Jordan Journal of Mathematics and Statistics

Analyzing New Estimations to the Best Approximation

Malik Saad Al-Muhja — Sun, 12 Jul 2026 00:00:00 +0300

A method to compute the best approximation is the main purpose of this paper. The realisation of approximation theory is critical in analysis. Our papers primary benefit is that it is built on Egoroffs principle, which we investigate in our theorems. We presented the findings of research on approximation using Remez algorithm. This algorithm is an effective tool for analysing the approximations used in our research.

Keywords: Best approximation; Modulus of smoothness; Jackson type estimates.

2010 Mathematics Subject Classification. 41A10; 41A25

Approximate Solution of Variable-Order Fractional Optimal Control Problems

Zahra Pirouzeh, Kamele Nassiri Pirbazari, Mohammad Hadi Noori Skandari — Sun, 12 Jul 2026 00:00:00 +0300

This paper introduces a robust and highly accurate numerical scheme for solving a general class of variable-order fractional optimal control (VOFOC) problems based on the Caputo definition. The proposed method leverages a shifted Legendre spectral collocation (SLSC) technique, which effectively combines the superior approximation properties of global polynomials with the precision of Gaussian quadrature. The core of our approach lies in the novel derivation of an operational matrix for the variable-order fractional derivative (VOFD) of shifted Legendre polynomials. This matrix allows for the exact representation of the VOFDof the state variable, thereby transforming the complex fractional dynamical system constraint into a computationally tractable system of algebraic equations. The state and control variables are approximated by finite expansions of shifted Legendre polynomials with unknown coefficients. The objective functional is discretized using the shifted Legendre-Gauss-Lobatto (SLGL) quadrature rule, which is exact for polynomials of sufficiently high degree. Consequently, the original continuous-time VOFOC problem is converted into a nonlinear programming (NLP) problem, which can be efficiently solved using standard optimization solvers. A rigorous convergence analysis is provided, establishing that under mild conditions, the sequence of approximate solutions generated by our method uniformly converges to the exact optimal solution of the original VOFOC problem. The efficacy, versatility, and superiority of the proposed framework are demonstrated through six comprehensive numerical examples, including a practical application to train motion control. Results show that our method achieves exponential convergence rates, outperforms existing techniques like the variational iteration method, wavelet methods, and other spectral schemes in terms of accuracy, and yields solutions very close to the exact ones even with a small number of basis functions. The method proves to be a powerful tool for handling the complexities inherent in variable-order fractional calculus, offering a blend of theoretical robustness and computational efficiency.

Keywords: Variable-order fractional derivatives; Variable-order fractional optimal control problems; Spectral-collocation method;
Nonlinear programming.

2010 Mathematics Subject Classification. 26A25; 26A35

Moments of kth Lower Record Values from Inverse-Rayleigh Distribution and Characterization

Haseeb Athar, Saima Zarrin, Rafiqullah Khan — Sun, 12 Jul 2026 00:00:00 +0300

This paper focuses on the inverse Rayleigh distribution, a widely used model for lifetime data. We derive expressions for the moments of k^th lower record values and establish recursive relations between these moments. Moreover, we present characterization results based on these recursive relations and conditional moments. We also compute key statistical properties, including mean, variance, skewness, kurtosis, and product moments. Finally, we demonstrate the application of a characterization theorem using both simulated data from this distribution and a real data set.

Keywords: Lower record values; Single moment; Product moments; Inverse Rayleigh distribution; Characterization.

2010 Mathematics Subject Classification. 62G30; 62E10; 60E05

New Exact Solutions for a New Family of (3+1)-Dimensional Rosenau’s Equations

MohammedSalem Ahmed AL-Amry, Eman Fadhl Abdullah AL-Abdali — Sun, 12 Jul 2026 00:00:00 +0300

In this paper, we present a new family of (3+1)-dimensional Rosenau’s equations. We use a new expQ(ξ)-expansion method for solve our new equations. We determine a variety of exact solutions for each equation and expressed in terms of hyperbolic functions, trigonometric functions and rational functions.

Keywords: exp(Q(ξ))-Expansion Method; soliton solution; Rosenau’s equation.

2010 Mathematics Subject Classification. 35B09, 35C08, 35C09

Employing Adaptive Bridge with Sliced Inverse Regression Methods to Identify Factors Influencing the Severity of Lung Cancer Infection

Saif Hosam Raheem — Sun, 12 Jul 2026 00:00:00 +0300

This paper proposes the Adaptive Bridge–Sliced Inverse Regression (SIR) method for simultaneous variable selection and dimension reduction in high-dimensional biomedical data. The approach integrates adaptive penalization with the SIR framework to achieve robust estimation and interpretability. Simulation experiments demonstrate that the proposed method consistently attains lower Mean Median Absolute Deviation (MMAD) and Standard Deviation (SD) values compared with SIR–LASSO and SIR–MCP. A real clinical application on lung cancer data confirms its practical efficiency in identifying the most influential factors affecting disease severity.

Keywords: Adaptive Bridge; Sliced Inverse Regression; Variable Selection; Dimension Reduction; Lung Cancer Severity.

2010 Mathematics Subject Classification. 26A25; 26A35

Kahlerian Spacetime and η-Einstein Solitons

S. K. Yadav, D. L. Suthar, S. Patel, L. K. Gautam, A. Singh — Sun, 12 Jul 2026 00:00:00 +0300

This paper is dedicated to the study of the geometric composition of a K¨ahlerian spacetime with a η-Einstein soliton. Here, we have delineated the nature such soliton on a K¨ahlerian spacetime to be expanding, steady, or shrinking under various physical conditions depend on isotropic pressure, cosmological constant, energy density, and gravitational constant relations. We have also discussed η-Ricci soliton on some special types of perfect fluid spacetime such as dust fluid, viscous fluid, dark fluid and radiation era.

Keywords: K¨ahler spacetime; Quasi-conformal curvature tensor; Weakly symmetric; Weakly Ricci symmetric; Perfect fluid; Dust fluid and viscous fluid.

2010 Mathematics Subject Classification. 53C15; 53C50; 53B15; 53B20

M-Projective Curvature Tensor and Ricci-Bourguignon Soliton on Lorentzian β-Kenmotsu Manifold

Pawan Prajapati, Gyanvendra Pratap Singh, Rakesh Kumar, Pranjal Sharma — Sun, 12 Jul 2026 00:00:00 +0300

The prime object of the present article is to explore the characteristics of a Lorentzian β-K enmotsu manifold (M_β) admitting an M-projective curvature tensor. We derived characteristic theorems for M_β satisfying M-projectively ϕ-recurrent and pseudo-symmetric conditions. ϕ −M-projectively flat M_β is the subject of our next analysis. Additionally, we deal with the M_β satisfying M-projectively Ricci pseudo-symmetric condition. Next, we describe the M_β satisfying R(ζ,B₃) · M = 0 condition.
Further, we discuss cyclic parallel Ricci tensor, V^♭-parallel Ricci tensor and Ricci-Bourguignon soliton in M_β. Finally, we have presented an example of an M_β.

Keywords: Lorentzian β-Kenmotsu manifold (M_β), M-projective curvature tensor, generalized V^♭-Einstein manifold, Ricci pseudo symmetric, and Ricci-Bourguignon soliton (RBS).

2010 Mathematics Subject Classification. 53C05; 53C15; 53C20; 53C25; 53D15; 53D10

Projective Curvature Tensor of C9-Manifolds

HumamT. S. Al-Attwani, Mohammed Y. Abass — Sun, 12 Jul 2026 00:00:00 +0300

This article determines on C₉− manifold only fifteen non-zero components of the projective curvature tensor. It proves a C₉− manifold of dimension > 3 with flat projective curvature tensor is just a cosymplectic manifold with flat Ricci tensor. Whereas, the C₉− manifold of dimension 3 with flat projective curvature tensor is Einstein manifold. On the other hand, it discovers fifteen projective invariant classes that denoted by P₁,P₂,...,P₁₅. It establishes some of these classes are equivalent on C₉− manifold and the C₉− manifold is Einstein manifold if it belongs to the class P1∩P11.

Keywords: C₉−manifold; projective curvature tensor; Einstein manifold.

2010 Mathematics Subject Classification. 53D15; 53C25

Finite Groups with Specific Subgroups Exhibiting Trivial Intersection Property

Khaled Ahmad Al-Sharo, Malak R. Anagreh — Sun, 12 Jul 2026 00:00:00 +0300

This paper studies finite groups in which every Sylow p-subgroup has a trivial intersection with its conjugates, forming the class of TIP-groups. While classical conditions, such as the normality of Sylow p-subgroups, are equivalent to the group being nilpotent, the trivial intersection property defines a broader and more flexible class. We provide structural characterizations of TIP-groups and examine their relationship with well-known classes of finite groups. In particular, we relate TIP-groups to the p-cores by introducing the β-condition and offer examples to illustrate their distinguishing features.

Keywords: TIP-subgroups, Sylow subgroups, Nilpotent group, Solvable group.

2010 Mathematics Subject Classification. Primary 20D10, 20D20, 20D35

Torse-forming Vector Field and Ricci–Bourguignon Soliton on a Generic Submanifold of a Kenmotsu Manifold

Lakshmi M. S., H. G. Nagaraja — Sun, 12 Jul 2026 00:00:00 +0300

The aim of this paper is to derive significant results related to generic submanifolds and the generic product of Kenmotsu manifolds equipped with torse-forming vector fields. In particular, we investigate the existence and non-existence of tangential component u^T of a vector u, which is a torse-forming vector field on D^T, the invariant distribution of a generic submanifold N.
Additionally, we establish necessary and sufficient condition for a submanifold of a Kenmotsu manifold to be umbilical. Furthermore, we present the necessary and sufficient conditions for D^T and D^⊥, representing the invariant and anti-invariant distributions of a generic submanifold admitting a Ricciourguignon soliton to be Einstein. Lastly, we illustrate a 5-dimensional generic submanifold within a 7-dimensional Kenmotsu manifold through an example.

Keywords: Generic submanifold; Torse-forming vector field; Ricci–Bourguignon soliton.

2010 Mathematics Subject Classification. 53C15; 53C25; 53D15

On the Prime Graphs of Finite and Dihedral Groups

Kurnia Tandi Palembangan, Amir Kamal Amir, Andi Muhammad Anwar — Sun, 12 Jul 2026 00:00:00 +0300

Let G be a finite group. The order of the group G, denoted |G| is the number of elements in G. For any element g∈G, the order of g denoted o(g) is the smallest positive integer n ∈ N such that gⁿ = e. A graph of a finite group is said to be a prime graph Γ(G) if two vertices p,q are primes that divide |G|, with the vertices p and q connected by an edge if and only if the product pq divides o(g), the order of a group element. In this research, we study the prime graph of finite groups by focusing on one of these finite groups, i.e. the dihedral group with n sides which has order 2n. Next, we define and study the prime graph generated from 2 prime graphs of dihedral group Γ(D_m)∗Γ(D_n) and obtain the form of the prime graph of dihedral group which is forms the graph of K_n.

Keywords: Finite group, Dihedral group, Prime graph, Order of the group, Order of the group element.

2010 Mathematics Subject Classification. 26A25; 26A35

On the Burning Number of the Generalized Heawood Graphs

Kai An Sim, Kok Bin Wong — Sun, 12 Jul 2026 00:00:00 +0300

Graph burning is a discrete-time process that models the spread of contagion or information in a network. The burning number b(G) of a graph G is defined as the minimum number of discrete time steps required to ensure that all vertices are “burned”, assuming that in each step, a new vertex is ignited and the fire spreads to all adjacent vertices. Suppose n,k are two natural numbers where k ≥3 is odd and n≥k. The generalized Heawood graph, which is a cubic bipartite graph of girth 4 or 6, denoted as H(n,k) is the graph consisting of a 2n-cycle r₀r₁r₂...r_2n−1r₀ together with edges of the form r_2ir_2i+k,i = 0,1,2,...,n−1. Here the operations on the subscripts are reduced modulo 2n. In this paper, we propose ways to burn the generalized Heawood graphs and hence determine the burning number of all H(n,k) of girth 4 and that of H(2k,k) which is of girth 6.

Keywords: Burning number; generalized Heawood graphs.

2020 Mathematics Subject Classification. 68R10, 05C85, 91D30

A New Regression Model for Multivariate Extremes Using the Peaks-Over-Threshold Method

Amina El Bernoussi, Mohamed El Arrouchi — Sun, 12 Jul 2026 00:00:00 +0300

This paper presents a new regression model tailored for analyzing multivariate extremes, particularly when both the response variable and the covariates exhibit extreme behavior. The methodology combines the Peaks-Over-Threshold (POT) approach with ARIMA-based preprocessing to ensure the stationarity of climatic time series data before extreme value modeling. A key innovation of our approach is the use of a Logistic-Normal prior for spectral density estimation, which provides a more flexible and expressive alternative to the classical Dirichlet priors typically used in Peaks-Over-Threshold (POT) modeling of multivariate extremes. This framework enables the construction of smooth regression manifolds that describe conditional quantiles of extreme responses given extreme covariates, offering improved interpretability and adaptability to complex dependence structures. The model is applied to temperature and precipitation data from Meknes, Morocco (1973–2024), revealing meaningful extremal dependence patterns. Validation is conducted through quantile regression manifolds and bootstrap-based uncertainty estimates, demonstrating the practical relevance and robustness of the proposed method in environmental applications.

Keywords: Spectral measure; Bivariate extreme value distribution; Joint distribution; Quantile regression; Peaks-Over-Threshold; ARIMA method.

2010 Mathematics Subject Classification. 26A25; 26A35

Some New Inequalities on e-Convex Functions

Nikhil Khanna, Tarachand Prajapati, A. M. Jarrah — Sun, 12 Jul 2026 00:00:00 +0300

In this paper, we investigate e-convex functions, presenting Jensen-type inequalities and integral bounds. We give some properties of e-convex functions, and exhibit their controlled growth through inequalities, offering new tools for mathematical analysis.

Keywords: Convex function, e-convex function.

2010 Mathematics Subject Classification. 26A51; 26D10; 26D15

Finite Element Analysis for Strongly Damped Wave Equation

MohammedHomodHashim, Sattar M. Hassan, Akil J. Harfash — Sun, 12 Jul 2026 00:00:00 +0300

Finite element methods (FEMs) for the strongly damped wave equation with semi- and fully discrete solutions are presented in this paper. First, a system of first-order equations with respect to time was created from the strongly damped wave equation. We established the solution spaces for the numerical solution by identifying the stability bounds of the solution. Convergence to the continuous solution is demonstrated as part of the analysis. Additionally, a practicable algorithm is suggested to effectively solve the fully-discrete formulation at each time step. The calculations are performed in one, two, and three spatial dimensions, demonstrating
the efficacy of the suggested methodology. The special characteristics of the study include the thorough transformation of the second-order equation into a first-order system in time, the establishment of weak solutions, the proof and derivation of stability bounds, and a convergence analysis of the proposed FEM schemes.

Keywords: damped wave equation; semi-discrete; fully-discrete; stability bounds; existence.

2010 Mathematics Subject Classification. 65M60; 65M12; 35D30

A New Approach to Solve Dynamical Fractional Model of Infertile Couples by the Finite Element Method

Kheira Hakiki, Muhammet Kurulay — Sun, 12 Jul 2026 00:00:00 +0300

In this paper, we propose a dynamic model designed to predict the treatment outcomes of infertility in couples. To this end, five main groups of couples are considered: susceptible couples, patient couples, those undergoing treatment only, those receiving treatment with surgery, and cured couples. Our primary contribution lies in the formulation of a fractional-order model that captures the dynamics of infertile couples and identifies asymptotically stable disease-free equilibrium points. The main objective is to develop a novel numerical approach based on the finite element method to solve a nonlinear system of fractional differential equations. This
method transforms the fractional system into a system of algebraic equations. Moreover, the proposed technique proves to be robust,
efficient, and particularly well-suited to modeling infertility. To validate our model, we apply the proposed method and conclude with a comprehensive numerical analysis.

Keywords: Infertility modeling; fractional differential equations; Caputo derivative; finite element method; stability analysis; basic reproduction number; numerical simulation.

2010 Mathematics Subject Classification. 26A25; 26A35

A Pair of One-step Optimized Spectral Hybrid Block Methods for the Direct Solution of PDEs

Sun, 12 Jul 2026 00:00:00 +0300

This paper introduces a pair of single-step, optimized spectral hybrid block methods for the direct solution of partial differential equations. The methods are derived using an optimization approach aimed at maximizing accuracy. The methods are consistent, zero stable, convergent, and A stable. Implementation is carried out using the linear partition iteration technique, where the PDE is solved in time t using the hybrid block method and in space x using the spectral collocation method, following a suitable linear transformation. The computed results are compared with those of other numerical methods to demonstrate the efficiency and accuracy of the proposed approach. The findings indicate that the methods are both reliable and efficient.

Keywords: Spectral collocation method; Optimized hybrid block method; Linear partitioning iteration method; Partial differential equations.

2010 Mathematics Subject Classification. 35A25; 65M12; 65M70