This study introduces the notion of pairwise meta-P-closed spaces, serving as a logical extension of pairwise P-closed spaces. It examines the inter connections among pairwise meta-P-closed, pairwise P-closed, and pairwise L-closed spaces, identifies their hereditary characteristics, and assesses their stability under pairwise homeomorphisms. Furthermore, we prove that every p.w.T2, pairwise regular, pairwise meta-P-closed bitopological space is pairwise normal under weaker covering assumptions than full paracompactness. Several characterizations and product results are obtained.
This paper introduces a new test for the homogeneity of several covariance matrices in high-dimensional data under the p-variate normal distribution. The test is constructed using U-statistic-based estimators to evaluate differences among covariance matrices, and applies an inverse-variance-weighted method to quantify the relative importance of these estimators. Its distribution under the null hypothesis is derived and follows a chi-square distribution as the dimension and sample sizes increase. Simulation results indicate that the test controls the Type I error rate better than three existing methods and achieves high power. To demonstrate its practical applicability, two real gene-expression datasets involving three- and four-group comparisons are analyzed.
This paper investigates the structural behavior of the exponential Pell-type Diophantine equation $$x^2 = 11y^2 - 7^t$$ for $$t \in \mathbb{Z}^+$$ and provides a complete characterization of its solvability. Using modular arguments and properties of the Legendre symbol, we show that the equation admits no integer solutions when the exponent $$t$$ is even, whereas infinitely many nontrivial solutions arise when $$t$$ is odd. In the solvable case, Brahmagupta’s composition law and the fundamental unit of the Pell equation $$x^2 - 11y^2 = 1$$ are employed to construct explicit solution sequences. These solutions satisfy second-order linear recurrences, admit closed-form expressions, and preserve quadratic and quartic algebraic invariants. Numerical computations support the theoretical results and highlight the sharp contrast between the solvable and unsolvable cases. This work extends classical Pell-type theory to exponential Diophantine equations with mixed quadratic–exponential structure.
This paper presents global computational problems related to establishing lower bounds for highdimensional continuous functions over a simplex. We propose a rigorous approach to constructing affine lower bounds (ALB) that remain closely beneath the original function. By extending the least squares method for control Bernstein, we develop a convergent AB to both polynomials and rational functions. Furthermore, we demonstrate that these bounds achieve high convergence rates to the original functions. Finally, we evaluate our approach by comparing it with previous methods using error bound approximation.
The zero-inflated Rayleigh distribution combines zero values and a standard Rayleigh distribution that represents positive values. Percentiles are widely used tools for measuring data, particularly in skewed continuous datasets. This study aims to construct confidence intervals (CIs) for the percentile of the zero-inflated Rayleigh distribution. The proposed approaches include the generalized confidence interval (GCI), normal approximation (NA), and the percentile bootstrap confidence interval (PBCI). The zero-inflation probability is estimated using the variance-stabilizing transformation (VST), Wilson's Score, and Hannig’s methods. Their performances were evaluated using Monte Carlo simulations in R programming, comparing coverage probabilities (CPs) and average lengths (ALs). The results indicate that the GCI based on the VST outperformed the other methods. Additionally, the proposed CIs were applied to car accident mortality data in central Thailand to evaluate their practical efficacy.
The proposed approximation of a function of several variables is based on the direct product of local splines of one variable. The approximation is built on each elementary parallelepiped separately and is reduced to calculating the sum of the products of the function values and the basis splines. The use of non-polynomial basis splines with different properties in different directions allows us to obtain a qualitatively better approximation. Solving the Fredholm integral equation of the second kind of several variables is reduced to calculating the integrals of the product of the kernel and the basis splines and solving a system of linear algebraic equations. A comparison of the results of the numerical solution of integral equations by the proposed method and the results of applying other methods is given.
This paper presents a rigorous mathematical analysis of a two-species chemotaxis-competition model on weighted networks, incorporating nonlinear degenerate chemotactic sensitivities and volume-filling effects. The aim is to understand long-term population dynamics in networked environments. Using a Lyapunov functional approach, we characterize the asymptotic behavior of solutions. Under weak competition, coexistence occurs with exponential convergence, while strong competition leads to the extinction of one species and algebraic convergence to a segregated state. These theoretical results are validated through numerical simulations that highlight the effects of competition parameters, network topology, and initial conditions. The proposed numerical scheme demonstrates convergence with exponential or algebraic decay of relative errors, in agreement with the analytical results. This study highlights the role of network structure in shaping chemotaxis-driven competitive dynamics.
The purpose of this article is to systematically explore the geometric properties of finite and infinite Blaschke products, as well as of the Dirichlet functions generated by them. Computer-generated graphics are intended to illustrate symmetries, to portray their fundamental domains, and to explore their global mapping properties. They are also instrumental in the extrapolation of the properties of finite Blaschke products to the case of infinite ones, where non-isolated singular points appear. The behavior of an analytic function in the neighborhood of an isolated essential singular point is described by Picard’s theorem, yet this theorem is not applicable to essential non-isolated singular points. The geometric approach we are using allows us to deal with such situations in both the cases of infinite Blaschke products and the Dirichlet functions generated by these products.
This paper establishes a common fixed point theorem for six weakly compatible mappings in complete M∗-metric spaces, generalizing previous results in D∗-metric and related spaces. We introduce enhanced versions of fixed point theorems under weak compatibility conditions, leveraging a continuous and increasing function ϕ to derive contraction inequalities. Our main theorem demonstrates the existence and uniqueness of a common fixed point, supported by illustrative examples. Additionally, we extend these findings to families of mappings, ensuring broader applicability. The results contribute to fixed point theory in generalized metric spaces, offering potential applications in nonlinear analysis and differential equations. This paper builds upon and refines existing literature, providing a foundation for further research in metric space fixed point theory.
This study surveyed the nonlinear dynamics of a discrete-time, stage-structured population model merging demographic memory through adult survival. The model develops the classical θ–Ricker formulation by introducing cross-stage feedback between juvenile and adult compartments governed by a set of biologically interpretable parameters. The analytical results show that the system admits a unique positive equilibrium, the local stability of which is determined by the trace and determinant of the Jacobian matrix. Loss of stability occurs via two primary mechanisms: flip (period doubling) and Neimark–Sacker bifurcations. Explicit conditions for both bifurcations are derived, and the first Lyapunov coefficient is computed to characterize the direction and criticality of the Neimark–Sacker (NS) transition. Numerical experiments, including one-parameter bifurcation diagrams and two-parameter Lyapunov maps, confirmed the analytical predictions. Increasing the reproductive rate or cross-stage feedback leads to successive period doubling and chaos, whereas higher maturation efficiency and adult survival expand the stability domain. The results revealed that demographic memory acts as an internal damping mechanism that delays the onset of instability and suppresses chaotic oscillations. Overall, this study provides a coherent analytical–numerical framework for understanding how feedback and memory interact to shape complex population dynamics in stage-structured ecological systems.
This paper presents the new extended Benney-Luke equation in (2+1)-dimensions, and various solutions have been found based on the bilinear neural network method. Using the Hirota bilinear operator, the (2+1)-dimensional Benney-Luke equation is transformed into a bilinear form and yields exact analytic solutions by establishing a sequence of neurons corresponding to the procedure.
The significance of this research lies in the generalization of curvature tensors, particularly the concircular curvature tensor, which is studied as a fifth recurrent tensor within the framework of Cartan’s fourth curvature tensor. It contributes to the fundamental understanding of geometric properties in Finsler spaces. This paper builds upon new the concircular curvature tensor 𝑀𝑖𝑗𝑘ℎ in generaralized fifth recurrent Finsler space that Cartan's fourth curvature tensor 𝐾𝑗𝑘ℎ 𝑖 in sense of Berwald (𝐺ℬ𝐾 − 5𝑅𝐹𝑛) via Lie derivative. We obtain the relation between the concircular curvature tensor 𝑀𝑖𝑗𝑘ℎ , conformal curvature tensor 𝐶𝑖𝑗𝑘ℎ , conharmonic curvature tensor 𝐿𝑖𝑘ℎ 𝑟 and associate curvature tensor 𝑅𝑖𝑗𝑘ℎ if the metric tensor 𝑔𝑟𝑗 = 1 by Lie - derivative. Also, we show these curvature tensors have the same extension and direction. In addition, the concircular curvature tensor and conharmonic curvature tensor 𝐿𝑗𝑘ℎ 𝑖 are co-directional. We prove that the concircular curvature tensor 𝑀𝑖𝑗𝑘ℎ behaves as fifth recurrent by Lie derivative in the main space.
The Erdös-Straus conjecture states that for every positive integer n ≥ 2, there exist three natural numbers x, y, and z, not necessarily distinct, so that 1/x + 1/y + 1/z = 4/n. In this paper, we consider the Diophantine equation 2/x+3/y+4/z =1/3. We find positive solutions of this Diophantine equation.
In this paper is developed a mathematical framework for uncertainty quantification in energy systems through Uncertainty Cost Functions (UCFs), in order to schedule the operation. We establish probabilistic models for solar photovoltaic generation, wind energy generation, and plug-in electric vehicles, deriving exact expressions for expected penalty costs using measure-theoretic probability. The main results include existence theorems for UCFs, closed-form solutions under specific distributional assumptions, and optimal scheduling policy.
This present paper extends the results of the authors on structured matrices in the work ”On properties between G-matrices and Hyper G-matrices”. In particular, Hessenberg, tridiagonal, companion, and backward matrices are investigated. Many examples are provided and some open questions are mentioned.
Any cryptographic technique plays a crucial role in ensuring the transfer of important, sensitive and confidential data through any sort of insecure medium and delivers the message intact to the intended and authenticated parties. Failing in any of these functionalities makes such cryptosystem obsolete in the modern technology. The study of any algorithm about its weakness and using that to decrypt the message without using any key is called cryptanalysis. In this paper, we present the cryptanalysis of two algorithms based on graph theory . The algorithms are studied in detail through different examples and explored all possible vulnerabilities.
In this paper, we consider the nonlocal Cahn-Hilliard equation with a fidelity term and singular nonlinearities, which has numerous applications in biology and image inpainting. First, we prove the existence of a unique solution. We approximate the singular nonlinearities by regular nonlinearities, from which we derive important priori-estimates for the solution of the approximating problem. We then establish the existence of a solution to the approximating problem using the Faedo-Galerkin method. Additionally, we demonstrate that the solution of the Cahn-Hilliard equation in question is of higher regular by applying Sobolev embedding theorems. Finally, we discuss the important separation property of the solution that allows us to obtain a global (in time) unique solution of the problem.
