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The paper presents a technique for determining the time index of growth of the slope of reverse voltage for double insulated cables, based on the body of the theory of series. It is proved that in the vicinity of the extremum point (maximum) the function of the reverse voltage is approximated by polynomials of the nth power. It is proposed to use second-degree polynomials for practical calculations. The method for calculating relevant indicators is illustrated using real data. Analysis of deviations made it possible to conclude that the calculation method proposed in the paper is far more accurate. In the final part of the study, it was concluded that there is a promising outlook for further development of methodological guidelines for determining complex indices of the remaining life of the cable, including but not limited to the use of various mathematical methods. [ABSTRACT FROM AUTHOR]

This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semi-groups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S · S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials. [ABSTRACT FROM AUTHOR]

The paper presents a technique for determining the time index of growth of the slope of reverse voltage for double insulated cables, based on the body of the theory of series. It is proved that in the vicinity of the extremum point (maximum) the function of the reverse voltage is approximated by polynomials of the nth power. It is proposed to use second-degree polynomials for practical calculations. The method for calculating relevant indicators is illustrated using real data. Analysis of deviations made it possible to conclude that the calculation method proposed in the paper is far more accurate. In the final part of the study, it was concluded that there is a promising outlook for further development of methodological guidelines for determining complex indices of the remaining life of the cable, including but not limited to the use of various mathematical methods. [ABSTRACT FROM AUTHOR]

Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms. [ABSTRACT FROM AUTHOR]

For the perturbed Hamiltonian of a multifrequency resonance harmonic oscillator, a new approach to calculating the coefficients in the procedure of quantum averaging is proposed. The procedure of quantum averaging is transferred to the space of the graded algebra of symbols by using twisted product introduced in the paper. As a result, the averaged Hamiltonian is represented as a function of generators of the quantum symmetry algebra of the harmonic part of the Hamiltonian. The proposed method is applied to the spectral problem for the Hamiltonian of the cylindrical Penning trap. [ABSTRACT FROM AUTHOR]

In their celebrated paper (Furst et al., Math. Syst. Theory 17(1), 13-27 (12)), Furst, Saxe, and Sipser used random restrictions to reveal the weakness of Boolean circuits of bounded depth, establishing that constant-depth and polynomial-size circuits cannot compute the parity function. Such local restrictions have played important roles and have found many applications in complexity analysis and algorithm design over the past three decades. In this article, we give a brief overview of two intriguing applications of local restrictions: the first one is for the Isomorphism Conjecture and the second one is for moderately exponential time algorithms for the Boolean formula satisfiability problem. [ABSTRACT FROM AUTHOR]

This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from [1] through two applications, referring to inequalities from papers [2] and [3]. [ABSTRACT FROM AUTHOR]

Refereed conferences require every submission to be reviewed by members of a program committee (PC) in charge of selecting the conference program. There are many software packages available to manage the review process. Typically, in a bidding phase PC members express their personal preferences by ranking the submissions. This information is used by the system to compute an assignment of the papers to referees (PC members). We study the problem of assigning papers to referees. We propose to optimize a number of criteria that aim at achieving fairness among referees/papers. Some of these variants can be solved optimally in polynomial time, while others are NP-hard, in which case we design approximation algorithms. Experimental results strongly suggest that the assignments computed by our algorithms are considerably better than those computed by popular conference management software. [ABSTRACT FROM AUTHOR]

Self-interference (SI) represents a bottleneck in the performance of full-duplex (FD) communication systems, necessitating robust offsetting techniques to unlock the potential of FD systems. Currently, deep learning has been leveraged within the communication domain to address specific challenges and enhance efficiency. Inspired by this, this paper reviews the self-interference cancellation (SIC) process in the digital domain focusing on SIC capability. The paper introduces a model architecture that integrates CNN and gated recurrent unit (GRU), while also incorporating residual networks and self-attention mechanisms to enhance the identification and elimination of SI. This model is named CGRSA-Net. Firstly, CNN is employed to capture local signal features in the time–frequency domain. Subsequently, a ResNet module is introduced to mitigate the gradient vanishing problem. Concurrently, GRU is utilized to dynamically capture and retain both long- and short-term dependencies during the communication process. Lastly, by integrating the self-attention mechanism, attention weights are flexibly assigned when processing sequence data, thereby focusing on the most important parts of the input sequence. Experimental results demonstrate that the proposed CGRSA-Net model achieves a minimum of 28% improvement in nonlinear SIC capability compared to polynomial and existing neural network-based eliminator. Additionally, through ablation experiments, we demonstrate that the various modules utilized in this paper effectively learn signal features and further enhance SIC performance. [ABSTRACT FROM AUTHOR]

This paper introduces cutting planes that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set S ∩ P , where S is a closed set, and P is a polyhedron. Given an oracle that provides the distance from a point to S, we construct a pure cutting plane algorithm which is shown to converge if the initial relaxation is a polyhedron. These cuts are generated from convex forbidden zones, or S-free sets, derived from the oracle. We also consider the special case of polynomial optimization. Accordingly we develop a theory of outer-product-free sets, where S is the set of real, symmetric matrices of the form x x T . All maximal outer-product-free sets of full dimension are shown to be convex cones and we identify several families of such sets. These families are used to generate strengthened intersection cuts that can separate any infeasible extreme point of a linear programming relaxation efficiently. Computational experiments demonstrate the promise of our approach. [ABSTRACT FROM AUTHOR]

The enhanced power graph of a group G is a simple undirected graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we obtain the Laplacian spectrum of the enhanced power graph of certain non-abelian groups, viz. semidihedral, dihedral and generalized quaternion. Also, we obtained the metric dimension and the resolving polynomial of the enhanced power graphs of these groups. At the final part of this paper, we study the distant properties and the detour distant properties, namely: closure, interior, distance degree sequence, eccentric subgraph of the enhanced power graph of semidihedral group, dihedral group and generalized quaternion group, respectively. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a numerical method for solving time-fractional diffusion equations. To obtain the numerical solution, a binary reproducing kernel space is defined, and the orthonormal basis is constructed based on Legendre polynomials in this space. In order to find the ε-approximation solution of time-fractional diffusion equations, which is defined in this paper, the algorithm is designed using the constructed orthonormal basis. Some numerical examples are analyzed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that the presented method is considerably accurate and effective, as expected. [ABSTRACT FROM AUTHOR]

For a simple, finite, and connected graph G, the spherical maximal operator is defined as ... where ... is the sphere with center at t and having radius r. In this paper, we consider the spherical maximal operator ... on ... spaces and calculate the ... for ... and estimate the ... for ..., when G is Km. Furthermore, We establish the maximum and minimum bounds for the spherical maximum operator on finite graphs and indicate the graphs that achieve these bounds. [ABSTRACT FROM AUTHOR]

Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

Let k be a field of characteristic 0, and let f : kn→kn be a polynomial map with components of the form fi=xi+hi, where the hi are monomials. If the Jacobian determinant of the map f is a nonzero constant, then f is a tame automorphism. If, in addition, each hi is either constant or of degree 2 or more, then f is linearly triangularizable. [Copyright &y& Elsevier]

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]

Abstract: Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in -norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result. [Copyright &y& Elsevier]

Full spherical views provide advantages in many applications that use visual information. Dual back-to-back fisheye cameras are receiving much attention to obtain this type of view. However, obtaining a high-quality full spherical view is very challenging. In this paper, we propose a correction step that models the relation between the pixels of the pair of fisheye images in polar coordinates. This correction is implemented during the mapping from the unit sphere to the fisheye image using the equidistant fisheye projection. The objective is that the projections of the same point in the pair of images have the same position on the unit sphere after the correction. In this way, they will also have the same position on the equirectangular coordinate system. Consequently, the discontinuity between the spherical views for blending is minimized. Throughout the manuscript, we show that the angular polar coordinates of the same scene point in the fisheye images are related by a sine function and the radial distance coordinates by a linear function. Also, we propose employing a polynomial as a geometric transformation between the pair of spherical views during the image alignment since the relationship between the matching points of pairs of spherical views is not linear, especially in the top/bottom regions. Quantitative evaluations demonstrate that using the correction step improves the quality of the full spherical view, i.e. IQ MS-SSIM, up to 7%. Similarly, using a polynomial improves the IQ MS-SSIM up to 6.29% with respect to using an affine matrix. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of meromorphic functions with q-shift difference-differential polynomials F = [P(f)L(z, f)s](k) and G = [P(g)L(z, g)s](k), where P(z) is a non-constant polynomial with degree n sharing a finite value. The results of this paper are an extension of the previous theorems given by Harina P. Waghamore and Rajeshwari S [19]. [ABSTRACT FROM AUTHOR]

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O (n 6) time, where n is the number of jobs. [ABSTRACT FROM AUTHOR]

Starting from a characterization of polynomial dichotomy by means of admissibility, recently proved in [Dragicevic, D.; Sasu, A. L.; Sasu, B. Admissibility and polynomial dichotomy of discrete nonautonomous systems. Carpath. J. Math. 38 (2022), 737-762.], the aim of this paper is to explore the roughness of polynomial dichotomy in the presence of perturbations and to obtain a new robustness criterion. We show that the polynomial dichotomy is robust when subjected to linear additive perturbations which are bounded by a well-chosen sequence. We emphasize that the new bounds imposed to the perturbation family improve and extend the previous approaches. Furthermore, we mention that the main result applies to discrete nonautonomous systems in Banach spaces with the only requirement that their propagators exhibit a polynomial growth. [ABSTRACT FROM AUTHOR]

In this paper, we study and characterize the nilpotent global centers of a generalized polynomial Kukles system with degree three. A sufficient and necessary condition of global centers is established under certain parametric conditions. [ABSTRACT FROM AUTHOR]

The primary aim of this paper is to investigate the asymptotic distribution of the zeros of certain classes of hypergeometric $ {}_{q+1}F_{q} $ q + 1 F q polynomials. We employ classical analytical techniques, including Watson's lemma and the method of steepest descent, to understand the asymptotic behavior of these polynomials: $$\begin{align*} & _{q+1}F_{q}\left(-n,kn+\alpha,\ldots, kn+\alpha+\frac{q-1}{q};kn+\beta,\ldots,kn+\beta+\frac{q-1}{q};z\right)\\ &\quad (n\rightarrow \infty), \end{align*} $$ q + 1 F q (− n , kn + α , ... , kn + α + q − 1 q ; kn + β , ... , kn + β + q − 1 q ; z) (n → ∞) , where n is a nonnegative integer, q is a positive integer and the constant parameters α and β are constrained by $ \alpha { α < β. By applying the general results established in this paper, we generate numerical evidence and graphical illustrations using Mathematica to show the clustering of zeros on certain curves. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping (- Δ) 2 θ v t with θ ∈ [ 1 2 , 1 ] . By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and θ ∈ [ 1 2 , 3 4 ] , the polynomial decay rate of the system is t - 1 / (10 - 4 θ) . When the inertia/elasticity ratios are not equal and θ ∈ [ 3 4 , 1 ] , the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent 2 θ from [0, 1] to [1, 2]. [ABSTRACT FROM AUTHOR]

In this paper, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by Fonseca and Mello, a homogeneous involution naturally appears when dealing with graded polynomial identities and a compatible involution. [ABSTRACT FROM AUTHOR]

Assume that we are given a sequence F of k homogeneous polynomials in n variables of degree at most d and the ideal ℐ generated by this sequence. The aim of this paper is to present a new and effective method to determine, within the arithmetic complexity d O (n) , whether F is regular. This algorithm has been implemented in Maple and its efficiency (compared to the classical approaches for regular sequence test) is evaluated via a set of benchmark polynomials. Furthermore, we show that if F is regular then we can transform ℐ into Nœther position and at the same time compute a reduced Gröbner basis for the transformed ideal within the arithmetic complexity d O (n 2) . Finally, under the same assumption, we establish the new upper bound 2 (d k / 2) 2 n − k − 1 for the maximum degree of the elements of any reduced Gröbner basis of ℐ in the case that n > k. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of a fourth-order Newtonian iterative method for finding roots of polynomials of degrees three and four. Unlike traditional fourth-order methods requiring third derivatives, this technique avoids them by using the same derivative order in each of its three steps per iteration. When applied to differentiable functions, the method generates chaotic dynamics, as shown for quartic polynomials. Specifically, we apply this root-finding approach to the bifurcation diagram of the logistic map over an interval. Our findings demonstrate the potential for complex behavior even in simple iterative methods, and highlight the usefulness of this approach for exploring polynomial system dynamics. The paper identifies examples of fourth-degree polynomials, explains bifurcation, and chaos. [ABSTRACT FROM AUTHOR]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

Polynomial multiplication is the most computationally expensive part of the lattice-based cryptography algorithm. However, the existing acceleration schemes have problems, such as low performance and high hardware resource overhead. Based on the polynomial multiplication of number theoretic transformation (NTT), this paper proposed a simple element of Montgomery module reduction with pipeline structure to realize fast module multiplication. In order to improve the throughput of the NTT module, the block storage technology is used in the NTT hardware module to enable the computing unit to read and write data alternately. Based on the NTT hardware module, a precalculated parameter storage and real-time calculation method suitable for the hardware architecture of this paper is also proposed. Finally, the hardware of polynomial multiplier based on NTT module is implemented, and its function simulation and performance evaluation are carried out. The results show that the proposed hardware accelerator can have excellent computing performance while using fewer hardware resources, thus meeting the requirements of lattice cipher algorithms in security chips. Compared with the existing studies, the computing performance of the polynomial multiplier designed in this paper is improved by approximately 1 to 3 times, and the slice resources and storage resources used are reduced by approximately 60% and 17%, respectively. [ABSTRACT FROM AUTHOR]

Let n be a positive integer. An NFSR of n stages is called irreducible if the family of output sequences of any NFSR of stages less than n is not included in that of the NFSR. In this paper, we prove that the density of the irreducible NFSRs of n stages is larger than 0.39. This implies that it is expected to find an irreducible NFSR of n stages among three randomly chosen NFSRs of n stages. [ABSTRACT FROM PUBLISHER]

In this paper, the sequence families of which maximum correlation is determined by the Weil bound of exponential sums are revisited. Using the same approach, two new constructions with large family sizes and low maximum correlation are given. The first construction is an analog of one recent result derived from the interleaved structure of Sidel'nikov sequences. For a prime p and an integer M\vert (p-1), the new M-ary sequence families of period p are obtained from irreducible quadratic polynomials and known power residue-based sequence families. The new sequence families increase family sizes of the known power residue-based sequence families, but keep the maximum correlation unchanged. In the second construction, the sequences derived from the Weil representation are generalized, where each new sequence is the elementwise product of a modulated Sidel'nikov sequence and a modulated trace sequence. For positive integers d

A color correction method for balancing the color appearances, among a group of images, about a specified object or scene, such as panoramic images and object movies, is developed and tested in this paper. In order to increase the running speed of color correction and reduce the out-of-gamut color pixels, we introduce the selection of principal regions. The average color values of principal regions are used to construct the low-degree (up to degree two) polynomial mapping functions from the source images to the corrected images. The functions are run in the decorrelated color spaces. Our method is tested using real and synthetic images. The results of these tests show the proposed method can get a better performance than other existing methods. [Copyright &y& Elsevier]

This paper introduces the operational rule for 2-iterated 2D Appell polynomials and derives its generalized form using fractional operators. It also presents the generating relation and explicit forms that characterize the generalized 2-iterated 2D Appell polynomials. Additionally, it establishes the monomiality principle for these polynomials and obtains their recurrence relations. The paper also establishes corresponding results for the generalized 2-iterated 2D Bernoulli, 2-iterated 2D Euler, and 2-iterated 2D Genocchi polynomials. [ABSTRACT FROM AUTHOR]

The modified RSA provides high efficiency against attacks and, as a result, it is considered the ideal choice for many applications. In this paper, we introduce an alternative to the modified RSA key encryption system called TPRSA, based on Tri-Cartesian algebra and polynomials, by modifying the mathematical structure of text encryption and decryption keys to obtain a high level of security. [ABSTRACT FROM AUTHOR]

In this paper, a new family of iterative methods for the simultane-ous approximation of simple complex polynomial zeros is presented. The proposed family of simultaneous methods is constructed on the basis of the well-known third order Ehrlich iteration, combined with an iterative correction from the sixth order Neta's method for nonlinear equations. It is proved that the use of this iterative correction allows to increase the convergence order of the basic method from three to eight. Numerical examples are given to illustrate the convergence and effectiveness of the proposed combined method. [ABSTRACT FROM AUTHOR]

This paper presents a modified version of Leibman's group-theoretic generalizations of the difference calculus for polynomial maps from nonempty commutative semigroups to groups, and proves that it has many desirable formal properties when the target group is locally nilpotent and also when the semigroup is the set of nonnegative integers. We will apply it to solve Waring's problem for general discrete Heisenberg groups in a sequel to this paper. [ABSTRACT FROM AUTHOR]