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We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we state that generalized convexity, invex sets, and the Fr'echet differentiability assumption associated with curvilinear integral type functionals represent some necessary and sufficient mathematical tools for establishing various connections between the solutions of some robust (weak) vector commanded variational inequalities and (weak, proper) robust efficient solutions of the corresponding multi-objective variational control problem. In addition, the physical motivation of the problem under investigation is formulated in the illustrative application given at the end of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for the nonlinear Schrodinger system {idtu1(x,t)== ∆u1(x, t)− |u1(x, t)| p−1u1(x, t)− |u2(x, t)| p−1u1(x, t), idtu2(x, t) = ∆u2(x, t) − |u2(x, t)| p−1u2(x, t) − |u1(x, t)| p−1u2(x, t), was investigated in d space dimensions. For 1 < p ≤ 1 + 2/d, the nonexistence of asymptotically free solutions for the nonlinear Schrödinger system was proved based on mathematical analysis and scattering theory methods. The novelty of this paper was to give the proof of pseudo-conformal identity on the nonlinear Schrödinger system. The present results improved and complemented these of Bisognin, Sepúlveda, and Vera(Appl. Numer. Math. 59(9)(2009): 2285–2302), in which they only proved the nonexistence of asymptotically free solutions when d = 1, p = 3. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is the underlying technology that has enabled connecting daily apparatus to the Internet and enjoying the facilities of smart services. IoT marketing is experiencing an impressive 16.7% growth rate and is a nearly USD 300.3 billion market. These eye-catching figures have made it an attractive playground for cybercriminals. IoT devices are built using resource-constrained architecture to offer compact sizes and competitive prices. As a result, integrating sophisticated cybersecurity features is beyond the scope of the computational capabilities of IoT. All of these have contributed to a surge in IoT intrusion. This paper presents an LSTM-based Intrusion Detection System (IDS) with a Dynamic Access Control (DAC) algorithm that not only detects but also defends against intrusion. This novel approach has achieved an impressive 97.16% validation accuracy. Unlike most of the IDSs, the model of the proposed IDS has been selected and optimized through mathematical analysis. Additionally, it boasts the ability to identify a wider range of threats (14 to be exact) compared to other IDS solutions, translating to enhanced security. Furthermore, it has been fine-tuned to strike a balance between accurately flagging threats and minimizing false alarms. Its impressive performance metrics (precision, recall, and F1 score all hovering around 97%) showcase the potential of this innovative IDS to elevate IoT security. The proposed IDS boasts an impressive detection rate, exceeding 98%. This high accuracy instills confidence in its reliability. Furthermore, its lightning-fast response time, averaging under 1.2 s, positions it among the fastest intrusion detection systems available. [ABSTRACT FROM AUTHOR]

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant. [ABSTRACT FROM AUTHOR]

Climate change has become a critical global issue and challenge, with significant implications for financial enterprises as an integral part of economic activities. A thorough analysis of the impact of climate change on the high-quality development of financial enterprises is of great importance for financial sustainability. This paper first conducts an indepth mathematical analysis of the intrinsic mechanisms through which climate change affects the high-quality development of financial enterprises by establishing a game theory model. Secondly, using data from listed companies for the years 2000-2020, an econometric model is constructed to empirically examine the relationship between climate change and the high-quality development of financial enterprises. The research findings demonstrate that climate change significantly inhibits the highquality development of financial enterprises, as evidenced by robust results obtained through various methods such as data truncation, variable substitution, and changes in sample periods. Furthermore, this study addresses the endogeneity of the regression model using propensity score matching (PSM), instrumental variable methods, and system generalized method of moments (GMM). Additionally, climate change impacts the high-quality development of financial enterprises through technological innovation. Given the backdrop of climate change, understanding the relationship and logic between climate change and the high-quality development of financial enterprises and discerning the channels and mechanisms through which climate change affects their development are crucial. This research provides a new perspective and expands the research frontier on the high-quality development of financial enterprises, enriching the theoretical foundations in this field. [ABSTRACT FROM AUTHOR]

Today, because infectious diseases have a large impact on people, control methods for all infectious diseases are crucial. In this paper, we propose a SIQR model with Crowley-Martin type incidence rate and saturated treatment. We have incorporated precautionary measures taken by the population through the saturated incidence rate. Screening of individuals who have come into contact with infected individuals is modelled. Thus, we explore a four-dimensional mathematical model to study the dynamics of the infectious diseases and their management. Stability and bifurcation analysis ofthe system is done. The Mensitivity analysis of all parameters in relation to the basic reproduction number has been performed and the theoretical results have been validated using numerical simulation. Mathematical results in this paper suggest that both government interventions and individual efforts must be incorporated to achieve better control of emerging infectious diseases in the population. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

This paper focuses on the projective Riemann quadratic (PR-quadratic) Finsler metrics, which are variant of the Finsler metrics in Finsler geometry. The paper introduces a special class of PR-quadratic Finsler metrics, called SPR-quadratic Finsler metrics, which is closed under projective changes with respect to a fixed volume form on M. This class contains the class of Douglas-Weyl metrics and is a subset of the class of Weyl metrics. The paper shows that any SPR-quadratic Finsler metric has a scalar flag curvature and a PR-quadratic Finsler metric has a scalar curvature if and only if it is of SPR-quadratic type. The results presented in this paper contribute to a deeper understanding of the behavior of PR-quadratic Finsler metrics and provide insights into the geometric properties of these metrics. [ABSTRACT FROM AUTHOR]

The Sombor index (SO) is a recently invented vertex-degreebased molecular structure-descriptor. LetM1 be the first Zagreb index. The fact that SO is bounded from below by M1/√2 and from above by M1 is well-known and easy to prove. In this paper, we improve these bounds. [ABSTRACT FROM AUTHOR]

This paper examines in a mathematically simplified form the incentive system of publication activity adopted by Bulgarian universities. The methodology of the study is a mathematical analysis of a competitive game between multiple players. All proofs are made in the generalised case. It is shown that in this (and similar) mathematical form of the basic formula for calculating players’ rewards, there exists an optimal number of publications at which each player reaches his maximum profit. It is shown that if individual players do not cooperate but follow competitive behavior, they will realise their maximum profits in a Nash equilibrium. It is shown that in this equilibrium some players will prefer to have zero publication activity, which depends on the costs they incur for their publications. Easy done and cheap publications will be more competitive and more numerous. It has been shown that it is more profitable for players to cooperate and minimise the amount of publications rather than compete. Potential problems and distortions in the implementation of incentives are commented. [ABSTRACT FROM AUTHOR]

Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros be 0. In this paper, we investigate the relative growth of a polynomial p(z) with respect to two circles z=r and z = R and obtain inequalities about the dependence of p(rz) on p(Rz), where z = 1, for 0 while taking into account the placement of the zeros of the underlying polynomial. Our results improve as well as generalize certain well-known polynomial inequalities. Some numerical examples are also given in order to illustrate and compare graphically the obtained inequalities with some recent results. [ABSTRACT FROM AUTHOR]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

In this paper, we investigate mathematical models of meteorological forecasting based on the work of neural networks, which allow us to calculate presumptive meteorological parameters of the desired location on the basis of previous meteorological data. A new method of grouping neural networks to obtain a more accurate output result is proposed. An algorithm is presented, based on which the most accurate meteorological forecast was obtained based on the results of the study. This algorithm can be used in a wide range of situations, such as obtaining data for the operation of equipment in a given location and studying meteorological parameters of the location. To build this model, we used data obtained from personal weather stations of the Weather Underground company and the US National Digital Forecast Database (NDFD). Also, a Google remote learning machine was used to compare the results with existing products on the market. The algorithm for building the forecast model covered several locations across the US in order to compare its performance in different weather zones. Different methods of training the machine to produce the most effective weather forecast result were also considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a Quasi B-algebra, building upon the foundational work on Post algebras by G. Epstein and the investigation of semi B-algebras. We systematically explore the properties of Quasi B-algebras, establishing equivalent conditions for the transition from a semi B-algebra to a Quasi B-algebra. [ABSTRACT FROM AUTHOR]

The k-deck of a graph is the multiset of its subgraphs induced by k vertices which is denoted by Dk(G). A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. Manvel proved that from the (n−l)-deck of a graph and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−1, the degree list of the graph is determined. In this paper, we extend this result and prove that if G is a graph with n vertices, then from the (n−l)-deck of G and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−3, where l ≥ 4 and n ≥ l + 6, the degree list of the graph is determined. [ABSTRACT FROM AUTHOR]

The paper is using the nonlocal field equations for modelling a nanocontact made from the thin films. The theory describes long-range interactions among the particles. An elastic layer loaded by a rigid indenter is considered. We show that the stress field is finite for all points and have a maximum value that does not occur at the boundary of the contact domain. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for T -contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered. [ABSTRACT FROM AUTHOR]

This paper proposes a new hybrid control strategy to solve the problem of bidirectional wide voltage range regulation in CLLC converters. On the (LLC) side (G2V direction), the SSSA control method is employed for voltage boost, combined with bus voltage and burst control to achieve wide voltage regulation. On the (C) side (V2G direction), the SSSA and full/half‐bridge mode switching control are used to achieve V2G direction wide voltage regulation. This hybrid control strategy also enables high conversion efficiency in both directions without the need for additional components to reduce the converter power density. This is particularly suitable for OBC applications with strict requirements for converter volume and weight. A detailed analysis with mathematical derivation, hybrid control strategy, and converter operation principles is introduced in this paper. The following subchapters supplement the converter voltage gain, soft switching implementation conditions, and design considerations. Finally, the feasibility of the proposed control strategy was verified through an experimental prototype with an input voltage ranging from 340 to 430 V to an output voltage ranging from 225 to 450 V and bidirectional rated power of 6.6/3.3 kW. This prototype achieved a maximum conversion efficiency of 97.7% in the G2V direction and 97.1% in the V2G direction. [ABSTRACT FROM AUTHOR]

In this paper, using improvement-valued maps, we define two types of E-Benson proper efficient elements for subsets within a linear space under a variable ordering map C. Consequently, we delve into studying two types of E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. We establish relationships among different types of E-Benson proper efficient elements. Furthermore, we demonstrate that the two types of E-Benson proper efficiency, in relation to the ordering map C, not only unify and extend certain notions of (weakly) nondominated elements but also extend some well-known notions of Benson proper efficiency under fixed ordering structures. Lastly, under suitable assumptions, we establish linear scalarization theorems for E-Benson proper efficient solutions of vector optimization problems under variable ordering structures. Several examples are also provided to illustrate the derived results. [ABSTRACT FROM AUTHOR]

Automated identification of mathematical expressions (MEs) is essential in transforming scientific and engineering documents into electronic form. Even though character and symbol recognizers have achieved commendable performance for digitizing documents, structure analysers still face a challenge in correctly interpreting the maths expressions. This review paper compares the salient aspects of past works dealing with structure analysis of printed and handwritten MEs. To the best of our knowledge, no previous work has done a systematic study of structural analysis methods in mathematical expression recognition. We present distinguishing aspects of different grammars and their production rules for semantic parsing of ME. Our study contributes by providing information on the existing datasets, their desirable properties, different evaluation measures, distinguishing aspects of techniques used and future research directions in structural analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and λ$$ \lambda $$‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors. [ABSTRACT FROM AUTHOR]

An analysis of an existing mathematical framework that describes the epidemiology of the Hepatitis A Virus (HAV) via dual modes of transmission is done in this paper. Sanitation and vaccination are taken into account by the model as mitigating techniques. Using the Homotopy perturbation method, the relevant six compartments like susceptible, vaccinated, latent, infectious, recovered and HAV population (S-V-L-I-R-P) of the model are solved analytically. For each of the six compartments, specific analytical formulations are provided. Several types of model parameters are illustrated graphically to demonstrate their impacts. Comparing the results with the numerical simulation (MATLAB) yields a good fit. [ABSTRACT FROM AUTHOR]

A stochastic model of leptospirosis with vector and environmental transmission is established in this paper. By mathematical analysis of the model, the threshold for eliminating the disease is obtained. The partial rank correlation coefficient was used to analyze the parameters that have a greater impact on disease elimination, and a sensitivity analysis was conducted on the parameters through numerical simulation. Further, combined with the data of leptospirosis case reports in China from 2003 to 2021, two parameter estimation methods, Least Squares method (LSM) and Markov Chain Monte Carlo-Metropolis Hastings method (MCMC-MH), are applied to estimate the important parameters of the model and the future trend of leptospirosis in China are predicted. [ABSTRACT FROM AUTHOR]

The primary focus of this paper lies in exploring the limiting dynamics of a neural field lattice model with state dependent superlinear noise. First, we established the well-posedness of solutions to these stochastic systems and subsequently proved the existence of periodic measures for the system in the space of square-summable sequences using Krylov-Bogolyubov's method. The cutoff techniques of uniform estimates on tails of solutions was employed to establish the tightness of a family of probability distributions for the system's solutions. [ABSTRACT FROM AUTHOR]

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, a new application of the Taylor series method (TSM) and its properties is used to solve partial differential equation problems with a singular limit value problem. We are particularly interested in applying this method to a certain class of physical problems such as Lane Emden–Fowler partial differential equations. The results obtained show that this analytical technique is very simple and effective compared to other methods. [ABSTRACT FROM AUTHOR]

In this paper, we have provided a mathematical analysis of an empirical result, namely, the Fahraeus–Lindqvist effect, a phenomenon that occurs in capillary tubes with a diameter lower than 0.3 mm. According to this effect, in capillary tubes under 0.3 mm in diameter, the apparent viscosity of blood decreases as the diameter of the tube decreases, making flow possible in these vessels. A two-phase blood flow mathematical model for human capillaries has been presented here. According to Haynes' theory, blood is separated into two layers when it flows from the capillary. It is assumed that the first layer is plasma, and the second layer is the core layer. The plasma layer flows near the wall of the capillary, and the core layer flows along the axis of the capillary. Further, the core layer is assumed to be a mixture of two phases: one is the plasma, and the other is that of RBCs. For mathematical modeling purposes, a curvilinear coordinate system has been adopted, with physical quantities used in tensorial form. Derived equations are solved to find the effective viscosity, which depends upon the radius of the capillary; that is, it reduces viscosity to make blood flow possible. A comparative study was conducted with the experimental result of this effect, and it was observed that the proposed two-phase blood flow model is much closer to the experimental data than the single-phase blood flow model, and both have the same trends. After validation of the model with the experimental result, this model was applied to human capillaries (diameter lower than 10 μ m ) to show the F-L effect, and the impact of various physiological quantities that are relevant to the flow of blood into human capillaries are also discussed here. The impact of hematocrit on various parameters has been demonstrated explicitly. [ABSTRACT FROM AUTHOR]

Experimental evidence supports the counterintuitive notion that rapid eradication of pathogens within a host, infected with both drug-sensitive and -resistant malaria parasites, can actually accelerate the evolution of drug-resistant pathogens. This study aims to analyze the competitive dynamics between these two strains through a mathematical model and evaluate the impact of aggressive treatment on the spread of drug resistance. We conducted equilibrium, uncertainty, and sensitivity analyses to assess the model, identifying and measuring the influence of key factors on the outcome variable (the population of drug-resistant parasites). Both equilibrium and local sensitivity analyses concurred that the density of drug-resistant parasites is notably affected by genetic instability, the production rate of red blood cells, the number of merozoites, and competition factors. Conversely, there is a negative relationship between genetic instability and one of the competition coefficients. Global sensitivity analysis offers a comprehensive examination of the impact of each input parameter on the temporal propagation of drug resistance, effectively accounting for the interplay among parameters. Both local and global sensitivity analyses underscore the continuous impact of drug treatment on the progression of drug resistance over time. This paper anticipates exploring the underlying mechanisms of drug resistance and providing theoretical support for developing more effective drug treatment strategies. [ABSTRACT FROM AUTHOR]

A combination of experimental measurement preparations using pressure and temperature sensors in conjunction with the theory of one-dimensional isentropic flow and mathematical physics analyses is presented as a tool for analysis in this paper. Furthermore, the subsequent development of a nozzle for use in environmental electron microscopy between the specimen chamber and the differentially pumped chamber is described. Based on experimental measurements, an analysis of the impact of the nozzle shaping located behind the aperture on the character of the supersonic flow and the resulting dispersion of the electron beam passing through the differential pumped chamber is carried out on the determined pressure ratio using a combination of theory and mathematical physics analyses. The results show that nozzle shapes causing under-expanded gas outflow from the aperture to the nozzle have a worse impact on the dispersion of the primary electron beam. This is due to the flow velocity control. The controlled reduction in the static pressure curve on the primary electron beam path thus causes a significantly higher course of electron dispersion values than variants with shapes causing over-expanded gas outflow. [ABSTRACT FROM AUTHOR]

In this paper, a new microstrip triplexer is designed to work at 2.5 GHz, 4.4 GHz and 6 GHz for mid-band 5G applications. All channels are flat with three low group delays (GDs) of 0.84 ns, 0.75 ns and 0.49 ns, respectively. Compared to the previously reported works, the proposed triplexer has the minimum group delay. The designed triplexer has 18.2%, 13.7%, 23.6% fractional bandwidths (FBW%) at 2.5 GHz, 4.4 GHz and 6 GHz, respectively. The obtained insertion losses (ILs) are low at all channels. These features are obtained without a noticeable increase in the overall size. A novel and simple resonator is used to design the proposed triplexer, which includes two pairs of coupled lines combined with a shunt stub. A perfect mathematical analysis is performed to find the resonator behavior and the layout optimization. The type of shunt stub is determined mathematically. Also, the smallness or largeness of some important physical dimensions is determined using the proposed mathematical analysis. Finally, the designed triplexer is fabricated and measured, where the measurement results verify the simulations. [ABSTRACT FROM AUTHOR]

Hybrid stochastic differential equations (HSDEs) have wide range of real-world applications. In this paper, we study a new kind of nonlinear delayed neutral stochastic differential equations with Markovian switched noises (NHSDE-MSN). Under the assumption that this type of equations satisfies the locally Lipschitz condition and general condition of monotonicity, the existence and uniqueness of global solutions are established. Then, based on the Lyapunov function, M-matrix theory, stochastic analysis techniques, and Barbalat lemma, taking into account the delay as a bounded function, different decay stabilities of solutions are investigated. Finally, a numerical example is given to illustrate the utility of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we present the fractional backward differentiation formulas for the numerical solutions of two-term fractional differential Sylvester matrix equations in the Caputo derivative sense, which includes the celebrated two-term fractional differential Lyapunov matrix equations. We give two applications in a two-term time-fractional telegraph equation with illustrative examples. In addition, we also consider two examples to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the local well-posedness and blow up of solutions for a class of time- and space-fractional diffusion wave equation in a fractional power space associated with the Laplace operator. First, we give the definition of the solution operator which is a noteworthy extension of the solution operator of the corresponding time-fractional diffusion wave equation. We have analyzed the properties of the solution operator in the fractional power space and Lebesgue space. Next, based on some estimates of the solution operator and source term, we prove the well-posedness of mild solutions by using the contraction mapping principle. We have also investigated the blow up of solutions by using the test function method. The last result describes the properties of mild solutions when α → 1 − . The main feature of the proof is the reasonable use of continuous embedding between fractional space and Lebesgue space. [ABSTRACT FROM AUTHOR]

This paper mainly studies the least-squares solutions of matrix equation A X B = C under a semi-tensor product. According to the definition of the semi-tensor product, the equation is transformed into an ordinary matrix equation. Then, the least-squares solutions of matrix-vector and matrix equations respectively investigated by applying the derivation of matrix operations. Finally, the specific form of the least-squares solutions is given. [ABSTRACT FROM AUTHOR]

Load-capacity has always been one of the performances that is paid much attention to in the development of bevel gear transmission applications. Consequently, the mathematical model of novel bevel gear with high load-capacity based on geometric elements is proposed in this paper, which could be applied to the aviation, aerospace and other fields. In parallel, the design principle and design method of the novel bevel gear are introduced in detail. Subsequently, the conditions for tooth surface continuity and non-interference are derived. Furthermore, the model of novel bevel gear is established. Finally, the load-bearing characteristics are analyzed, revealing that an increase in the number of contact points could significantly enhance the load capacity of the bevel gear pairs. When the load torque applied to bevel gear II is 100 Nm, the contact pressure endured by the bevel gear pair with five-point contact is decreased by 41.37% compared to the bevel gear pair with single-point contact. When the number of contact points is the same, increasing the distance between the contact points could also reduce the contact stress. This provides strong theoretical support for the application of the bevel gear based on the geometric elements. [ABSTRACT FROM AUTHOR]

The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of this classical problem, particularly the relationship between its canonical and Liouville normal (Schrödinger) forms. While the conversion from the canonical to Schrödinger form using Liouville's transformation is well known in the literature, the inverse transformation seems to be neglected. Our study attempts to fill this gap by investigating the inverse of Liouville's transformation, that is, given any SLP in the Schrödinger form with some invariant function, we seek the SLP in its canonical form. By closely examining the second Paine–de Hoog–Anderson (PdHA) problem, we argue that retrieving the SLP in its canonical form can be notoriously difficult and can even be impossible to achieve in its exact form. Finding the inverse relationship between the two independent variables seems to be the main obstacle. We confirm this claim by considering four different scenarios, depending on the potential and density functions that appear in the corresponding invariant function. In the second PdHA problem, this invariant function takes a reciprocal quadratic binomial form. In some cases, the inverse Liouville transformation produces an exact expression for the SLP in its canonical form. In other situations, however, while an exact canonical form is not possible to obtain, we successfully derived the SLP in its canonical form asymptotically. [ABSTRACT FROM AUTHOR]

In this paper, we explore the properties of the generalized Lambert transform, the L-transform, the generalized Stieltjes transform, and the Stieltjes–Poisson transform within the framework of Lebesgue spaces. We establish Parseval-type relations for each transform, providing a comprehensive analysis of their behaviour and mathematical characteristics. [ABSTRACT FROM AUTHOR]

In the 1990s, the united nations development programme (UNDP) introduced the human development index (HDI) to determine the development degrees of countries. One deficiency in the HDI calculation is the use of equal weights for its sub-indicators. Many scholars have tried to solve this problem using a data envelopment analysis (DEA) method, particularly the one enhanced by weight restrictions. Indeed no specific method has been yet suggested to determine the parameters of the weight restrictions. In this paper, we use four DEA/benefit of the doubt (BoD) models enriched by the assurance regions type I (AR-I) constraints to assess human development; we aim to objectively determine the AR-I bounds. Therefore, we consider a basis as the accepted human development values and propose a bi-level optimization problem to extract the AR-I bounds in such a way that the efficiency scores are almost the same as the basic values. On the other hand, the HDI is a globally accepted index that shows small changes year by year. So, if the UNDP decides to apply a BoD model for calculating the HDI instead of the traditional method, then it is better than the scores obtained by the BoD model, showing small changes in comparison with the HDI, at least in the first few years. Therefore, the HDI values are considered as the basis. Moreover, the objectively achieved AR-I bounds provide us with an insight into the way the sub-indicators affect the development scores. The bounds can be modified by the experts opinions, in the future. [ABSTRACT FROM AUTHOR]

Atherosclerosis is one of the most common diseases in the world. Medication with metal stents plays an important role in treating this disease. There are many models for delivering drugs from stents to the arterial wall. This paper presents a model that describes drug delivery from the stent coating layers to the arterial wall tissue. This model complements the previous models by considering the mechanical properties of the arterial wall tissue, which changes due to atherosclerosis and improves results for designing stents. The stability behavior of the model is analyzed, and a number of numerical results are provided with explanations. A comparison between numerical and experimental results, which examine a more accurate match between the in vivo and in vitro, is shown. [ABSTRACT FROM AUTHOR]

This paper describes a theoretical framework and computational methods of a thin layer coating of a non-Newtonian polymeric material while it moves through a tiny space among two inverted rollers. Order of magnitude is accustomed to clarify the nondimensional forms of the governing equations. Semi-analytical solutions of pressure gradient, velocity profile and rate of the flow are acquired via optimal homotopy asymptotic method (OHAM). The graphical representation depicts the physical quantities of the effects of velocity profile ratio k and Weissenberg number We. It is observed that by increasing the values of k and We, velocity profile decreases while pressure distribution increases. [ABSTRACT FROM AUTHOR]

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice. [ABSTRACT FROM AUTHOR]

In this paper, we presented a review on some recent progress achieved for simulating Maxwell's equations in perfectly matched layers and complex media such as metamaterials and graphene. We mainly focused on the stability analysis of the modeling equations and development and analysis of the numerical schemes. Some open issues were pointed out, too. [ABSTRACT FROM AUTHOR]

Ricci bi-conformal vector fields have find their place in geometry as well as in physical applications. In this paper, we consider the Siklos spacetimes and we determine all the Ricci bi-conformal vector fields on these spaces. [ABSTRACT FROM AUTHOR]