voltage versatile mixed-mode filter which uses a multi-ple-input/output differential difference transconductance amplifier (MIMO-DDTA). The multi-ple-input of the DDTA is realized using a multiple-input bulk-driven MOS transistor (MI-BD-MOST) technique to maintain a single differential pair, thereby achieving simple structure with minimal power consumption. In a single topology, the proposed filter can provide five standard filtering functions (low-pass, high-pass, band-pass, band-stop, and all-pass) in four modes: voltage (VM), current (CM), transadmittance (TAM), and transimpedance (TIM). This provides the full capability of a mixed mode filter (i.e., twenty filter functions). Moreover, the VM filter offers high-input and low-output impedances and the CM filter offers high-output impedance; therefore, no buffer circuit is needed. The natural frequency of all filtering functions can be electronically controlled by a setting current. The voltage supply is 0.5 V and for a 4 nA setting current, the power consumption of the filter was 281 nW. The filter is suitable for low-frequency biomedical and sensor applications that require extremely low supply voltages and nano-watt power consumption. For the VM low-pass filter, the dynamic range was 58.23 dB @ 1 % total harmonic distortion. The proposed filter was designed and simulated in the Cadence Virtuoso System Design Platform using the 0.18 µm TSMC CMOS technology.

Background: Ultrasonography (US) represents the gold standard imaging method for the assessment of testicular lesions (TL). The gray-scale (GSUS) and color-Doppler (CDUS) ultrasound examination allow sonographers to investigate size, margins, echotexture and vascular features of TL, with the effort to differentiate benign from malignant lesions. Recently, the use of contrast-enhanced US (CEUS) and sonoelastography (SE) led to further improvements in the differential diagnosis of TL. Although GSUS and CDUS are often sufficient to suggest the benign or malignant nature of TL, CEUS can be decisive in the differential diagnosis of unclear findings, while SE can help to strengthen the diagnosis. The contemporary combination of GSUS, CDUS, CEUS and SE led to a new diagnostic paradigm named multiparametric US (mp-US), able to provide a more detailed characterization of TL than the single techniques alone. This narrative and pictorial review is aimed to describe the mp-US appearance of several TL. Methods: An extensive Medline search was performed identifying studies in the English language focusing on mp-US evaluation of TL. Results: a practical mp-US “identity card” and iconographic characterization of several benign and malignant TL is provided herein. Conclusions: the mp-US characterization of TL reported herein can be useful in daily clinical practice.

We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.

The susceptible-infected-recovered/removed-vaccinated (SIRV) epidemics model is an important generalization of the SIR epidemics model as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemics outbreaks. Additional to the time-dependent infection ($a(t)$) and recovery ($\mu (t)$) rates, regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively, the time-dependent vaccination rate $v(t)$ accounts for the transition between the compartments $S\to V$ of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections $J(t)\ll 1$. As vaccination campaigns automatically reduce the rate of new infections by transferring susceptible to vaccinated persons, the limit $J(t)\ll 1$ is even better fulfilled than in the SIR-epidemics model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections $\jt(t)=a(t)S(t)I(t)$, the corresponding cumulative fraction $J(t)$, and $V(t)$, respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction $\jinf $ after infinite time allows us to check the validity of the original assumption $J(t)\le \jinf \ll 1$.

Homotopy perturbation and analysis methods have been widely used to obtain both approximate and exact so- lutions to nonlinear problems. In general, these two methods are based on the Taylor series with respect to an embedding parameter. Many researchers have compared the two methods and raised more concerns on the homo- topy perturbation method (HPM) because the homotopy analysis method (HAM) contains a convergence-control parameter ~: For this reason, in this article, a more general form of HPM is introduced as the -homotopy per- turbation method (-HPM), which contains a control parameter : The introduction of parameter  in this new modication gives a better way to adjust and control the convergence region and the rate of the series solution. We conrm through the given examples in this study that the HPM is a special case of the -HPM. The error and convergence analysis of this proposed method are also presented

In this paper we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra. Making use of this we construct two examples of transposed Poisson superalgebra. One of them is the graded differential algebra of differential forms on a smooth finite dimensional manifold, where we use the Lie derivative as an even degree derivation. The second example is the commutative superalgebra of basic fields of the quantum Yang-Mills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We prove several identities, which hold in a transposed Poisson superalgebra.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

The information data accuracy affects the working reliability of production management system directly. Mobile equipment is an important part of integrated manufacturing system, in the course of its works, due to the complex working environment and the dynamic change of its position, it lead to the important problem of information detection distortion. Because the application of fractional differential operator has the dual functions of enhancing signal strength and reducing data error, we puts forward a data processing method of obtaining production information data of various accuracy by changing the parameters of fractional differential operator. Establish a mobile equipment detection data fusion processing model based on fractional order partial differential equations and apply it in the processing experiment of mobile equipment testing information detection data in an integrated manufacturing system, the feasibility and effectiveness of the method are verified. We conclude that the fractional order partial differential equations used in the processing of mobile equipment monitoring information data of an integrated manufacturing system has the function of obtaining production information data of various accuracy, which are of great significance to improve the working reliability in integrated manufacturing system. which is of great significance to improve the working reliability and scientific decision of integrated manufacturing system.

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we obtained, analytically, the corresponding solutions for the conditional moment generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case. We believe that the The aforementioned model encompasses a range of processes similar to that produced by a bivariate square-root process in which entries are correlated in the standard way, i.e., via a constant correlation coefficient. Note that, for the latter, closed-form solutions for the conditional characteristic functions are not available. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices via a Fourier cosine series method.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

The differential-equation of second order for space-time oscillation in flat tangential-spacetime of Minkowski-type can be written as an energy-equation. For this energy-equation the analogon of damping energy in two coupled Minkoswki-spacetimes with ftl can be calculated and formulated over Lamberts W-function or via Euler-equation.

TmMgB5O10 spontaneous crystals were synthesized via flux-growth technique from a K2Mo3O10-based solvent. The crystal structure of the compound was solved and refined within the space group P21/n. The first principles calculations of the electronic structure reveal that TmMg-pentaborate is an insulator with an indirect energy band gap of approximately 6.37 eV. Differential scanning calorimetry measurements and powder X-ray diffraction studies of heat-treated solids show that TmMgB5O10 is an incongruent melting compound. A characteristic band of Tm3+ cation corresponding to the 3H6 → 1D2 transition is observed in the photoluminescence excitation spectra of TmMg-borate. The as-obtained crystals exhibit intense blue emission with the emission peaks centered at 455, 479, 667 and 753 nm. The most intensive band corresponds to the 1D2 3F4 transition.

The global prevalence of type 2 diabetes mellitus (T2DM) has surged in recent decades and the identification of differential glycemic responders can aid tailored treatment for prevention of pre-diabetes and T2DM. A mixed meal tolerance test (MMTT) based on regular foods offers potential to uncover differential responders in dynamical postprandial events. We aimed to fit a simple mathematical model on dynamic postprandial glucose data from repeated MMTTs among partic-ipants with elevated T2DM risk, to identify response clusters and investigate their association with T2DM risk factors and gut microbiota. Data were used from a 12-week multi-center dietary inter-vention trial involving high-risk T2DM adults, comparing high- versus low-glycemic index foods within a Mediterranean diet context (MEDGICarb). Model-based analysis of MMTTs from 155 participants (81 females, 74 males) revealed two distinct plasma glucose response clusters that were associated with baseline gut microbiota. Cluster A, inversely associated with HbA1c and waist circumference and directly with insulin sensitivity, exhibited a contrasting profile to cluster B. Findings imply that a standardized breakfast MMTT using regular foods could effectively distin-guish non-diabetic individuals at varying risk levels for T2DM using a simple mechanistic model.

FACTS devices provide significance to enhance the functioning of both static and dynamic power systems. The type, size, and location of FACTS devices determine how well they achieve the goals of enhancing voltage stability, loadability, and loss minimization simultaneously. The aim of the function in this study includes voltage stability, line loadings, and loss minimization, which are expected to obtain the most benefits from their installation and other weights allocated to them. It has been determined how installing TCSC, and SVC will improve loadability under situations of continuously increasing load. In this study, a novel optimization technique known as differential evolution invasive weed optimization (DEIWO) is utilized to locate the optimal location for FACTS devices within the IEEE 14 bus system by considering valve point effects. DEIWO was a recently developed, dominant, and simple metaheuristic algorithm for genuine parameter optimization. DEIWO was inspired by the natural process of weed colonization and dissemination, and it is highly effective at addressing broad multi-dimensional, linear and nonlinear optimization problems. The proposed method was implemented in the IEEE 14 bus testing system. Different methods from the research papers have been used to compare and analyze the results. The results demonstrate the DEIWO algorithm's capability and show how it may be used in practice to locate FACTS devices in deregulated electricity networks in the most advantageous place. A comparison of the proposed process to existing algorithms found in the literature and implemented using traditional techniques reveals that it performs better in terms of precision and convergence

In order to solve the problems of complicated steering control of unmanned vehicles in the field and difficult steering on complex roads, we designed a wheel-track composite vehicle equipped with a novel power differential steering mechanism with dual driving, which drove the steering of the vehicle through the differential rotation of the rear two wheels. The unmanned vehicle was simple to control, small in size, and able to work under the conditions of complex roads, such as hills, mountains, and muddy land. Firstly, a steering mechanism with both differential speed and force was designed to prevent the vehicle from skidding into muddy land and stopping motionless. Secondly, the kinematics model and dynamics model of the two drive shafts and the two output shafts (wheel shafts) were established. Thirdly, according to the relationship between the rotational speed of the two output shafts and the steering radius of the vehicle, the kinematic model of the rotational speed of the two input shafts and the steering radius of the wheel-track composite vehicle was obtained. Finally, according to the test data, the mathematical model of rotational speeds of the two input shafts and the actual steering radius of the vehicle was obtained by neural network fitting, and the maximum relative error between the model results and the actual steering radius value was 3.53%. The combination of power differential steering mechanism and wheel-track composite unmanned vehicle increased the adhesion with the ground and could better adapt to the complex road environment. In conclusion, the unmanned vehicle had the advantages of continuous radius steering, deceleration and torsion increase, differential lock, etc. It was suitable for all-terrain military and civilian vehicles and various special equipment mobile platforms of the walking device, and the research results could provide theoretical references for the steering control and structural optimization of the wheel-track composite vehicle under the environment of complex road surface.

The method for quantitative analysis is based on the direct measurement of the analyte using differential pulse voltammetry (DPV), exploiting its oxidation peak. Calibration curves are set up to evaluate the figures of merit of the analytical method (LOD, LOQ, linear range). The application of the sensor for the dosing of GA in real matrices is carried out by analyzing non-alcoholic and alcoholic beverages and comparing the results with those reported in the literature and with the content of total polyphenols determined by the Folin-Ciocalteu method. In all cases, concentrations of GA align with those previously found in the literature for the beverages examined. Moreover, the values are always lower than the total polyphenols content; this demonstrates the good selectivity of the sensor that can discriminate the target molecule from other polyphenols present.

The present study aimed to investigate the effect of cold deformation on the precipitation kinetics of a binary CuSc alloy containing 0.4 wt.% scandium using the experimental analysis method of differential scanning calorimetry (DSC). Non-deformed and 75% cross-section reduced cold-rolled, supersaturated specimens were tested at non-isothermal DSC runs at up to five different heating rates. The DSC results showed that cold deformation significantly accelerated the precipitation process in the binary alloy, leading to a decrease in the initial and peak temperatures of the exothermic reactions. The activation energies calculated with the Kissinger method, indicated that the precipitation activation energy decreased with increasing cold deformation. The findings of this study provide worthy implications to further optimize the processing of Cu-Sc alloys with improved mechanical properties.

In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of solution are given. At the same time, modifying the classical definitions of continuous dependence and Ga^teaux differentiability, some results on continuous dependence and Ga^teaux differentiable of solution relative to the initial value also are presented in new topology sense. For the autonomous impulsive system, the periodicity of solution is given. As an application, properties of solution for a type of controlled nonlinear ordinary differential equation with impulses at variable times is obtained. These results are foundation to study optimal control problems of systems governed by the differential equations with impulses at variable times.

An approach of implementing X-bar and R control charts as a statistical control tool to monitor changes in the melting profile of fresh and stored flaxseed oils by differential scanning calorimetry (DSC) was used. Phase transition melting profiles were collected after 0, 2, 4, 6 months of storing flaxseed oils, originated from five different cultivars. Four peaks at around -36, -30, -25, -12 °C were identified using the deconvolution analysis procedure, which enabled data to be collected on peak temperature (T), peak height (h) and the peak area (A), as well as the ratio calculated from these parameters. Control charts of DSC parameters, linked to the second peak (h2, A2) and calculated ratios of those parameters showed an increasing or decreasing trend within the storage time, thus were considered to be indicators of oil deterioration. Since DSC parameters related to the first peak (h1, A1) and third peak (h3, A3) remained unchanged within storage, they were established as the markers of flaxseed oil authenticity.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

Vectorial Boolean functions and codes are closely related, and each corresponding domain gives been to each other. On the one hand, various requirements of binary linear codes are needed for their theatrical interests but, more importantly, for their practical applicants (such as few-weight codes or minimal codes for secret sharing, locally recoverable codes for storage, etc.). On the other hand, various criteria and tables have been introduced to analyse the security of S-boxes that are related to vectorial Boolean functions, such as the Differential Distribution Table (DDT), the Boomerang Connectivity Table (BCT), and the Differential-Linear Connectivity Table (DLCT). In previous years, two new tables have been proposed for which the literature was pretty abundant: the $c$-DDT to extend the DDT and the $c$-BCT to extend the BCT. In the same vein, we propose extended concepts to study further the security of vectorial Boolean functions, especially the $c$-Walsh transform, the $c$-autocorrelation, and the $c$-differential-linear uniformity, and its accompanying table, the $c$-Differential-Linear Connectivity Table ($c$-DLCT). We study these properties of the novel functions at their optimal level concerning these concepts and describe the $c$-DLCT of the crucial inverse vectorial (Boolean) function case. Finally, the derived functions could lead to new families of binary minimal codes, as the recent achievements on minimal codes from low differential uniformity. We draw new avenues for future research toward linear code designs.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

Bismuth oxides are well-known electro-catalysts in fuel cells systems; they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of BiO₂ and MnO₂ as catalysts in the pharmaceutical analysis is analytical method for the determination of heavy metal antibacterial agents in Pharmaceutical Dosage form is developed. The method is based on the voltammetric determination of heavy metal using Bidified platinum electrode by Bismuth oxide. The two components are oxidized at the Bidified electrode surface with the development of current that is linearly proportional to their concentrations in the range of 7.04*10^-7- 1*10^-3 M heavy metal. The oxidation reaction of the two components is pH-dependent, in which the buffer used is Britton-Robinson at pH = 7.00 where maximum peak current and maximum peak separation is obtained. The regression factors obtained from the calibration curves are 0.9812. The method of analysis was validated, where the limit of detection (LOD) and the limit of quantitation (LOQ) were calculated to be 1.44*10^-4 M, 4.36*10^-4 M and 1.27*10^-4 M, 3.84*10^-4 M respectively, the percentage recovery of both components was also calculated to 77 % for heavy metal.

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employ a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

The structural evolution and phase composition of multi-block thermoplastic polyurethanes, with different nature of the soft segments based on poly(butylene adipate) (PBA), were analyzed during in-situ thermal treatments. A combination of synchrotron small- and wide-angle X-ray scattering, differential scanning calorimetry, thermogravimetric analysis, and FTIR spectroscopy was used to determine the influence of macrodiol nature and crystallization conditions on the polymorphic behavior of PBA. Using a new synthesis scheme, a relatively high degree of crystallinity for urethane blocks was achieved, which depends on the diisocyanate type in the structure of the soft segment. The hard segment domains impose geometrical constraints on PBA, thereby altering its crystallization process compared to the neat oligomer. Thus, crystallization after annealing at a low temperature (80 °C) is fast, predominantly yielding a metastable β-phase. When heated to 180 °C, which is higher than the hard-segment melting temperature, a phase-separated structure is observed. Subsequent crystallization is slower, favoring the formation of the stable α-PBA modification. The phase separation can be observed even after the hard block melting. A notably slow crystallization from an isotropic melt was documented after the disruption of phase separation at 230 °C.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

The main object of this work is to establish the existence and uniqueness of a solution to the 3D Navier-Stokes (NS) system for an incompressible fluid with viscosity. The nonlinearity of the NS system, as well as the need to estimate velocity and pressure for every value of the viscosity parameter [1] make them challenging to solve. In this regard, in the present work, we study the Navier-Stokes system, which describe the flow of a viscous incompressible fluid and the solution was obtained for velocity and pressure in an analytical form. In addition, the found pressure distribution law, which is described by a Poisson type equation and plays a fundamental role in the theory of Navier-Stokes systems in constructing analytic smooth (conditionally smooth) solutions.

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.

Key thermophysical properties necessary for the successful design and use of CoCrFeNi alloy in thermophysical applications have been measured experimentally, and the results have been compared with literature values and results previously obtained for commercial Ni-Cr alloys and equiatomic CoCrFeNi alloy. In particular, the thermal diffusivity, coefficient of thermal expansion (CTE), and specific heat capacity were measured for the as-cast and homogenized equiatomic CoCrFeNi alloy over a temperature range allowing the thermal conductivity to be calculated up to 1173 K. The thermal conductivity and thermal diffusivity of the equiatomic CoCrFeNi alloy were found to deviate from monotonic behavior in the temperature range from 773 to 1100 K. Such a deviation was previously observed in the behavior of the temperature dependence of CTE and specific heat capacity of the equiatomic CoCrFeNi alloy. The non-linear behavior is primarily the result of order/disorder phenomena for the as-cast and homogenized sample, as well as additionally for the as-cast sample, non-equilibrium solidification under arc melting conditions. The measured data of thermophysical properties are provided for thermally differently treated samples, and it is shown that there is a difference in the behavior of the temperature dependences of CTE, thermal diffusivity, and heat capacity.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

The influence of polysialic acid (PSA) and sialic acid (SA) on the gut microbial community composition and metabolites in healthy human was investigated using a bionic gastrointestinal reactor. The results indicated that PSA and SA significantly changed the gut microbiota and metabolites in different degrees. PSA can increase the relative abundances of Faecalibacterium and Allisonella, whereas SA can increase those of Bifidobacterium and Megamonas. Both can significantly increase the content of short-chain fatty acids. The results of metabolome analysis showed that PSA can upregulate ergosterol peroxide and gallic acid and downregulate the harmful metabolite N-acetylputrescine. SA can upregulate 4-pyridoxic acid and lipoic acid. PSA and SA affect gut microbiota and metabolites in different ways and have positive effects on human health. These results will provide reference for the further development of PSA- and SA-related functional foods and health products.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

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.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

This research explores the depolymerization of waste polymethyl methacrylate (PMMAW) from dental material in fixed-bed semi-batch reactors, focusing on three production scales: laboratory, technical, and pilot. The study investigates the thermal degradation mechanism and kinetics of PMMAW through thermogravimetric (TG) and differential scanning calorimetry (DSC) analyses, revealing a two-step degradation process. The heat flow during PMMAW decomposition is measured by DSC, providing essential parameters for designing pyrolysis processes. The results demonstrate the potential of DSC for energetic analysis and process design, with attention to standardization challenges. Material balance analysis across the production scales reveals a temperature gradient across the fixed bed negatively impacting liquid yield and methyl methacrylate (MMA) concentration. Reactor load and power load variables are introduced, demonstrating decreased temperature with increased process scale. The study identifies the influence of temperature on MMA concentration in the liquid fraction, emphasizing the importance of controlling temperature for efficient depolymerization. Furthermore, the research highlights the formation of aromatic hydrocarbons from the remaining char, indicating a shift in liquid composition during the depolymerization process. The study concludes that lower temperatures below 450 °C favor liquid fractions rich in MMA, suggesting the benefits of lower temperatures and slower heating rates in semi-batch depolymerization. The findings contribute to a novel approach in analyzing pyrolysis processes, emphasizing reactor design and economic considerations for recycling viability. Future research aims to refine and standardize the analysis and design protocols for pyrolysis and similar processes.

Evolutionary algorithms find applicability in reinforcement learning of neural networks due to their independence from gradient-based methods. To achieve successful training of neural networks using evolutionary algorithms, careful considerations must be made to select appropriate algorithms due to the availability of various algorithmic variations. In Part1 and Part2, the author previously reported experimental evaluations on Genetic Algorithm and Evolution Strategy for reinforcement learning of neural networks, utilizing the Acrobot control task. This article constitutes Part3 of the series of comparative research. In this study, Differential Evolution is adopted as the third instance of major evolutionary algorithms. The experimental results show a statistically significant superiority of DE over both GA and ES (p < .01). In addition, DE exhibits its robustness to variations in hyperparameter configurations (the number of offsprings and generations). In the previous experiments, both ES and GA showed significant performance differences depending on the configurations, whereas in the experiment reported in this article, such differences are not detected for DE.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

The pollution caused by nitrogen dioxide is a major environmental problem in China. This study introduces a new type of atmospheric trace gas remote-sensing instrument, an airborne fiber imaging spectrometer. This spectrometer has a spectral range of 300–410 nm and works in push-broom mode with a 30° field of view on a flight path. Flight experiments were conducted on December 30, 2022 and January 5, 2023, covering heavily polluted areas of east of Beijing and Tangshan. This equipment obtained the density distribution of NO2 over the flight area. The results showed that pollution was mainly concentrated in the Caofeidian area and at the power station in the north, and the main source of pollution was anthropogenic. Satellite and airborne data near the pollution points were compared, and the two datasets showed a positive correlation with a correlation coefficient of 0.78 and 0.7, on the two days, respectively. This study demonstrates the capability of an airborne fiber imaging spectrometer for NO2 regional emission remote sensing and identifying the pollution points.

In a previous paper, we solved the partial differential equation of Mullins problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed 〖y'〗^2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

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.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

N-maleimide-derivatized phospholipids are often used to facilitate protein anchoring to membranes. In autophagy studies, this is applied to the covalent binding of Atg8, an autophagy protein, to a phosphatidylethanolamine (PE) in the nascent autophagosome. However, the question remains on how closely the N-maleimide PE derivative (PE-mal) mimicks the native PE in the bilayer. In the present paper, spectroscopic and calorimetric techniques have been applied to vesicles containing either PE or PE-mal (together with other phospholipids) to compare the properties of the native and derivatized forms of PE. According to differential scanning calorimetry, and to infrared spectroscopy, the presence of PE-mal did not perturb the fatty acyl chains in the bilayer. Fluorescence spectroscopy and microscopy showed that PE-mal did not alter bilayer permeability either. However, fluorescence emission polarization of Laurdan and DPH probes indicated an increased order, or decreased fluidity, in the bilayers containing PE-mal. In addition, infrared spectral data from the phospholipid phosphate region revealed a PE-mal-induced conformational change of the polar heads, accompanied by an increased hydration. Globally considered, the results suggest that PE-mal would be a reasonable substitute for PE in model membranes containing reconstituted proteins.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

Ditching-rotary tiller was widely used in tillage and ditching furrow during rapeseed sowing. As its ditching furrow system (consist of four identical ditching plows) would bear great drag resistance from the soil during operation, the ditching plow was optimized based on differential geometry analysis and EDEM simulation. Resistance-velocity simulation indicated the plow with parabolic type guide curve had better reduce-drag characteristics. Differential geometry analysis indicated decay rate of E and growth rate of G could represent the variable regularity of drag resistance with the increase of velocity. The L value could represent the magnitude of drag resistance. The smaller L value, decay rate of E and growth rate of G, the better drag-reduce characteristics. Quadratic rotation orthogonal combination design shown the optimal structural parameter values were: Δθ=15°, θmin=45°, h=250mm, l=100mm. The minimum average drag resistance was 230.1N. The differential geometry analysis of optimal ditching plow shown |dE/dκ| and |dG/dκ| could obtain minimum value, indicating growth rate of drag resistance for optimal plow was the lowest within the experimental level. Field experiment indicated the operation effect of optimized ditching furrow system could met the requirements of rapeseed sowing. The research provided in-depth theoretical guidance for Drag-reduce design of plow.

1,3,5-Tris-(α-naphthyl)benzene is an organic non-electrolyte with notable stability of an amorphous phase. Its glassy and supercooled liquid states were previously studied by spectroscopic and calorimetric methods. However, the thermodynamic parameters of phase transitions available from the literature are inconsistent. In this work, the heat capacities of crystalline and liquid phases, the temperature dependence of the saturated vapor pressures, fusion and vaporization enthalpies were determined using differential and fast scanning calorimetry and verified using the estimates based on solution calorimetry. The structural features of 1,3,5-tris-(α-naphthyl)benzene are discussed based on the computations performed and the data on the molecular refractivity. The consistency between the values obtained by independent techniques was demonstrated. The deviations in the previously published data were attributed to possible polymorphism.

The work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

The paper examines rational Darboux-Crum transforms (RDCTs) of the Jacobi-reference (JRef) potential on the line, with an emphasis on the transformations using only normalizable seed solutions. The Cooper-Ginocchio-Khare (CGK) potential constitutes the simplest example of this rich family of exactly solvable one-dimensional (1D) potentials. It was explicitly confirmed that that an arbitrary Darboux-Crum transformation (DCT) of the given Sturm-Liouville equation (SLE) can be represented as a chain of sequential Darboux deformations of the associated Liouville potentials. If the rational SLE (RSLE) under consideration is exactly solvable and the transformation function (TF) used at each step is nodeless then each RSLE constructed in such a way was proven being exactly solvable itself. The exact solvability of RDCTs of the JRef canonical SLE (CSLE) was also confirmed for the DCTs using pairs of juxtaposed eigenfunctions (an extension of the renowned Adler theorem to the RCSLEs of our interest). By re-expressing the reference polynomial fraction (RefPF) of the transformed CSLE in terms of the Krein determinant (KD), instead of Crum Wronskian (CW), it was shown that the eigenfunctions under consideration are expressible in terms of polynomial solutions of a generalized Heun equation with positions of the most poles dependent on the exponent parameters. The outlined technique was extended to two isospectral SUSY partners of the JRef potential (as well as to its third sibling with the inserted new lowest-energy level) which, by analogy with the CGK potential, are quantized by polynomial solutions of the 2-Heun equation with all four poles at some fixed positions on the real axis.

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.

This study proposes a methodology for identifying time intervals in which time-of-use (ToU) energy tariffs can be set. This is achieved by analyzing the variability in electric power demand and esti-mating the potential for demand flexibility. The proposed methodology is as follows: first, data preprocessing is performed, focusing on the organization and cleaning of individual consumption records. Subsequently, the data are processed and classified by using consumption variability analysis and clustering techniques. Then, representative clusters are selected and time intervals are analyzed to identify periods of high electric power consumption variability. This methodology was tested with real data from smart meters in the Colombian electrical system, in which time intervals with potential for settinh ToU tariffs were ultimately identified. This work promotes the implementation of demand response strategies that enhance sustainability and facilitate the transition to a more resilient energy landscape both nationally and internationally. The findings are expected to contribute to the formulation of tariff schemes that encourage con-scious changes in electric energy consumption patterns.

This experimental research presents an easier model for fitting experimental results that can be simulate the dynamical behaviour of a single degree freedom system, SDFS, subjected in a forced vibration in a shaking table. The fractional damping using a Kelvin-Voigt fractional derivative rheological model, KVFRdm, to represent a fractional oscillator and compare with the experimental model.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

Trichothecene mycotoxin T-2 toxin is an important environmental pollutant and poses a global threat to human and animal health. T-2 toxin could induce nephrotoxicity, however, the precise molecular mechanism remains unclear. In this study, the mice were intraperitoneally administrated with a single dose of 2 mg/kg T-2 toxin. The kidney function and ultrastructural observation were also assessed and found T-2 toxin exposure could cause kidney damage. Transmission electron microscopy showed a significant swelling and vacuolization of the mitochondria of renal cell. A total of 1122, 58, and 391 differential expression genes (DEGs) that were predominantly expressed in kidney tissues at 1 d, 3 d, and 7 d after T-2 toxin exposure, respectively. Early transcriptomic changes at 1 d after exposure were down-regulation of DEGs involved in the cell cycle, p53 signaling pathway, and cellular senescence, while up-regulation of DEGs referred to the ribosome pathway. The temporal variations in gene expression pattern in T-2 toxin exposure in mice kidney were presented and cellular metabolism was disturbed at the exposure recovery period with 7 d. In conclusion, this study, for the first time, provided a comprehensive comparative transcriptomic analysis of gene regulation in T-2 toxin exposure-induced nephrotoxicity at different temporal periods and explored the nephrotoxicity mechanism of T-2 toxin at the mRNA level.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.

A scientific investigation into visual preferences of rural recreation path landscapes is crucial for enhancing visual qualities and visitors' experience. Taking Baofeng, a representative traditional village in Yunlong, as an example, this study analyzed the visual preference of three typical linear recreational paths with different landscape attributes. We used eye-tracking technology to collect eye movement data and conducted a subjective semantic differential evaluation. Our findings manifest a general inclination amongst individuals to favor closer views and paths with clear trajectories and rich elevation changes while walking, despite preference differences on different types of paths. Regarding group diversity, more inclusive design should be made to meet the sensory needs of different groups. Moreover, despite the limited level of correlation between subjective and objective evaluation methods, combining these two approaches remains indispensable. This synthesis advances prior quantitative landscape evaluation with a specific focus on rural path landscapes and upholds the integrity of results by combining objectivity with subjectivity. It also provides relevant design suggestions for further rural renewal and path planning of Baofeng village.

Use of MS Excel as a platform for teaching simple iterative solution of partial differential equations runs into issues of reliability of the computation because of the large number of calculations required. This article documents the problem and an empirical solution. The cause of this unreliability was found by detailed examination of the numerical results from three simultaneous iterations. Computers of several types from different manufacturers were found to fail occasionally in updating variables in the numerical iteration. A simple work-around is suggested and was tested on several platforms.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

Partial Differential Equations (PDEs) constitute a fundamental framework for modeling various physical phenomena across diverse fields such as physics, engineering, and finance. Solving PDEs accurately and efficiently remains a significant challenge, particularly when dealing with complex systems or high-dimensional data. In this paper, we present a novel approach based on deep learning techniques to investigate the effective factors in solving PDEs. Our methodology leverages the expressive power of deep neural networks to learn and represent the underlying relationships between input parameters and the solutions of PDEs. By incorporating domain knowledge into the network architecture and training process, our approach aims to provide insights into the key factors influencing the solution of PDEs. We demonstrate the effectiveness of our method through numerical experiments on various PDEs, showcasing its capability to identify important features and improve predictive accuracy. Our findings suggest that deep learning techniques offer a promising avenue for understanding and analyzing the complex dynamics inherent in PDEs, paving the way for enhanced computational methods in scientific and engineering applications.

Background. Escherichia coli commonly causes catheter-related bloodstream infection (C-RBSI) in specific populations. The differential time to positivity (DTTP) technique is the recommended conservative procedure for diagnosing C-RBSIs. Methods. We conducted a retrospective study of episodes in which E. coli was isolated from catheter lumens obtained using the DTTP technique. We analysed microbiological and clinical data based on the DTTP technique as either catheter colonization, C-RBSI, or non-C-RBSI. Results. We included 89 catheter blood cultures classified as follows: catheter colonization, 33.7%; C-RSBI, 9.0%; and non-C-RBSI, 57,3%. Catheter withdrawal was 15.7% without positive catheter-tip cultures. We found no statistically significant differences in catheter type, antibiotic treatment, or clinical outcome among groups, except for the frequency of catheter lock therapy or in the frequency of successful treatment. Mortality was associated with C-RBSI in only 1 patient. Conclusion. E. coli bacteremia diagnosed by the DTTP technique was non-catheter related in most patients. As the majority of the catheters were retained, E. coli bacteremia could not be microbiologically confirmed or ruled out as catheter related by catheter-tip culture. Future studies are needed to assess the profitability of the DTTP technique for diagnosing E. coli C-RBSIs..

Addressing the issue of low bonding strength in Ti/Mg laminated composites due to interfacial oxidation, this study employs a differential temperature rolling method using longitudinal induction heating to fabricate Ti/Mg composite plates. The entire process is conducted under an argon gas protective atmosphere, which prevents interfacial oxidation while achieving uniform deformation. The effects of reduction on the mechanical properties and microstructure of the composite plates are thoroughly investigated. Results indicate that as the reduction increases, the bonding strength gradually increases, mainly attributed to the increased mechanical interlocking area and a broader element diffusion layer. This corresponds to a transition from brittle to ductile fracture at the microscopic tensile-shear fracture surface. When the reduction reaches 47.5%, the Ti/Mg interfacial strength reaches 63 MPa, which is approximately a 20% improvement compared to the bonded strength with previous oxidation at the interface. Notably, at a low reduction of 17.5%, the bonding strength is significantly enhanced by about 1 time. Additionally, it is found that a strong bonded interface at high reduction is beneficial in hindering the propagation of interfacial cracks during tensile testing, enhancing the ability of the Ti/Mg composite plates to resist interfacial delamination.

Sensory descriptive analysis was used to evaluate the aged Feng-flavored baijiu. The results indicated that there are notable differences in the samples of different ages. The samples with shorter storage times and fresh distilled Baijiu present bran flavor, and fresh green flavor. with the increase of storage time, the fragrance of honey, sweetness, flowers, and aging gradually increases. The samples of Feng-flavored baijiu were dected by Headspace solid-phase microextraction (HS-SPME) combined with comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC–TOFMS) , in total, 496 sustances were identified in all samples, mainly containing 14 types of substances, such as esters, aldehydes etc., of which 42 substances were found in Feng-flavored baijiu for the first time. Chemometrics was used to analyze the key differential compounds. 143 differential compounds closely related to aging were preliminarily screened, and principal component analysis revealed that these samples were separated by year. 65 differential compounds were selected out by partial least squares discriminant analysis(PLS-DA). Furthermore, 43 key differential compounds were selected from the aged Feng-flavored baijiu combined with variable importance in projection and Pearson correlation coefficients. Partial least squares regression (PLSR) was used to research the correlation of sensory properties and key differential compounds, and the results indicated that most compounds were closely related to the aged Baijiu . This study afford theoretical basis and reference for flavor research of Feng-flavored baijiu.

The paper describes the new method for image compression based on coordinated group signal transformation. The algorithm is a type of difference coding. Coordinated processing significantly simplifies the difference signal conversion scheme using a single group codec for all signals. The described method considers color channels as correlated signals of a multi-channel communication system. The specifics of the processed data required modification of the coordinated group processing algorithm. First, we changed how to calculate the difference signals to prevent data loss. Secondly, the group codec was supplemented with a neural network to improve the quality of reconstructed images. We considered the following types of neural networks: fully connected, recurrent, convolution, and convolution in the Fourier space. Based on the simulation results, it is best to use fully connected neural networks if the goal is to minimize processing delay time. These networks have a response time of 13 ms. On the other hand, if the priority is to improve quality in cases where delays are not critical, then convolution neural networks in the Fourier space should be used. These networks have a response time of 140 ms and are of significant interest.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.