Volume 31, Issue 1

In this paper the Walsh system will be considered in the Kaczmarz rearrangement. We estimate the difference between matrix transform means of Walsh–Kaczmarz–Fourier series and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also prove norm convergence with similar conditions.

In this paper, we extend our analysis of the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials, from [W.-P. Düll, B. Hilder and G. Schneider, Analysis of the embedded cell method in 1D for the numerical homogenization of metal-ceramic composite materials, J. Appl. Anal. 24 2018, 1, 71–80]. We show the convergence of the iteration scheme of this algorithm and the coincidence of the material properties predicted by the limit with the effective material properties provided by the analytical homogenization theory for two-dimensional linear hyperelastic isotropic materials with constant shear modulus and slightly varying first Lamé parameter.

The problem of weighted integrability of the Laguerre–Bessel transform in terms of the moduli of smoothness related to generalized translations is considered. Sufficient conditions are given to solve this problem. These results generalize a famous Titchmarsh’s theorem, due to [L. Rakhimi and R. Daher, An analog of Titchmarsh’s theorem for the Laguerre–Bessel transform, Arab. J. Math. Sci. 2023, 10.1108/AJMS-04-2022-0101] in the Laguerre–Bessel hypergroup. Also some results connected with the integrability of Laguerre–Bessel transforms are given.

In this work, we will study the existence of an infinity of solutions of a Navier problem governed by the p ⁢ ( x ) {p(x)} -triharmonic operator using the theory of Ljusternick–Shrilemann and the theory of the variable exponent Sobolev spaces.

In the present paper, some inequalities regarding Csiszár divergence are generalized for diamond integrals by utilizing Green function and Fink’s identity. By selecting various kinds of convex functions, bound of different entropies and divergence measures are obtained. Furthermore, in seek of applications, bounds of different divergence measures are estimated on diverse fixed time scales. These divergence measures are fundamental in problems pertaining to source and channel coding, large deviations theory, and other sorts of problems.

The aim of the present paper is to study invariant pseudoparallel submanifolds in an SQ-Sasakian manifold with respect to semisymmetric metric connection. We search the necessary and sufficient conditions for an invariant submanifold to be totally geodesic under the some hypotheses.

In this research article, we introduce ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables in five different aspects of uncertainty, namely: in mean, in measure, in distribution, in almost sure, and in uniformly almost sure. We also explore the connection between ℐ {\mathcal{I}} -statistically pre-Cauchy sequences and ℐ {\mathcal{I}} -statistically convergent sequences using complex uncertain variables. Additionally, we initiate the study of ℐ {\mathcal{I}} -statistically pre-Cauchy sequences of complex uncertain variables through Orlicz functions.

In this note we consider a family 𝖪𝖡𝖭 {\sf KBN} of filters on ω which are null, with respect to the standard product measure on 2 ω {2^{\omega}} in some strong sense and we prove in 𝖹𝖥𝖢 {{\sf ZFC}} that this class includes all universally measurable filters. Also, we construct 2 𝔠 {2^{\mathfrak{c}}} -many 𝖪𝖡𝖭 {\sf KBN} filters which are not universally measurable and show that the Filter Dichotomy Principle ( 𝖥𝖣𝖯 {{\sf FDP}} ) of A. Blass and C. Laflamme implies that every member of 𝖪𝖡𝖭 {\sf KBN} is meager. In addition, we prove that if the identity min ⁡ { 𝖺𝖽𝖽 ⁢ ( 𝒩 ) , 𝔱 } = 𝔡 {\min\{{\sf add}(\mathcal{N}),\mathfrak{t}\}=\mathfrak{d}} holds, there are non-meager filters in 𝖪𝖡𝖭 {\sf KBN} . Thus, the existence of non-meager 𝖪𝖡𝖭 {\sf KBN} filters is independent of the axioms of 𝖹𝖥𝖢 {{\sf ZFC}} .

In this paper we investigate the concept of ℐ {\mathcal{I}} -monotonic convergence of sequences of bi-complex numbers. We also discuss some partial order relations ≼ i 2 {\preccurlyeq_{i_{2}}} and ≼ i id {\preccurlyeq_{i_{\rm id}}} between two bi-complex numbers and ℐ {\mathcal{I}} -convergence, ℐ {\mathcal{I}} -monotonic sequences with respect to different partial order relations, ℐ {\mathcal{I}} -Cauchy sequences, ℐ {\mathcal{I}} -bounded monotonic sequences of bi-complex numbers. The analysis indicates that ℐ {\mathcal{I}} -monotonicity with respect to ≼ i 2 {\preccurlyeq_{i_{2}}} is not comparable with ℐ {\mathcal{I}} -monotonicity with respect to ≼ i id {\preccurlyeq_{i_{\rm id}}} .

The object of this paper is to conduct an in-depth examination of semi-slant submanifolds within the framework of a conformal Kenmotsu manifolds. Our investigation is centered around identifying and understanding the conditions that ensure the integrability of both invariant and slant distributions, which play a pivotal role in defining semi-slant submanifolds. Additionally, we prove some interesting results for semi-slant submanifolds with parallel canonical structures.

In this paper, we consider the second-order three point boundary value problem on time scales with integral boundary conditions on a half-line. We will use the upper and lower solution method along with the Schauder’s fixed point theorem to establish the existence of at least one solution which lies between pairs of unbounded upper and lower solutions. Further, by assuming two pairs of unbounded upper and lower solutions, the Nagumo condition on the nonlinear term involved in the first-order derivative, we will establish the existence of multiple unbounded solutions on an infinite interval by using the topological degree theory. The results of this paper extend the results of Akcan and Çetin (2018), Akcan and Hamal (2014), Eloe, Kaufmann and Tisdell (2006), and generalize the results of Lian and Geng (2011). Examples are included to illustrate the validation of the results.

In this work, we study stability properties of a well-known integer-order SEIRS model with nonlinear incidence and vertical transmission. Firstly, we introduce a simple approach to the analysis of global asymptotic stability (GAS) of the integer-order model. This approach is based on general quadratic Lyapunov functions and characteristic of quadratic forms associated with real matrices. The result is that the GAS of disease-free and disease-endemic equilibrium points is completely established. This provides an important improvement for results constructed in two previous works. Secondly, we generalize the integer-order SEIRS model by considering it in the context of the Caputo fractional-order derivative. After that, the present approach is utilized to investigate the GAS of the proposed fractional-order model. As an important consequence, not only the GAS but also the uniform stability of the fractional-order model are determined fully. Therefore, the applicability of the approach is shown. Finally, a series of numerical experiments is conducted to illustrate and support the theoretical findings.

The primary objective of this paper is to create a novel infinite Toeplitz matrix by leveraging Tetranacci numbers. This matrix serves as the foundation for defining new sequence spaces denoted as c 0 ⁢ ( G ) {c_{0}(G)} , c ⁢ ( G ) {c(G)} , ℓ ∞ ⁢ ( G ) {\ell_{\infty}(G)} , and ℓ p ⁢ ( G ) {\ell_{p}(G)} , where 1 ≤ p < ∞ {1\leq p<\infty} . By utilizing this newly constructed matrix, the paper also explores and examines various algebraic and topological properties inherent to the sequence spaces c 0 ⁢ ( G ) {c_{0}(G)} , c ⁢ ( G ) {c(G)} , ℓ ∞ ⁢ ( G ) {\ell_{\infty}(G)} , and ℓ p ⁢ ( G ) {\ell_{p}(G)} for values of p within the range of 1 ≤ p < ∞ {1\leq p<\infty} . At last, we also prove existence theorem with example for infinite systems of differential equations in ℓ p ⁢ ( G ) {\ell_{p}(G)} .

The applications of a Fibonacci sequence in mathematics extend far beyond their initial discovery and theoretical significance. The Fibonacci sequence proves to be a versatile tool with real-world implications and the practical utility of manifests in various fields, including optimization algorithms, computer science and finance. In this research paper, we introduce new versions of convergence and summability of sequences in normed spaces with the help of the Fibonacci sequence called weak Fibonacci φ-lacunary statistical convergence and weak Fibonacci φ-lacunary summability, where φ is a modulus function under certain conditions. Furthermore, we obtain some relations related to these concepts in normed spaces.

In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: (i) continuous and (ii) discrete random variables. First, a recursive formula of the joint cumulative distribution function (CDF) is derived in both cases. Then recurrence relations of the joint probability density function (PDF) and the joint probability mass function (PMF) are given in the former and the latter case, respectively. Interestingly, there is a fundamental difference between the joint PDF and PMF. The proofs are simple and mainly based on the following tools from calculus and discrete mathematics: differentiation under the integral sign (also known as Leibniz’s integral rule), the law of total probability, and mathematical induction. In addition, this work generalizes previous results in the literature, and finally presents several extensions of the methodology.

In this article, we introduced the idea of lacunary weak convergence of sequences defined by the class of Orlicz function. Various topological and algebraic properties, such as solidity, symmetry, and monotonicity, have been studied. To validate the failure instances, we gave appropriate examples and detailed discussions. Additionally, we have established some inclusion relationships between these spaces.

In this paper, we focused on a one-dimensional elastic system with a double porosity structure and frictional damping acting on both porous equations. We introduce two stability numbers χ 0 {\chi_{0}} and χ 1 {\chi_{1}} and prove that the solution of the system decays exponentially provided that χ 0 = 0 {\chi_{0}=0} and χ 1 ≠ 0 {\chi_{1}\neq 0} . Otherwise, we prove the absence of exponential decay. Our results improve the results of [N. Bazarra, J. R. Fernández, M. C. Leseduarte, A. Magaña and R. Quintanilla, On the thermoelasticity with two porosities: Asymptotic behaviour, Math. Mech. Solids 24 2019, 9, 2713–2725] and [A. Nemsi and A. Fareh, Exponential decay of the solution of a double porous elastic system, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 83 2021, 1, 41–50].