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Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [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]

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 discuss the isoperimetric-type inequalities for the closed convex curve in the Euclidean plane R². The main result of this paper is that we establish a family of parametric inequalities. By adjusting the parameters, we can derive some well-known isoperimetric inequalities and some new improved isoperimetric-type inequalities. Furthermore, we investigate the stability property of the main inequality. [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]

In this paper, we present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by G'orka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution. [ABSTRACT FROM AUTHOR]

In this paper, a signal model and a mathematical analysis of an efficient approach are derived to acquire the approximate magnitude of a complex signal by inducing a pre-biased or a pre-scaled factor in the design criteria. According to the deductive results, the pre-biased or pre-scaled factor can be 2∼3 dB, which is determined through its application. The numerical evaluations show that the mean square error (MSE) of the proposed efficient approach for the random signal is around −33 dB. Based on the design templates for the considered approaches, the occupied areas of the proposed type-1 and -2 approaches are merely 0.13 and 0.09 times the area of the direct-method, respectively. As a result, the proposed efficient approach is certainly a cost-efficient method for obtaining the approximate magnitude of a complex signal. [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]

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]

This paper is devoted to the analysis of mathematical models of chemotherapy for malignant tumors growing according to the Gompertz law or the generalized logistic law. The influence of the therapeutic agent on the tumor dynamics is determined by a therapy function depending on the time-varying concentration of the drug in the patient's body. The case of a non-monotonic therapy function with two maxima is studied. It reflects the use of two different therapeutic agents. The state variables of the dynamics are the tumor volume and the amount of the therapeutic agent able to suppress malignant cells (concentration of the drug in the body). The treatment protocol (the rate of administration of the therapeutic agent) is the control in the dynamics. The optimal control problem for this models is considered. It is the problem of the construction of treatment protocols that provide the minimal tumor volume at the end of the treatment. The solution of this problem was obtained by the authors in previous works via the optimal control theory. The form of the considered therapy functions provides a specific structure for the optimal controls. The managerial insights of this structure are discussed. In this paper, the structure of the viability set is described for the model according to the generalized logistic law. It is the set of the initial states of the model for which one can find a treatment protocol that guarantees that the tumor volume remains within the prescribed limits throughout the treatment. The description of the viability set's structure is based on the optimal control theory and the theory of Hamilton–Jacobi equations. An inverse problem of therapy is also considered, namely the problem of reconstruction of the treatment protocol and identification of the unknown parameter of the intensity of the tumor growth. Reconstruction is carried out by processing information about the observations of the tumor volume dynamics and the measurements of the drug concentration in the body. A solution to this problem is obtained through the use of a method based on the calculus of variations. The results of the numerical simulations are presented herein. [ABSTRACT FROM AUTHOR]

In this paper, we establish some embedding relationships between Muckenhoupt and Gehring classes Ap and Gr by proving transition and inclusion relations. We also identify the exact range of τ > 1 for which wτ ∈ Ap. Additionally, we show that the weights that satisfy the Ap -condition also meet the A∞ -condition. Next, we prove the Jones factorization property of Ap weights in terms of two A1 weights by employing the discrete Rubio De Francia iterated algorithm. Finally, we determine the specific ranges of indices (sharp exponents) for which w belongs to Gr (Ap) if w belongs to Ap (Gr) and the precise range of q< p for which w belongs to Aq given that it belongs to Ap. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of composite multiobjective optimization problems, subject to a closed convex constraint set, defined on Riemannian manifolds. To tackle this problem, we propose the generalized conditional gradient method with two step size strategies, including Armijo step size and the nonmonotone line search step size. Under some reasonable conditions, the global convergence result is established, and the iteration-complexity bound for composite multiobjective optimization problems is presented on Riemannian manifolds. [ABSTRACT FROM AUTHOR]

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [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]

In this paper, over an arbitrary number field, we prove subconvexity bounds for selfdual GL3 L-functions in the t-aspect and for self-dual GL3 x GL2 L-functions in the GL2 Archimedean aspect. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic hybrid predator-prey model with Beddington-DeAngelis functional response and Lévy jumps is studied. Firstly, it is proved that the model has a unique global solution. Secondly, sufficient conditions for weak persistence in the mean and extinction of prey and predator populations are established. Finally, sufficient conditions for the existence and uniqueness of ergodic stationary distribution are established. Moreover, several numerical simulations are presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we give a generalization of Euler's pentagonal number theorem. As an application, we derive a recursion formula for successively determining the coefficients ak of 1=nk. We conclude this paper by presenting brief descriptions for some related results and other motivating developments. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the effectiveness of the element interaction model in a vehicular ad hoc network (VANET). An analysis of the mathematical model and its numerical solution for the system of boundary device interactions in the traditional configuration of roadside unit (RSU) placement using single- and dual-channel connection between on-board units (OBU) and RSU is given. In addition, the model efficiency is improved using a clustering approach. The efficiency evaluation is based on calculating the percentage of unprocessed requests generated by OBUs during their mobility, the average power consumption and the magnitude of the delay in transmitting and processing the generated requests in the OBU–RSU system. The traditional and cluster models are compared. The results obtained in this paper show that each of the proposed models can be effectively implemented in mobile nodes and will significantly reduce the overall expected query processing time to improve the organization and algorithmic support of VANET. Along with this, it is shown that the developed approach allows for efficient power consumption when combining RSUs into clusters with a shared cache. The novelty of solving the problems is due to the lack of a comprehensive model that allows the distribution and prediction of the parameters and resources of the system for different computational tasks, which is essential when implementing and using V2X technology to solve the problems of complex management of VANET elements. [ABSTRACT FROM AUTHOR]

In this paper, as a further generalization of ideals, we introduce the notion of tri-quasi ideals as a generalization of ideals, left ideals, right ideals, tri-ideals, bi-ideals, quasi ideals, interior ideals, bi-interior ideals, weak interior ideals, bi-quasi ideals, quasi-interior ideals and bi-quasi-interior ideals of a semiring. Some charecterizations of a regular semiring and a simple semiring using tri-quasi ideals are given and study the properties of tri-quasi ideals of semirings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel concept termed a semi B-algebra, which acts as an extension of the existing B-algebra. Our investigation delves into the derivation of essential arithmetical properties unique to semi B-algebras, coupled with diverse characterizations shedding light on various aspects of this particular algebraic structure. [ABSTRACT FROM AUTHOR]

This paper aims to solve two enduring challenges in existing trajectory similarity measures: computational inefficiency and the absence of the ‘uniqueness’ property that should be guaranteed in a distance function: dist(X, Y ) = 0 if and only if X = Y, where X and Y are two trajectories. In this work, we present a novel approach utilizing a distributional kernel for trajectory representation and similarity measurement, based on the kernel mean embedding framework. It is the very first time a distributional kernel is used for trajectory representation and similarity measurement. Our method does not rely on point-to-point distances which are used in most existing distances for trajectories. Unlike prevalent learning and deep learning approaches, our method requires no learning. We show the generality of this new approach in anomalous trajectory and sub-trajectory detection. We identify that the distributional kernel has (i) a data-dependent property and the ‘uniqueness’ property which are the key factors that lead to its superior task-specific performance, and (ii) runtime orders of magnitude faster than existing distance measures. [ABSTRACT FROM AUTHOR]

In this paper, we study the multiplicity of solutions to the following Kirchhoff type equation with zero mass and Hardy-Littlewood-Sobolev critical nonlinearity ... where N ≥ 3, λ > 0, μ ∈ (0, min{N, 4}), 2μ* = 2n-μ/n-2 is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, and m satisfies some local monotonicity conditions near zero. The non- linearity f is odd in u and satisfies some classical superlinear and quasi-critical growth conditions. For any given k ∈ ℕ, k pairs of nontrivial solutions are obtained for λ large enough by a version of the symmetric mountain pass theorem and a version of the second concentration compactness principle. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two within-host mathematical models that are based on differential equations. These mathematical models include healthy cells, tachyzoites, and bradyzoites. The first model is based on ordinary differential equations and the second one includes a discrete time delay. We found the models' steady states and computed the basic reproduction number R 0 . Two equilibrium points exist in both models: the first is the disease-free equilibrium point and the second one is the endemic equilibrium point. We found that the initial quantity of uninfected cells has an impact on the basic reproduction number R 0 . This threshold parameter also depends on the contact rate between tachyzoites and uninfected cells, the contact rate between encysted bradyzoite and the uninfected cells, the conversion rate from tachyzoites to bradyzoites, and the death rate of the bradyzoites- and tachyzoites-infected cells. We investigated the local and global stability of the two equilibrium points for the within-host models that are based on differential equations. We perform numerical simulations to validate our analytical findings. We also demonstrated that the disease-free equilibrium point cannot lose stability regardless of the value of the time delay. The numerical simulations corroborated our analytical results. [ABSTRACT FROM AUTHOR]

The paper investigates whether foam glass could reduce the structural thickness of the protection layer in the construction of the railway track (saving of natural materials - crushed aggregate) and, at the same time, also provide sufficient thermal protection of the frost-susceptible subgrade surface. It also discusses whether the incorporation of foam glass would have a relevant effect on the increase of the deformation resistance of the railway track structure at the level of the sub-ballast upper surface. Following these assumptions, the paper presents the results of experimental measurements of the deformation resistance of the modified structural composition of the sub-ballast layers (with an embedded foam glass layer) and their comparison with the results determined on a structure with a standard composition of the sub-ballast layers (crushed aggregate sub-ballast layer/protective layer). Also, numerical and mathematical analysis of the influence of the built-in thermal insulation foam glass layer on the reduction of the structural thickness of the protective crushed aggregate layer in terms of the effect of climatic factors is conducted in the paper. The mathematical model, developed by the research, provides the possibility of continuous monitoring of the change in the railway track structure freezing depending on climatic characteristics. [ABSTRACT FROM AUTHOR]

The Security of Rivest, Shamir and Adleman Cryptosystem known as RSA and its variants rely on the difficulty of integer factorization problem. This paper presents a short decryption exponent attack on RSA variant N= p² q² based on the key equation ed - kφ(N) = 1 where prime difference |b²q²| < Nγ was carefully analyzed and came up with an approximation of φ(N) as a N- a+b/√ab √N which enabled us to obtain an improved bound d<2√2/3 N3/4 −γ that led to the polynomial time factorization of the variant N= p² q² [ABSTRACT FROM AUTHOR]

Graphs give a mathematical model of molecules, and thery are used extensively in chemical investigation. Strategically selections of graph invariants (formerly called "topological indices" or "molecular descriptors") are used in the mathematical modeling of the physio-chemical, pharmacologic, toxicological, and other aspects of chemical compounds. This paper describes a new technique to compute topological indices of two types of chemical networks. Our research examines the mathematical characteristics of molecular descriptors, particularly those that depend on graph degrees. We derive a compact mathematical analysis and neighborhood multiplicative topological indices for product of graphs (L) and tetrahedral diamond lattices (Ω). In this paper, the fifth multiplicative Zagreb index, the general fifth multiplicative Zagreb index, the fifth multiplicative hyper-Zagreb index, the fifth multiplicative product connectivity index, the fifth multiplicative sum connectivity index, the fifth multiplicative geometric-arithmetic index, the fifth multiplicative harmonic index and the fifth multiplicative redefined Zagreb index are determined. The comparison study of these topological indices is also discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems for two pairs of self-mappings satisfying (CLR)-property and some Φ-type contractive condition in the framework of S-metric spaces. We also give some examples to validate the results. The results presented in this paper generalize, extend and unify several previous results in the existing literature. [ABSTRACT FROM AUTHOR]

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition. [ABSTRACT FROM AUTHOR]

Transformer-less connection schemes can provide a feasible solution for lowering the economic cost, occupied space, and device weight of modular multilevel converter (MMC) systems. However, due to the reduction in the converter transformer, the current flow loop is changed; as a result, the existing MMC model is not suitable. In this paper, the ac- and dc-side equivalent circuit models of the MMC system using a transformer-less connection scheme are established in both a–b–c stationary and d–q rotating coordinate systems. Then, a highly accurate mathematical analysis model is proposed, in which the interactions among the electrical quantities can be fully seen. The mathematical model is established in the time domain, and hence the amplitude and phase angle of every harmonic component in each quantity can be directly obtained. The proposed model is verified under various typical situations by comparing the calculated values with the actual waveforms. The comparison results prove that the calculation error is small enough to be negligible. The mathematical model in this paper can provide a powerful tool in terms of the performance analysis and the main circuit parameter design for MMCs in transformer-less applications. [ABSTRACT FROM AUTHOR]

Minimizing closed geodesics on surfaces are linearly unstable. By starting with this classical Poincaré's instability result, in the present paper we prove a result that allows to deduce the linear instability of periodic solutions of autonomous Lagrangian systems admitting an orbit cylinder (condition which is satisfied for instance if the periodic orbit is transversally non-degenerate) in terms of the parity properties of a suitable quantity which is obtained by adding the dimension of the configuration space to a suitably defined spectral index. Such a spectral index coincides with the Morse index of the periodic orbit seen as a critical point of the free period action functional in the case the Lagrangian is Tonelli, namely fibrewise strictly convex and superlinear, and it encodes the functional and symplectic properties of the problem. The main result of the paper is a generalization of the celebrated Poincaré 's instability result for closed geodesics on surfaces and at the same time extends to the autonomous case several previous results which have been proved by the authors (as well as by others) in the case of non-autonomous Lagrangian systems. [ABSTRACT FROM AUTHOR]

Many types of decision problems can be solved using mathematical modeling and analysis. Such techniques are also developed on the border of mathematical logic and computer science. A good example is the translation of the issues examined into the Satisfiability Problem (SAT) of a logical propositional formula. Unfortunately, this method is not always practical, considering the high computational complexity of solving the SAT problem. It often happens that in the studied cases, the encoding formulas contain even hundreds of thousands of clauses and propositional variables. However, even in these cases, modern SAT solvers can sometimes successfully solve these problems. This approach can be used to cryptanalyze some symmetric ciphers or parts/modifications. In this case, the encryption algorithm is first translated into a boolean formula. Then additional formulas are created to encode randomly selected plaintext and the key bits. Using the SAT solver; we can count the values of the ciphertext bits. Then, using the SAT solver again, we proceed to the cryptanalysis of the cipher with the selected plaintext and proper ciphertext, looking for the bits of the encryption key. In this paper, we will present the new results of how SAT techniques behave against representative fragments of the AES cipher, the current standard for symmetric encryption. We also compare the results obtained in this case by several SAT solvers. In addition, we present the results of the SAT-solver CryptoMiniSat obtained during the attack on the 1st round of the AES-128 cipher. [ABSTRACT FROM AUTHOR]

The adaptive interference cancellation technique has been widely utilized in radar, GPS, data link, etc., systems to address challenges from external interference, such as co-site and hostile interference. Since the anti-jamming performance of the adaptive interference cancellation technique is sensitive to group delay mismatch between channels, the group delay mismatch becomes one of the main factors that limit the system's anti-jamming capability. However, the traditional adaptive interference cancellation system's mathematical model cannot quantitatively characterize the group delay mismatch effect on the wideband interference cancellation performance. In this paper, the mathematical model of the wideband adaptive spatial interference cancellation (ASIC) system is established, which considers the group delay mismatch, to quantitatively analyze the impact of group delay mismatch on the hostile interference cancellation. The mathematical model utilizes the weighted multi-tone signals to fit the wideband interference, and then, delay differences are attached to each tone signal to simulate the group delay mismatch. Then, the analytic expressions of weight and interference cancellation ratio are derived, which consider the interference bandwidth and group delay mismatch, to quantitatively analyze the group delay mismatch effect on the anti-jamming performance of the wideband ASIC system. Simulation results indicate that the theoretical analysis based on the mathematical model of wideband ASIC system are accurate, which can achieve the quantitative analysis of the group delay mismatch effect on the WIC performance. [ABSTRACT FROM AUTHOR]

An operator T ∈ B(H) is called p-quasi-n-hyponormal if T*(T*nTn)pT > T*(TnT*n)pT for a positive number 0 < p < 1 and a positive integer n, which is a further generalization of normal operator. In this paper we introduce the class of p-quasi-n-hyponormal operators and show its structural properties via Hansen inequality and L?owner-Heinz inequality. As important applications, we obtain that every p-quasi-n-hyponormal operator has a scalar extension. In addition, we prove that if T is a quasiaffine transform of p-quasi-n-hyponormal, then T satisfies Weyl's theorem. Finally some examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we define the bi-periodic hyper-Horadam sequence {w(k)n }n∈N and present its combinatorial properties. Moreover, we obtain upper and lower bounds for the spectral norms of different forms of the r -circulant and geometric circulant matrices with the bi-periodic hyper-Horadam sequence. Then we give some bounds for the spectral norms of the Kronecker and Hadamard products of these matrices. [ABSTRACT FROM AUTHOR]

Any two points are close together in a  -contraction by a factor of  . The function  Δ  is implied to be a contraction under this condition, but with a tighter bound on the contraction factor. In this paper, we introduce the notions of orthogonal  -contraction and orthogonal  α − -contraction and prove several fixed point results by utilizing these contraction mappings in the context of orthogonal metric spaces. Further, we provide several non-trivial examples to show the validity of our results. [ABSTRACT FROM AUTHOR]

This paper aims to construct some nonlinear weak separation functions in image space analysis by virtue of the Gerstewitz and topical functions. Then, applying these separation functions, a framework of conjugate type duality for constrained vector optimization problems is introduced. The primal problem is scalarized and then the separation functions are applied to give a scalar dual problem. Meanwhile, equivalent characterizations of the zero duality gap as well as the strong duality are established via subdifferential calculus, separation properties, and saddle point assertions. [ABSTRACT FROM AUTHOR]

The article considered the three types of description of the material behavior model: elastic, elastic–plastic, and viscoelastic. The problem is considered in the framework of deformable solid mechanics. The paper considers the possibility of describing modern polymeric and composite materials used as antifriction sliding layers in the viscoelasticity framework. A numerical procedure for finding the coefficients to describe the viscoelastic material behavior using the Prony model has been implemented. Numerical results and experimental data are compared. The model problem of spherical indenter penetration into polymer half-space is realized. The influence of the system discretization on the numerical solution is analyzed. The influence of the polymer behavior description in static and dynamic problem formulations is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a positive equilibrium under the delays of τ = 0 and τ ≠ 0 . Furthermore, through numerical simulation, it has been verified the delay, τ , exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. [ABSTRACT FROM AUTHOR]

A scheme for the integration of CD(1/n)-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that CD(1/n)-type FDEs can be transformed into equivalent (CD(1/n))n-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the decay rates of the higher-order spatial derivatives of solution to the Cauchy problem of 3D compressible nematic liquid crystals system. The Ḣs (1/2

In this paper, we introduce a generalized delta q-Mittag-Leffler function. Also, we solve some Caputo delta q-fractional dynamic equations and these solutions are expressed by means of the newly introduced delta q-Mittag-Leffler function. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented for the mathematical modeling and analysis of the DC–DC Buck Converter output voltage. This paper consists of the demonstration of a mathematical model for the converter transient response submitted to a pulse width modulated (PWM) input voltage, resulting in accurate symbolic expressions for the output voltage. The novelty of the method is the capability of the expressions derived to describe correctly the behavior of the converter submitted to time-varying control reference input signals modulating the switch pulse width. The mathematical model was then validated by comparing it with the responses obtained using the Runge–Kutta numerical method. By using different circuit parameters and PWM input signals with constant and time-varying duty cycles, it was possible to validate the model for different cases, showing the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Bipolar R-metric space that in a way enriches the present literature. Here, on associating a binary relation R with bipolar metric space, we obtain a fixed point result which is well supported with an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed points properties and demiclosedness principle for mean nonexpansive mapping in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a common fixed point of two mean nonexpansive mappings and establish some strong and △-convergence theorems for these mappings in uniformly convex hyperbolic spaces. The results obtained in this paper extend and generalize corresponding results in uniformly convex Banach spaces, CAT(0) spaces and other related results in literature. [ABSTRACT FROM AUTHOR]

In recent years, more and more countries are paying attention to maglev transportation because of its outstanding advantages. However, because the structure of a maglev train is more complex than a wheel-rail train, there is no systematic theory method for kinematic modeling of a maglev vehicle. Based on the screw theory and the product of exponentials (PoE) formula in the field of open-chain robotics, this paper presents a method of kinematic mathematical modeling and analysis for a maglev train and track. By analyzing the characteristics of the closed chain running mechanism of a maglev train, the kinematic mathematical model of a maglev train and track is established, and the motion state of each moving part of the vehicle on a typical track is calculated and analyzed. At last, compared with the results of experiment, the correctness of modeling method proposed in this paper is verified. [ABSTRACT FROM AUTHOR]