Spatial and temporal variation of the free electron concentration in the ionosphere affects SAR interferograms, in particular at low radar frequencies. In this work the identification, estimation and compensation of ionospheric path delay phases in PALSAR-3 and NISAR-L interferograms is discussed. Both these L-band sensors acquire simultaneously SAR data in a main spectral band and in an additional, spectrally separated, narrower second band to support the mitigation of ionospheric path delays. The methods presented permit separating the dispersive and the non-dispersive phase terms based on the double-difference interferogram between the two available spectral bands and the differential interferogram of the main band. The applicability of the proposed methods is demonstrated using PALSAR-3-like data that was simulated based on PALSAR-2 SM1 mode data.

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.

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.

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.

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.

The coseismic surface three-dimensional deformation fields were significant for quantified the geometric and kinematic characteristics of earthquake rupture faults. Traditional geodetic techniques were constrained by their intrinsic limitations, such as InSAR, which could only extract far-field deformation fields due to its incoherence, and GNSS, which could only acquire deformations at discrete points. The recently developing optical pixel correlation technique based on high resolution remote sensing images could acquire the near-field coseismic horizontal deformation. In this study, the vertical displacement field of the 2022 Mw 6.6 Menyuan earthquake was obtained by differencing the pre- and post-earthquake DEMs from GaoFen-7 stereo satellite images. Further, the line-of-sight (LOS) and azimuthal (AZI) directions far-field deformations by InSAR, the horizontal near-field deformation by optical pixel correlation based on pre- and post-earthquake GF-2/7 images, and the vertical deformation by differencing the pre- and post-earthquake DEMs, were incorporated to comprehensively solve the complete three-dimensional deformation fields of the 2022 Mw 6.6 Menyuan earthquake. Firstly, the vertical displacement field by differencing DEMs indicated there were significant vertical displacements about 1 m at the bend region, which was induced by the local compressive stress. In addition, at the epicenter on the middle segment of ruptured Lenglongling fault (LLLF), the maximum lifting occurred on the southern sides of the main and secondary faults exceeded 2 m. Secondly, the three-dimensional deformation fields solved by multiple deformation data demonstrated that the near-field deformation field calculated by optical pixel correlation method could quantify the displacements distributed over the rupture fault zone, which were not available on the InSAR deformation maps. Finally, the surface 2D strain derived from the displacement maps calculated by optical pixel correlation revealed high strain concentration on the rupture fault zone. Our study focused on the complete surface three-dimensional deformation estimation from multiple far- and near-field deformation data, and provided a new perspective for a deeper understanding of the characteristics of coseismic surface deformation and the rupture pattern of the fault.

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.

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..

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.

This study examines the optimization of ground source heat pump (GSHP) systems and energy piles for sustainable urban development, with a focus on Southeast Asia. GSHPs, which utilize geothermal energy for indoor HVAC needs, offer a sustainable alternative to traditional systems by utilizing consistent subsurface temperatures for heating and cooling. The study highlights the importance of understanding thermal movement within the soil, especially in soft marine clays prevalent in Southeast Asia, to improve GSHP system efficiency. Using a one-dimensional finite-difference model, the study examines the effects of soil thermal conductivity and density on system performance. The results show that GSHP systems, especially when integrated with energy piles, significantly reduce electricity consumption and greenhouse gas emissions, underscoring their potential to mitigate the urban heat island effect in densely populated areas. Despite challenges posed by the region's hot and humid climate, which could affect long-term effectiveness, the study highlights the need for further study, including field experiments and advanced modeling techniques, to optimize GSHP configurations and fully exploit geothermal energy in urban environments. The study's insights into soil thermal dynamics and system design optimization contribute to the advancement of sustainable urban infrastructure development.

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.

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.

This paper presents a compartmental model aimed at investigating the pharmacokinetics of medical THC after oral administration. The model was developed to be multi-compartmental, describing the kinetics of THC and its metabolites in bodily tissues. Utilizing the law of mass action, the model was converted into ordinary differential equations (ODEs), illustrating the rate of concentration changes of THC and its metabolites in each compartment. Subsequently, we applied the nonstandard finite difference (NSFD) method to construct numerical solution schemes. These schemes were implemented in the MATLAB program, along with estimated pharmacokinetic rate constants. The results of the investigation demonstrate that the simulation curves depicting the plasma concentration-time profiles of THC and THC-OH closely resemble the actual data samples, indicating that this model accurately describes the pharmacokinetics of medical THC and its metabolites. Moreover, the model exhibits predictive capabilities regarding the pharmacokinetics of THC and its metabolites in various tissues. Consequently, the model serves as a valuable tool for enhancing our understanding of the pharmacokinetics of THC and its metabolites and for guiding adjustments to dosage and administration durations for oral medical THC products.

The penetrability and directivity of ultrasound in different media is of interest in engineering and medical applications (imaging, nondestructive testing, sonochemistry, among others). The nonlinearity of a liquid can be used in the parametric antenna framework to generate low-frequency components with particular features from several ultrasonic signals at the source. Bubbly liquids are dispersive liquids in which a small amount of tiny gas bubbles leads to the increase of the nonlinear parameter of the media over certain frequency ranges. Parametric antenna applied to this huge nonlinear media gives rise to low-frequency components with relatively small intensity at the source. The evolution of a low-frequency component (difference-frequency component obtained from two primary signals) during its propagation in a bubbly liquid is somehow unknown. It is thus interesting to analyse its characteristics to establish whether this component can benefit from the quality of its own frequency and from the primary frequencies in terms of directivity and penetrability into the medium. It must be noted that no such study in bubbly liquids exists in the litterature, but only for homogeneous media. To this end, several numerical models developed previously are used here to analyse the difference-frequency component obtained from a parametric antenna emitting from two ultrasonic signals at the source in one and two-dimensional domains. These models allow us to observe the behavior of this frequency component. An angle that measures the directivity of a beam is also defined. Our results show a point hardly found in the literature: the high directivity and the huge penetrability of the secondary beam associated to the difference-frequency component into the bubbly liquid, compared to the same frequency signal excited directly from the source in the bubbly liquid and to the parametric acoustic array in homogeneous fluids.

To get more data concerning the influence of fertilizers (organic and mineral) on different forage plants existing in North-eastern Romanian grassland, the mass fractions of 14 essential, enzymatic, or considerd toxic elements was determined by Instrumental Neutron Activation Analysis together with the amount of crude proteins, ash, fibres as well as ether fact extract. Final results showed a significant variance of the content of analysed elements on organic as well as on mineral fertilized experimental plots, i.e. the content increased in 24% of plots, decreased in 23%, and remained unchanged in 45% while in 8% of plots their content was below the detection limits, as the case of Se. At the same time, an increase content of crude protein and ether extract was evidenced in fertilized grasses for all applied fertilizers while other global indicators such as neutral and acid fibre of sufuric lignin content decreased, suggesting significant higher nutritional values of fertilized forage plant.

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.

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.

Due to the significant price difference, expensive oils like olive oil are often blended with cheaper edible oils. This practice of adulteration in edible oils, aimed at increasing profits for producers, poses a major concern for consumers. Furthermore, adulteration in edible oils can lead to various health issues impacting consumer well-being. In order to meet the requirements of fast, non-destructive, universal, accurate and reliable quality testing for edible oil, the oblique-incidence reflectivity difference (OIRD) method combined with machine learning algorithms was introduced to detect a variety of edible oils. The prediction accuracy of Gradient Boosting, K-Nearest Neighbor, and Random Forest models exceeded 95%. Experimental results indicate that the OIRD method can serve as a powerful tool for detecting edible oils.

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.

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.

Agricultural activities are the second largest source of greenhouse gas emissions, and carbon emissions from agricultural land use (CEALU) have become a hot issue across the world. However, few scholars explored the impact of agricultural land policies on carbon emissions, such as the High-standard farmland construction(HSFC) in China.Thus，by relying on provincial panel data for China for the period 2005-2017, the effect of the high-standard basic farmland construction policy on carbon emissions from agricultural land use per unit area and its regional differences were quantitatively analyzed using the difference-in-difference (DID) model. The results showed that: 1) China's CEALU per unit area presented a fluctuating upward trend during the period 2005-2017, from 392.58 kg/ha to 457.72 kg/ha, with an average annual growth rate of 1.31%. 2) The high-standard farmland construction(HSFC) policy produced a significant carbon emission reduction effect in agricultural land use, and reduced the CEALU per unit area by 10.80% on average. With the promotion of this policy, its carbon emission reduction effect in agricultural land use presented an overall increasing trend. 3) The carbon emission reduction effect of the high-standard farmland construction policy in agricultural land use was significant in central China, but non-significant in eastern China and western China.

Balsam fir trees are a specialty agricultural species that are largely used as Christmas trees. Soil or tissue sampling is seldom performed to assess balsam fir nutrition needs, which can contribute to over or under fertilization and subsequent environmental challenges. Remote sensing to determine the normalized difference vegetation index (NDVI) has had strong relationships with nutrition in other plants. This research aimed to determine whether there is a relationship between NDVI and nutrition in balsam fir. A random sample of 45 trees was selected in autumn of 2021 and then another 70 trees selected in spring of 2022. Soil and needle tissue samples were analyzed for N, P, K, Ca, Mg, S, Fe, Zn, Mn, B, and Cu. An uncrewed aerial vehicle equipped with a multispectral camera was flown over the orchard to determine the NDVI for each tree. Nutrition and NDVI were analyzed for correlations through all sampled trees. Separate correlation analyses were repeated for mature trees (greater than 5 years old) and young trees (less than 5 years old). Soil nutrients N, P, K had a significant relationship with NDVI in autumn sampling. Only N was correlated consistently in both autumn and spring, with R2 of 37% and 33% respectively. Relationships were much stronger when only mature trees were considered, increasing to 60% and 51% respectively. NDVI was found to offer predictive power for tissue N that can be useful to producers to help optimize fertilizer input. However, further work is needed to refine these relationships.

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.

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 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.

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.

In our study we investigated the accelerated aging process of PLA under 253.7 nm UV-C irradiation with the use of GPC, NMR, FTIR, DSC methods and formal kinetic analysis. The results of GPC and DSC indicated a significant degree of destructive changes in PLA macromol-ecules, while spectroscopic methods NMR and FTIR showed maintenance of PLA main structural elements even after a long time of UV exposure. In addition to that, the GPC method displayed the formation of a high-molecular fraction starting from 24 hours of irradiation, and an increase in its content after 144 hours of experiment. It has been showed for the first time that a distinctive feature of prolonged UV exposure is the occurrence of intra- and intermolecular radical recom-bination reactions, leading to the formation of a high-molecular fraction of PLA decomposition products. This causes the observed slowdown of the photolysis process. It was concluded that photolysis of PLA is a complex of physicochemical processes, the mechanism of which depends on morphological changes in a solid phase of the polymer under UV radiation.

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.

This study investigates the long-term stability of the Suomi National Polar-orbiting Partnership (S-NPP) Visible Infrared Imaging Radiometer Suite (VIIRS) moderate-resolution Thermal Emissive Bands (M TEBs; M12 – M16) covering a period from February 2012 to August 2020. It also assesses inter-sensor consistency of the VIIRS M TEBs among three satellites-S-NPP, NOAA-20, and NOAA-21 over eight months spanning from March 18 to November 30, 2023. The field of interesting is limited to the ocean surface between 60°S and 60°N, specifically under clear-sky conditions. Taking radiative transfer modeling (RTM) as the transfer reference, we employed the Community Radiative Transfer Model (CRTM) to simulate VIIRS TEB brightness temperature (BTs), incorporating European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis data as inputs. Our results reveal two key findings. Firstly, the reprocessed S-NPP VIIRS TEBs exhibit a robust long-term stability, as demonstrated through analyses of the observation minus background BT differences (O-B ∆BTs) between VIIRS measurements (O) and CRTM simulations (B). The drifts of the O-B BT differences are consistently less than 0.105 K/Decade across all S-NPP VIIRS M TEB bands. Notably, observations from VIIRS M14 and M16 stand out with drifts well within 0.04 K/Decade, reinforcing their exceptional reliability for climate change studies. Secondly, excellent inter-sensor consistency among these three VIIRS instruments is confirmed through the double-difference analysis method (O-O). This method relies on the O-B BT differences obtained from daily data. The mean inter-VIIRS O-O BT differences remain within 0.08 K for all M TEBs, except for M13. Even in the case of M13, the O-O BT differences between NOAA-21 and NOAA-20/S-NPP have values of 0.312 K and 0.234 K, respectively, which are comparable to the 0.2 K difference between some TEBs among VIIRS and MODIS. These disparities are primarily attributed to the significant differences in the Spectral Response Function (SRF) of NOAA-21 compared to NOAA-20 and S-NPP. Our study confirms the RTM-based TEB quality evaluation method’s versatility and effectiveness in assessing long-term sensor stability and inter-sensor consistency. The double-difference approach effectively mitigates uncertainties and biases inherent to CRTM simulations, establishing itself a robust mechanism for assessing inter-sensor consistency. In addition, we’ve observed that, except for M13, M12 always exhibits larger spatial variations of O-O BT differences with greater uncertainties compared to the other M TEBs. The influence of solar contribution through sea surface reflection on the Top of Atmosphere (TOA) radiance measurements during daytime in M12 should not be underestimated.

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.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

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.

The Black population, often treated as ethnically homogenous, faces a constant challenge in accessing and utilizing healthcare services. This study examines the intragroup differences in health-seeking behavior among the multiple ethnic subgroups that comprise the Black community. A cross-sectional study was conducted among 239 adults ≥18 years who self-identified as Black in the United States and Canada. A multiple logistic regression model was fitted to evaluate the relationship between health-seeking behaviors and ethnic origin controlling for selected social and health related factors. The mean age of participants was 38.6 years, 31% were male, and 20% were unemployed. Sixty-one percent reported very good or excellent health status, and 59.7% reported not being treated for chronic disease at the time of the survey. Aging (OR=1.05, CI:1.01–1.09) and being female (OR= 0.30, CI: 0.14–0.65) were associated with favorable health-seeking behaviors. Compared with participants who had earned high school diplomas only, those who reported having earned graduate degrees were 75% less likely to have engaged in favorable health-seeking behavior (OR=0.25, 95% CI: 0.07–0.86). In the Black community of our sample, regardless of ethnic origins or country of birth, the factors associated with health-seeking behavior were age, gender, and educational attainment. Keywords: African American; African; Caribbean; Healthcare Utilization; Ethnic Disparities; Health-seeking behavior; intragroup difference, black populations, ethnic subgroups

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.

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.

This research delves into the intricate challenges confronting the agricultural sector, with a specialized focus on mitigating infections in tomato crops, particularly powdery mildew induced by the Leveillula Taurica pathogen. Tomatoes, renowned for their nutritional richness, are vital to global food security. However, conventional methodologies for disease detection exhibit both laborious processes and limited accuracy. In response to these challenges, this study advocates for an innovative fusion of hyperspectral imaging and deep learning methodologies to detect crop disease and its severity. The systematic workflow commenced with the curation of a dataset, involving the acquisition of live images through OpenCV, followed by conversion to RGB format and subsequent feature extraction utilizing a pre-trained visual geometry group (VGG-16) model for enhanced analysis. Sequentially, RGB images were transformed into simulated hyperspectral images (SHSI) leveraging a Neural Network generator model, offering a distinctive viewpoint on spectral information. This novel approach transcends conventional constraints by delivering a three-dimensional perspective, seamlessly integrating spatial and spectral dimensions for holistic data acquisition. The SHSI is further transmuted into a 3D visualization cube comprehensive grasp of spatial and spectral aspects encompassing spectral, spatial, and Haralick features. The research concludes with severity detection, categorized as low, moderate, or high, employing a Gaussian Mixture Model (GMM) and K-means for visualization.

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.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Carbon fiber reinforced polymer (CFRP) bending structure is widely used in the aviation field. The occurrence and propagation of delamination damage will reduce the safety of in-service bending structures. As a detection tool with high damage sensitivity, Lamb wave can effectively identify delamination damage. In this study, the signal difference coefficient (SDC) was introduced to quantify delamination damage and evaluate the sensitivity of A0 and S0 mode lamb waves to delamination damage. The simulation results show that compared with the S0 mode Lamb wave, the A0 mode Lamb wave exhibits higher delamination damage sensitivity. The delamination damage can be quantified based on the strong correlation between the SDC and the delamination damage size. The control effect of the linear array PZT phase time-delay method on Lamb wave mode was investigated by simulation. The phase time-delay method realizes the generation of a single-mode Lamb wave, which can separately excite the A0 mode and S0 mode Lamb wave to identify delamination damage of different sizes. The A0 mode Lamb wave was excited by the developed one-dimensional linear comb transducer (LCT), which was used to conduct the detection experiment on the CFRP bending plate with delamination damage sizes of Φ6.0 mm, Φ10.0 mm, and Φ15.0 mm. The experimental results verify the correctness of the simulation. According to the Hermite interpolation results of the finite-element simulation data, the relationship between the delamination damage size and the SDC was fitted by the Gaussian function, which can accurately quantify the delamination damage. The absolute error of the delamination damage quantification with fitting expression is not larger than 0.8 mm, and the percentage error is not more than 8%.

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.

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.

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.

The paper focuses on the different dynamical systems for the prey-predator model for different cases which includes greater depth of the food chain and varying number of preys and predators. We simulate the different postulated models and provide a comparative study for the same.

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.

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

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.

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.

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.

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.

The object of study is a transversely bent triangular plate made of orthotropic material fixed along the edges of the plate under the action of a uniformly distributed load. Fourth-order differential equilibrium equations with variable orthotropy parameters were used. The equations were approximated by finite differences for a grid of scalene triangles. This type of mesh accurately describes the boundary contour of the triangular-shaped plates. The boundary conditions for the mesh consider the orthotropy of the plate material. Seven standard finite-difference equations have been developed considering the boundary conditions along the three edges of the plate and the presence of three angles of an irregularly shaped triangle. A finite difference matrix is obtained. The matrix structure makes calculating a triangular plate at different base angles possible. The boundary conditions were varied in the form of rigid or hinged support of triangular plates. The calculation method considers the orthotropic parameters of the material in two mutually perpendicular planes. The adaptation of the numerical method to the calculation of orthotropic plates of arbitrary shape is described. Relationships are given for determining the rigidity characteristics of orthotropic materials. An algorithm for simple engineering calculation of triangular orthotropic plates is proposed, which makes it possible to perform accurate calculations in variant design.

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,

Digital infrastructure is the basic guarantee for digital transformation, it is of practical significance to discuss how to effectively use digital infrastructure construction to promote the digital transformation of tourism enterprises. This paper examines the impact of digital infrastructure construction on tourism enterprises based on the "Broadband China" policy as a quasi-natural experiment. A-share tourism listed enterprises from 2010 to 2021 are studied using the double difference method. Findings indicate that digital infrastructure construction positively and significantly influences the digital transformation of tourism enterprises, driven by digital leadership and innovation capabilities. State-owned, small-scale, and high-growth tourism enterprises benefit more from this transformation. The results suggested that the state should develop differentiated digital infrastructure plans based on the specific conditions of different tourism enterprises. Additionally, tourism enterprises should enhance digital leadership and innovation capabilities through strategic changes and digital applications to amplify the impact of digital infrastructure on their transformation.

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 $J(t)\le \jinf \ll 1$.

The energy-intensive sector of the cement industry needs to find technologically advanced methods to produce cement with as little energy as possible, without polluting the environment and without sacrificing the quality (fineness) of the cement. In addition, the stress on the machines changes the behavior of the data. By combining the k-means method, two (2) feature selection methods, nine (9) machine learning methods, and the differential evolution (DE) method, a dynamic system is created where the user determines the key performance indicators (KPIs) each time. The user has the potential to control the distribution of the data, the input of machine learning models, and the ability to switch the system to the suggested values without damage. The selection of the best-performing models is based on the normalized root mean squared error (NRMSE). The DE method optimizes the dynamic objective function. The optimal values of the manipulated variables are evaluated compared to the value of the objective function from the actual values of the variables. In all experiments, the recommendations are acceptable. The final results show an improvement in the operation of both the cement mill and kiln compared to the current operating condition.

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.

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 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 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.

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.

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.

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.

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 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.

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.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

This article describes the choice of an optimization algorithm for solving problems and the optimal design of an unmanned aerial vehicle propeller. To solve the problem using evolutionary algorithms, it was transformed into an unconstrained optimization problem using a penalty function. The airfoil contours were constructed using a Bezier curve. Design variables were divided into two types: those that describe in general terms the propeller geometry or operation, such as propeller diameter, number of blades, and rev/min; and those that vary with propeller radius, such as chord length, effective airfoil angle, and airfoil geometry. The objective function is the calculation of the propeller power required to achieve a given thrust. The differential evolution algorithm was used to solve this problem.

India ranks among the top ten nations in the world for grape production. Fungal pathogens inflict damage to crop plants in turn making cultivators bear huge economical losses. With an output of 1.21 million tons (about 2% of 57.40 million tons produced globally). 1.2% of the nation’s total fruit cropland is covered by grapes. But due to fungal diseases the effect of the yield produced ranges from 5-80% depending on the severity of diseases which will affect the yield of grape vineyard. In precision agriculture, new sensing technologies and artificial intelligence could be used to automatically identify grapevine and disease pest symptoms. Traditional manual disease-monitoring methods are inefficient, labor-intensive, and ineffective. Timely effective and precise evaluation of grape diseases is admitted as a critical step in the field management. In this paper, we are explaining about different optical sensing methods applied for RGB, Multispectral and Thermal cameras. Section-wise we will be describing environmental set up for image-aquation, data-preprocessing, different modelling methods, evaluation matrix, result, and reviewer’s comment.

Polyvinyl Alcohol (PVA)/ Graphene Quantum Dots (GQDs) polymer nanocomposite films have been prepared, and the relationship between their structural, thermal and nanoscale morphologi-cal properties, and their photoluminescent response, has been investigated. Although according to X-ray Diffraction (XRD), Fourier-Transform Infrared Spectroscopy (FT-IR) and Differential Thermal Analysis (DTA) the incorporation of GQDs does not significantly affect the percentage crystallinity of the PVA matrix, for a range of added GQD concentrations, Atomic Force Micros-copy (AFM) showed the formation of islands with apparent crystalline morphology on the surface of the PVA/GQD films, with GQD presumably acting as a nucleating agent for island growth. The incorporation of GQD also led to the formation of characteristic surface pores with increased stiffness and frictional contrast, according to Ultrasonic Force Microscopy (UFM) and Frictional Force Microscopy (FFM) data. The photoluminescence (PL) spectra of the films were found to de-pend both on the amount of GQD incorporated and on the film morphology. For GQD loads > 1,2wt%, a GQD-related band was observed at ~ 1650 cm-1 in FT-IR, along with an increase in the PL band at lower energy. For a load of ~2wt% GQD, the surface morphology was characterized by extended cluster aggregates with lower stiffness and friction than the surrounding matrix, and the PL signal decreased.

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

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.

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.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

Effective sports training should be attuned to the athlete's specific conditionings and characteristics. In motor learning research, two often neglected factors that influence this resonance are the learner's athletic background and the structural diversity of exercises (e.g., relative similarity). This study examines the effects of three learning approaches (i.e., contextual interference (CI), differential learning (DL), and free-play control condition (CO)) on the parallel learning of Handball (HB), Volleyball (VB), and Basketball (BB) skills, considering participants' prior sport backgrounds. Forty-five males (15 HB, 15 VB, and 15 BB players) with a mean age of 22±1.4 years and at least 6 years of experience in the mastered discipline voluntarily participated in this study. A pre-post-retention test design including a 6-week-intervention program was employed. In terms of short-term (pre-post) gain, only the DL- group significantly improved their performance in both non-mastered disciplines (p=0.03 for the BB free-throw and p=0.05 for the HB shooting tests), with a trend (ES=0.53) towards an improvement in the performance of the mastered VB underarm-pass skill. In terms of relatively permanent gains, the CI group significantly improved their performances from pre- to retention-test only in the non-mastered BB free-throw skill (p=0.018). In contrast, the DL group significantly improved their performance at retention compared to the pre-test in both non-mastered BB (p=0.004) and HB (p=0.003) skills, with a trend (ES=0.4) towards improvement in the mastered VB test. In both short, and relatively permanent terms, higher composite score gains were observed in DL compared to CI (p=0.001 and 0.002) and CO (p=0.001 and <0.0001). In conclusion, the present findings provide additional support for the potential advantages of the DL model over those of CI. These findings can serve as the basis for tailored training and intervention strategies and provide a new perspective for addressing various issues related to individual and situational learning.

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.

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.

The extent of micro-phase separation in polyurethanes (PUs) depended on the molecular weight, the chemical nature and the structure of the polyol/soft segments. Balanced properties in PUs were obtained by using blends of polyols during synthesis. No previous studies have been devoted to understand the interactions between the soft segments that affect the properties of the PUs. In this study, different blends of two polyols of different nature (polyester – PE - and polycarbonate diol - CD) and similar molecular weight were prepared and their structural, thermal, surface, viscoelastic and self-adhesion properties were assessed. PE showed larger number of structural repeating units and higher number of polar groups than CD, but the carbonate-carbonate interactions in CD were stronger than the ester-ester interactions in PE. The blending of CD and PE imparted synergic structural properties, particularly in the ones containing less than 50 % PE, they were associated to the disrupt of carbonate-carbonate interactions in CD and the formation of new ester-carbonate and hydroxyl-carbonate interactions. Therefore, higher glass transition temperatures, a new diffraction peak at 2θ = 24°, one additional thermal degradation at 426-436 °C, and less steeper decline of the storage moduli to lower temperature were found in CD+PE blends with less than 50 wt.% PE. Furthermore, the different interactions between the polyol chains in the blends were also evidenced on their surface properties, and all CD+PE blends showed self-adhesion property which seemed related to the existence of ester-carbonate and carbonate-carbonate interactions.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

The requirement for developing tools capable of detecting and monitoring heavy metals (HMs) has recently taken on more significance due to worries about their toxic effect on human health and aquatic habitats. In this study, a simple electrochemical sensing carbon paste electrode (CPE) based on composite of Zinc/Iron layered double hydroxide (LDH) and polyaniline (PANI) was developed for the determination of lead ions in aquatic solutions. For this purpose, Zn-Fe LDH/PANI was prepared and characterized by Fourier transform infrared (FTIR), X ray diffraction (XRD), and scanning electron microscopy (SEM). Modified carbon electrode based Zn-Fe LDH/PANI was electrochemically characterized compared with unmodified electrode in FCN as a redox probe using cyclic voltammetry (CV). Thus, Zn-Fe LDH/PANI was utilized as sensing material for the electrochemical determination of lead ions using differential pulse voltammetry (DPV). Zn-Fe LDH/PANI/CPE show limits of detection (LOD) and quantification (LOQ) of 167.8 nM and 559.4 nM, respectively. Zn/Mg/Fe LDH was prepared using co-precipitation method and characterized by XRD, FTIR, SEM and BET, used for removal of Pb+2 ions. Removal process was investigated at different conditions as pH, metal ion concentrations, starting adsorbent dose at first and contact time. Zn/Mg/Fe LDH was evaluated as an effective adsorbent material for lead ions elimination in aquatic solutions, with capacity of adsorption 700 mg/g. The elimination of lead ions on Zn/Mg/Fe LDH fitted the pseudo first-order kinetics model and the isotherm was matched with Langmuir model. Studies revealed that the ideal removal conditions were pH = 5.0, an adsorbent mass of 0.05 g, and 20 ml of 50 ppm metal ion concentration at 60 min. The Zn-Fe LDH/PANI composite also showed potential anti-cancer properties against lung cancer cells (A549) while maintaining safety for normal lung fibroblast cells (WI-38). Collectively, advancements in electrochemical sensors offer promising solutions for lead ion detection, with wide-reaching applications in wastewater treatment and cytotoxicity assessment. These innovations have the potential to enhance environmental monitoring and public health safety.

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.

This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.

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.

β3-Adrenoceptors mediate several functions in rodents that could be beneficial for the treatment of obesity and type 2 diabetes. This includes promotion of insulin release from the pancreas, of cellular glucose uptake, of lipolysis, and of thermogenesis in brown adipose tissue. In combination, they lead to a reduction of body weight in several rodent models including ob/ob mice and Zucker diabetic fatty rats. These findings stimulated drug development programs in various pharmaceutical companies, and at least nine β3-adrenoceptor agonists have been tested in clinical trials. However, all of these projects were discontinued due to lack of clinically relevant changes of body weight. Following a concise historical account of discoveries leading to such drug development programs we discuss species differences that explain why β3-adrenoceptors are not a meaningful drug target for the treatment of obesity and type 2 diabetes in humans.

A systematic and comprehensive review of critical applications of Blockchain Technol-ogy with Differential Privacy integration lies within the privacy and security enhancement. This paper aims to highlight the research issues in the e-health domain (e.g., Electronic Medical Rec-ords) and to review the current research directions in Differential Privacy integration with Blockchain Technology.(1) Background: The current state of the art in the e-health domain is identified as follows: (a) healthcare information poses a high level of security and privacy concerns due to its sensitivity; (b) due to vulnerabilities surrounding the healthcare system, a data breach is common and presents a risk for attacks by an adversary; and (c) the current privacy and security apparatus needs further fortification. (2) Methods: The methodology uses a systematic literature review (SLR) to identify and select relevant research papers and academic journals in DP and BT. (3) Results: The results are categorized into: e-Health Record Privacy, Real-Time Health Data, and Health Survey Data Protection to identify inherent issues with Differential Privacy integra-tion with Blockchain and technical challenges.(4) Conclusion: This review thoroughly surveyed and summarized Differential Privacy mechanisms in EMR privacy, real-time health data, and health survey data protection while highlighting challenges.

The importance of various markers such as sclerostin, Dickkopf-1 (DKK-1), Irisin, receptor activator of NF-kB ligand (RANKL), and Vitamin D have been well studied in bone metabolism. Additionally, inflammatory cytokines such as tumor necrosis factor-alpha (TNF-α) and Interleukine-6 (IL-6) have been identified to hinder muscle protein synthesis, leading to the loss of muscle and strength. However, a research gap exists in the understanding their role in muscle function and physical activity. Therefore, this study aims to explore the serum levels of sclerostin, DKK-1, irisin, IL-6, RANKL, Vitamin D, and TNF-α and assess their relationships with upper and lower body strength in young adults. In this study, 38 college-aged students 18-23 years participated and completed the protocols. The participants’ lower and upper body strength were assessed by the vertical jump test (Just Jump, Probotic, AL) with a Tendo FitroDyne (Tendo Sports Machines, Trencin, Slovak Republic) and handgrip (HG) dynamometry (Takei Scientific Instruments, Yashiroda, Japan), respectively. Fasting morning blood samples were analyzed for serum levels of the biomarkers by ELISA. The results indicate significant sex differences in sclerostin, DKK-1, irisin, and vitamin D levels (p<0.05). Furthermore, a positive association was observed between sclerostin, DKK-1, and vitamin D, with lower body muscle performance variables (p<0.05). Conversely, a significant negative correlation was observed between TNF-α and upper-body muscle performance variables (p<0.05). The results suggest that these markers may have a distinct effect on muscle performance, underscoring the need for further investigation to elucidate the concept of muscle-bone crosstalk.

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.

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.

A complete model was developed to simulate the behavior of a circular clamped axisymmetric fluid-coupled Piezoelectric Micromachined Ultrasonic Transducer (PMUT). Combining Finite Difference and Boundary Element Matrix (FD-BEM), this model is based on the discretization of the partial differential equation used to translate the mechanical behavior of a PMUT. In the model, both the axial and the transverse displacements are preserved in the equation of motion and used to properly define the neutral line position. To introduce fluid coupling, a Green’s function dedicated to axisymmetric circular radiating sources is employed. The resolution of the behavioral equations is used to establish the equivalent electroacoustic circuit of a PMUT that preserves the average particular velocity, the mechanical power, and the acoustic power. Particular consideration is given to verifying the validity of certain assumptions that are usually made across various steps of previously reported analytical models. In this framework, the advantages of the membrane discretization performed in the FD-BEM model are highlighted through accurate simulations of the first vibration mode and especially the cutoff frequency that many other models do not predict. This high cutoff frequency corresponds to cases where the spatial average velocity of the plate is null and is of great importance for PMUT design because it defines the upper limit above which the device is considered to be mechanically blocked. These modeling results are compared with electrical and dynamic membrane displacement measurements of AlN-based PMUTs in air and fluid. This complete PMUT model using the FD-BEM approach is shown to be very efficient in terms of computation time and accuracy.

The investigation on the issue of damage diagnosis based on strain modal parameters is conducted in this paper using simply supported wooden Beams as the study's object. First, ABAQUS is utilized to create finite element models of intact wooden beams as well as wooden beams with varying degrees of damage and perform modal analyses on them. Next, damage identification studies are conducted on the wooden beam structure using various strain modal parameters (strain mode strain modal difference, strain modal curvature difference), the timber beam damage identification test then yields the modal parameters of timber beams under various damage situations, and the test findings are contrasted with those of the numerical simulation. The outcomes demonstrate that the damage identification of the test data using the three types of damage identification indexes is consistent with the results of the numerical simulation; the three types of damage identification indexes can locate the damage to timber beams, but the identification effect of the indexes is different, the best-recognized metric is the strain mode curvature difference; the next best is the strain mode difference, and the worst is the strain modes. The study's findings can serve as a guide for future damage detection on wood beams.

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

We report a diode pumped solid state (DPSS) laser used for intracavity pump-enhanced difference frequency generation (DFG) to create a 3.5 micron laser. Using a 50 mm-long periodically poled lithium niobate (PPLN) crystal inside the cavity of an Nd:YVO4 solid state laser at 1064 nm with 4.5 W pump power at 808 nm, and a 310 mW C-band signal at 1529 nm, up to 31 mW of mid-infrared output power at 3499 nm is obtained. The cavity requires no active stabilization and/or locking, and the entire cavity is &lt;8 cm in length. The obtained output power corresponds to a black box efficiency of 2.20 %W-1, which is the highest value reported to date for continuous wave DFG based on a bulk nonlinear optical crystal with no active stabilization. Potential future applications in free space optical communication are discussed as well.

With the escalating water scarcity in agriculture, a novel water-saving technique has emerged: drip irrigation with plastic-film mulch (DI). Root function is crucial for sustaining rice production, and understanding its response to DI is essential. However, few studies have evaluated root systems in rice varietals and examined which kind of root system contributes to improving rice grain yield and water productivity in DI. To fill this knowledge gap, we conducted a two-year field experiment comparing two irrigation systems: continuous flooding (CF) and DI. We analyzed their effectiveness with four rice varieties, including upland, F1 lowland, animal feed lowland, and lowland varieties. Vertical root distribution, root bleed-ing rate, photosynthetic-associated parameters, water productivity, and yield performance were analyzed. In our study, the average grain yield of varieties in the DI system (6.4t/ha) was equivalent to those in the CF system (6.6 t/ha). Compared to CF, DI demonstrated significant water-saving potential, saving approximately 35% of the total water supplied, resulting in higher water productivity. Among the varieties, the deep-root weight of the upland variety significantly increased by 51%. The deep-root ratio was positively correlated to transpiration rate, grain yield, and water productivity, which suggested that it contributed to high transpiration, thus maintaining a high carbon assimilation rate resulting in high yield and water productivity. Therefore, deep roots deserve consideration as a trait potentially corresponding to high yield under DI.

In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce operators that can learn solutions to the whole system of partial differential equations. However, the existing methods are only evaluated on simple flow equations (e.g., Burger's equation), and only consider the generalization ability on different initial conditions. In this paper, we construct CFDBench, a benchmark with four classic problems in computational fluid dynamics (CFD): lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. Each flow problem includes data with various boundary conditions, fluid physical properties, and domain geometries. Compared to existing datasets, the advantages of CFDBench are (1) comprehensive. It contains common physical parameters such as velocity, pressure, and cavity fraction. (2) realistic. It is very suitable for deep learning solutions of fluid mechanics equations. (3) challenging. It has a certain learning difficulty, prompting to find models with strong learning ability. (4) standardized. CFDBench facilitates a comprehensive and fair comparison of different deep learning methods for CFD. We make appropriate modifications to popular deep neural networks to apply them to CFDBench and enable the accommodation of more changing inputs. The evaluation on CFDBench reveals some new shortcomings of existing works and we propose possible directions for solving such problems.

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.

In this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

Workplace bullying is a prevalent issue with a significant impact on employees’ mental health. This study aimed to explore the relationship between workplace bullying and the prevalence of depression with a particular focus on the role of gender. A total of 12,344 Korean employees aged 19–65 years were included in the study. They completed questionnaires including the Korean version of the Occupational Stress Scale, the Oldenburg Burnout Inventory, and the Center for Epidemiologic Studies Depression Scale (CES-D). A score of 16 or higher in CES-D indicated depression. The association between workplace bullying and depression was analyzed using logistic regression analyses. The average CES-D scores were higher for both male and female employees who experienced bullying than for those who did not (p &lt; 0.001). The association between the experience of workplace bullying and the prevalence of depression was statistically significant for both genders, with a stronger correlation observed among male employees (p for interaction &lt;0.001). Organizations are urged to address workplace bullying, particularly for male employees, through the implementation of anti-bullying strategies and policies, as well as the provision of mental health resources and support.

Consciousness is a special type of interaction between subjects exchanging by lingua quanta (phonemes). A set of lingua quanta composes a thesaurus placed on the edge of chaos. Its library is a memory, modification of which is due to tuning of memristive neural elements scattered in the brain volume. The memristive neural model takes into consideration two types of neurons - excitatory and inhibitory and the current leakage, all at the body temperature, T = 309 K. At such temperatures only heavy ions like hydrogen ions - protons can pass robustly through the water medium of the brain. The robust ion transport is proton water wires supported by the Grotthuss mechanism. Final aims of the ions are the gap junctions (electric synapses) linking nearest neurons. Following these observations, a model of excitable nervous tissue is constructed. Namely, a difference mapping on the basis of sigmoid curves can reproduce chaotic modes of neural activity proved by positive values of the Lyapunov exponent. The edge of chaos is placed near the bifurcation boundary dividing the chaos and the periodic convulsive activity typical at the epileptic discharges. In this region the self-sustained spiral waves occur. An intermittent activity of the competing excitatory and inhibitory neurons is observed on the edge of chaos. The intermittent electrical activity of neural tissues is demonstrated by records both from different literature issues and records made by the author together with DR. A. Dudkin on slices of CA1 field of the hippocampus.

Perilla frutescens leaves are expected to exhibit antioxidant activity and amyloid-β (Aβ) aggregation inhibitory activity due to the presence of polyphenol-type compounds, etc. These activities fluctuate daily; however, measuring the contents of constituents and functionalities is cumbersome and unsuitable for instantaneous measurements in the field. In this study, we developed a facile method to analyze the activity and content of the components in leaves on-site based on the fluorescence spectra obtained by irradiating the perilla leaves with excitation light. The constituent contents (Chlorophyl (Chl), Total polyphenol content (TPC), Total flavonoid content (TFC), rosmarinic acid (RA) and functional properties DPPH radical scavenging activity, ferric reducing antioxidant power (FRAP), oxygen radical absorbance capacity (ORAC), Aβ aggregation inhibitory activity) were evaluated using established analytical techniques. The correlation between the fluorescence spectrum and the contents and activities was calculated using normalized difference spectral index (NDSI), ratio spectral index (RSI), and difference spectral index (DSI) analyses. We identified a predictive model with a high coefficient of determination R² ≥ 0.57 for content of the constituents, and R² ≥ 0.49 for functional properties. This allows convenient, simultaneous, and non-destructive monitoring of the constituent contents and the functionalities of perilla leave and a simple harvest-time diagnosis. The model established using this method is simple and suggesting that it can simultaneously infer the constituents and functionalities of perilla leaves.

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.

Pacing strategy refers to the distribution of effort and speed throughout the race to achieve optimal performance. The study aims to understand whether the choice of pacing strategy in swimming depends on the length of competitions and how sex, age, and performance level influence this strategy. Participants were the finalists of the 800-meter and 1500-meter freestyle events at the elite and junior world championships in 2022-2023. Race outcomes and pacing parameters were compared between the two distances and across different groups of swimmers. Swimmers in both distances did not break world records. Pacing strategy generally followed a U-shape with significant differences in the frequency and duration of speed changes between the two distances. The 800-meter exhibited more frequent changes in acceleration while the 1500-meter events generally followed a more consistent time series pattern. There were differences in pacing strategies between males and females and between junior and elite swimmers. Swimmers closer to world records showed more consistent pacing patterns compared to those farther from records. The study suggests that pacing strategies are influenced by race distance, sex, age, and performance level. The research highlights the complex interplay between physiological and psychological factors that shape a swimmer's decision-making during a race.