878 Results Found

We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a conjecture of Bernevig and Haldane stated in the context of the fractional quantum Hall ef...

We investigate the computational complexity of deciding whether a given univariate integer polynomial $p\left(x\right)$ has a factor $q\left(x\right)$ satisfying specific additional constraints. When the only constraint imposed on $q\left(x\right)$ is to have a degree smaller than the deg...

The Rivest–Shamir–Adleman (RSA) cryptosystem is currently the most influential and commonly used algorithm in public-key cryptography. Whether the security of RSA is equivalent to the intractability of the integer factorization problem is...

We introduce and study several conditions related to the factorization problem of composite numbers. For this purpose, we employ cyclotomic polynomials, Sylvester resultants, and the Fermat equation. For instance, we show that for $m\in \mathbb{N}$ and distin...

This article has a motive to derive a new class of differential equations and associated integral equations for some hybrid families of Laguerre–Gould–Hopper-based Sheffer polynomials. We derive recurrence relations, differential equation...

The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ${\rho }_0={}_2{F}_1\left[\begin{array}{c}a,b\\ c+1\end{array};\eta \right]$. For the Gauss h...

In this paper, we propose a discrete model for the quantum harmonic oscillator. The eigenfunctions and eigenvalues for the corresponding Schrödinger equation are obtained through the factorization method. It is shown that this problem is also co...

In this paper, we introduce and study the Tricomi continuants, a family of tridiagonal determinants forming a Sheffer sequence closely related to the Tricomi polynomials and the Laguerre polynomials. Specifically, we obtain the main umbral operators...

The normality polynomial and multi-linear regression approaches are revisited for estimating the reliability index, its precision, and other reliability-related values for coastal and structural engineering applications. In previous studies, neither...

In this study, we investigated the recent deterioration of the radiation pattern performance of conformal arrays, which are applied to fields such as aircraft and vehicles. We analyzed the radiation pattern of conformal arrays in the array factor sta...

To realize the in-motion alignment of the strapdown inertial navigation system (SINS) under the geographic latitude uncertainty, we propose a latitude estimation and in-motion alignment method based on the integral dynamic window and polynomial fitti...

The non-Gaussian property and its influence on peak factors and extreme wind pressures on the long-span cylindrical roof are studied in this paper. Firstly, the moment-based Hermite polynomial model (HPM), which is used to determine peak factors of n...

Innovative designs such as morphing wings and terrain adaptive landing systems are examples of biomimicry and innovations inspired by nature, which are actively being investigated by aerospace designers. Morphing wing designs based on Variable Geomet...

In this paper, a lifetime estimation method for underground cable systems is proposed by combining a health index (HI) and conditional factor (CF). The underground cable system consists of underground cable, joint, termination, manhole, and duct bank...

This paper explores the effect of meteorological factors such as rainfall, temperature, sunshine, wind speed, and relative humidity on the yield of maize (Zea mays L.) and sorghum (Sorghum bicolor L.) at different growth stages in Togo’s Platea...

Security and access control aspects are becoming more and more essential to consider during the design of various systems and the tremendous growth of digitization. One of the related key building blocks in this regard is, essentially, the authentica...

This paper proposes a semiparametric local polynomial estimator for modelling agricultural time-series. We consider the modelling of the crop yield variable according to determined financial risk factors in Turkey. The derivation of a semiparametric...

We study high-order predictor–corrector schemes for the simultaneous computation of polynomial roots with known multiplicities. The proposed method, BKM_*, combines a fourth-order two-step modified Newton approximation, a coupled Ehrlich-type pr...

Motivation: We aim to study the boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is largely a review work, which attempts to congregate the fie...

We study two-tone factors in edge-connected regular graphs and claw-free cubic graphs under red-blue vertex colorings. A two-tone factor is a spanning subgraph in which vertices of different colors are assigned different allowed degree sets. For edge...

Fully Homomorphic Encryption (FHE) allows computations on encrypted data without decryption, providing strong security for sensitive information. However, computational and memory demands for FHE are significant challenges, particularly in the Number...

The subject of the work was the evaluation of maize protein yield conditioned by various agrotechnical factors. The test results are derived from two different field experiments covering a total of seven years of observation. Protein yield was signif...

Let M be a torsion-free module over an integral domain D. We define a concept of a unique factorization module in terms of v-submodules of M. If M is a unique factorization module (UFM), then D is a unique factorization domain. However, the converse...

The classical method of quantitative structure-activity relationships (QSAR) is enriched using non-linear models, as Thom’s polynomials allow either uni- or bi-variate structural parameters. In this context, catastrophe QSAR algorithms are applied to...

The design and implementation of efficient photovoltaic (PV) plants and wind farms require a precise analysis and definition of specifics in the region of interest. Reliable Artificial Intelligence (AI) models can recognize long-term spatial and temp...

Let ${\mathbb{F}}_q$ be a finite field, and let n be a positive integer such that $\gcd (q,n)=1$. The irreducible factors of $x^n-1$ and $x^n-\lambda$ are fundamental concepts with wide applications in cyclic codes and constacyclic codes. Furthermore, the numbe...

In the field of mechanical engineering, inclined rubber bearings reduce vertical stiffness through tilted arrangement to effectively isolate environmental vibrations. When applied to large-scale structural engineering, however, further attention must...

We generalize Schrödinger’s factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach is the fact that the Hamiltonian is represented...

The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become ge...

Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, the (edge-)Mostar index, and the (vertex-)PI index. For these indices, the corresponding polynomials were also...

We present an adaptive certifying semi-algorithm for rational second-order ordinary differential equations (ODEs) in the Darboux-representative, non-degenerate subclass of the Liouvillian setting considered here. The method first computes a nonlocal...

For a fixed orthogonal polynomial sequence, classical orthonormalization changes the polynomials by degree-dependent scalar factors. If the polynomials themselves are kept fixed, scalar-measure normalization is usually impossible; on a compact interv...

This study investigates the algebraic and differential properties of balancing-like polynomials, which constitute a polynomial extension of balancing-like sequences. Several fundamental properties are established, including matrix representations, ad...

A divisor B of a nonzero polynomial A, defined over the prime field of two elements, is unitary (resp. bi-unitary) if $gcd(B,A/B)=1$ (resp. $gc{d}_u(B,A/B)=1)$, where $gc{d}_u(B,A/B)$ denotes the greatest common unitary divisor of B and $A/B$. We denote by ${\sigma }^{}$...

Let k be a positive integer. A polynomial $A\in {\mathbb{F}}_2\left[x\right]$ is called k-unitary perfectif the sum of the k-th powers of its distinct unitary divisors equals $A^k$. In this paper, we study the case $k=2^n$ and prove that every $2^n$-unitary perfect polynomial over...

Several variants of the edit distance problem with block deletions are considered. Polynomial time optimal algorithms are presented for the edit distance with block deletions allowing character insertions and character moves, but without block moves....

In this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius–Euler–Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomi...

We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expand...

The efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems’ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a tradi...

In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial diffe...

In this paper, we have obtained the prime factorization form of positive integers N for which the number of true different fourth- and fifth-degree permutation polynomials (PPs) modulo N is equal to zero. We have also obtained the prime factorization...

In this paper, we consider the generalized degenerate Bernoulli/Euler polynomial matrices and study some algebraic properties for them. In particular, we focus our attention on some matrix-inversion formulae involving these matrices. Furthermore, we...

This study examines the relationship between the Potts model in statistical mechanics and mathematical knots. This is done by transforming the Potts model into knot polynomials. The knot polynomial in the Kauffman square brackets is used. Temperley&n...

For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs). This paper proposes a method of pre...

This paper proposes a lightweight polynomial-based encryption architecture for resource-constrained IoT and wireless communication hardware. Instead of substitution boxes, the method uses key-dependent polynomial multiplication with minimal polynomia...

Bairstow’s method employs synthetic division to express a polynomial $p\left(x\right)$ of degree n in the form $p\left(x\right)=q\left(x\right)(x^2+Bx+C)+R(B,C)x+S(B,C)$, where $q\left(x\right)$ is the quotient polynomial of degree $n-2$, and $R(B,C)$, $S(B,C)$ are the remainder coefficients th...

In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to counting points on a...

The reflectivity of the bare soil surface (BSS) is influenced by soil type, moisture, salinity, tillage, erosion, and other factors. To investigate the direct impact of erosion on the spectral characteristics of the BSS (SCBSS), a study site in the f...

We provide a comprehensive presentation of algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers as implemented in the freely available Basic P...

Background: Machine learning (ML) can keep improving predictions and generating automated knowledge via data-driven predictors or decisions. Objective: The purpose of this study was to compare different ML methods including random forest, logistics r...