Journal of Mathematics Research, Issue: Vol.18, No.2

Almost Hermitian Statistical Manifolds

Fri, 19 Jun 2026 08:48:36 +0000

Statistical manifolds which were developed to provide a set of probability distributions with a differentiable structure (Amari, 1985), play a major role in the geometric study of information. These manifolds are now regarded as the foundation for the study of the geometry of information transfer, data analysis and quantification. These manifolds with quasi-complex structures are naturally appear in many geometric contexts, notably in information geometry and statistical inference. The using these methodologies is intended to facilited the quantification and extraction the best information from a statistical model (Amari and Nagaoka, 2000). Thus, the study of statistical manifolds with quasi-complex structures allows us to understand the possible interactions between information geometry and complex structures. It has been shown in (Zhang and Fei, 2018) that assuming the existence of a quasi-complex structure J on a statistical manifold (M,g,\nabla), then (M,g,J,\nabla) is (para-)K?hlerian on the condition that (J,\nabla) is a Codazzi pair. Manifolds with quasi-complex structure which a metric is Norden have been the subject of detailed inverstigation (Leila et al., 2022). In this work, the condition for the compatibility of the Hermitian structure and that of statistical manifolds are examined.For document, after the first section reserved for the introduction, section 2 devoted to the presentation of the different structures is presented. Section 3 presents the main results obtained and the construction of a more general example. Finally, section 4 examines the special case of parametric statistical models of even dimension. We have also considered such a mo

A Modified Firefly Algorithm Adaptive to the Single-Stage Fixed Charge Transportation Problem

Fri, 19 Jun 2026 09:18:44 +0000

The transportation problem is primarily concerned with the ways in which resources can be transported from supply centers to final customers with minimum total transportation costs. In addition to variable transportation costs, the single-stage fixed charge transportation problem (FCTP) has become a more challenging and complex optimization problem due to the inclusion of fixed route activation costs. Therefore, since it is difficult to obtain optimal solutions for these problems in a reasonable time, heuristic algorithms are used to obtain more qualitative and accurate solutions. This study proposes a modified firefly optimization algorithm to efficiently obtain high-quality near-optimal solutions. The enhanced algorithm improves convergence behavior and robustness and is implemented in Python for computational efficiency. The performance is observed and evaluated on numerical experiments across different problem scales. Here, the solutions of the proposed algorithm are compared with other existing heuristic algorithms through numerical experiment analysis. The numerical experiments conducted across different problem scales show that the proposed method performs competitively with existing heuristics and provides superior results for large-scale cases.

Convergence of Numerical Method for Solving Hyperbolic Equation

Fri, 19 Jun 2026 09:45:06 +0000

In this parer,we investigate the convergence of explicit schemes for solving hyperbolic equations. Traditionally, the well-known (CFL)(Couryant-Friedrichs-Lewy)condition imposes a restriction on the ratio of step size, specifically k h≤C where k is time step-size and h is the spatial step size. This is crucial for ensuring the convergence of the explicit differffence scheme. We focus on a hyperbolic equation defined over domain 0 ≤ x < ∞ and 0 ≤ t ≤ tfwith boundary condition defined as u(x,t) = f(x,t).In this study,we will demonstrate that nude certain conditions. the numerical solution obtained from the difference scheme converge to the true solution without aforementioned restriction on the step size ratio k h. Our results contribute to the understanding of explicit scheme in the numerical method for hyperbolic equation,offeringpotential improvements in the practical computations.

A Kernel-Lattice Criterion Equivalent to the Riemann Hypothesis

Sat, 20 Jun 2026 06:36:35 +0000

We develop a kernel--based analytic framework that yields a criterion equivalent
to the Riemann Hypothesis defined on the continuum interval $x \in (0,1)$. For each real parameter $a>0$ we induces a discrete sampling for this continuum kernel.
we construct a-Lattice ...

A Geometric Interpretation of the Analytic Continuation of the Riemann Zeta Function via the Lambert W_(-1) Function

Tue, 23 Jun 2026 00:16:03 +0000

Starting from a compact planar set of measure (1-ln2), previously shown to encode the values ζ(k) for integers k≥2, we introduce a family of real parameters R_k whose associated boundary points x_k∈1,2 satisfy a transcendental equation involving the branch W_(-1) of the Lambert W function. We show that the transition from the divergent harmonic series ζ(1) to its analytically continued finite part admits a geometric interpretation governed by the unique inflexion point of W-_(1), which maps the boundary point x_1=1 of a rectangular compact of area R_1=2. Extending the construction to s=0 yields R_0=γ+ln2+1, consistent with ζ0=-1/2. Using the functional equation, we further show that the same geometric mechanism extends coherently to all negative integers, with the trivial values ζ(-n) appearing as rational increments in the extended sequence {R_k}_k∈Z. Altogether, these results highlight the structural role of the Lambert W_(-1) function in the analytic behaviour of ζ(s) and provide a unified geometric interpretation of its continuation at all integer arguments.

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 18, No. 2

Fri, 26 Jun 2026 09:51:27 +0000

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 18, No. 2