Jordan Journal of Mathematics and Statistics

New Two Parameter Inverse Gaussian Regression Estimators: Applications and Simulation

Issam Dawoud — 2025-04-09

In situations where the response variable is positively skewed and has an inverse Gaussian distribution, the inverse Gaussian regression (IGR) model is employed. Due to the significant multicollinearity, the variance of the Maximum Likelihood (ML) Estimator is overestimated. In order to tackle multicollinearity in the IGR model, we present a new estimator in this study that combines two parameter estimators. In terms of mean squared error, the suggested estimator’s performance is theoretically compared to that of the
ML and a few other current estimators, as well as through Monte Carlo simulation and various real-data applications. The proposed estimators are found to perform better than the ML, ridge, Liu, Kibria-Lukman, and modified ridge type estimators under several circumstances.

Keywords: Multicollinearity; Inverse Gaussian ridge; Inverse Gaussian Regression model; hybrid estimator; Simulation.

On the Hilbert 5-Class Field Towers of Some Pure Metacyclic Fields and Total Capitulation

Fouad Elmouhib — 2025-04-09

In this paper, we study the length of the Hilbert 5-class field towers of some pure metacyclic fields of degree 20 over Q, which are the normal closure of some pure quintic fields, by means of some results of 5-groups. The capitulation problem is investigated too.

Keywords: Groups of maximal class, 5-class field, Transfer, 5-class groups.

2020 Mathematics Subject Classification. 20D15; 20D35; 11R29; 11R37

The Continuous Classical Optimal Control for a Couple Fourth Order Linear Elliptic Equations

Eman Hussain Al-Rawdanee — 2025-04-09

In this paper, the finite element Galerkin method (FEGM) with piecewise cubic Hermite basis function is applied to prove the existence and uniqueness of a couple state vector solution for a system of fourth-order linear partial differential equations (PDEs) of elliptic type with Dirichlet-Neumann boundary conditions (DNBCs), when the continuous classical couple control vector (CCCPCV) is considered. An existence theorem for a coupled continuous classical optimal control vector associated with the fourth-order linear PDEs of elliptic type is formulated and proved under appropriate conditions. The paper also discusses the existence and uniqueness of the solution to the coupled adjoint equations involving the couple state vector, when the classical couple optimal control vector is given.
Finally, the derivation of the Fr´echet derivative (FrD) of the cost function (CFn) to establish the theorem of the necessary condition (NEC) for optimality of the considered problem is demonstrated.

Keywords: A continuous classical couple optimal control; The finite element Galerkin method ;The necessary condition for optimality; Fourth order linear elliptic PDEs.

2010 Mathematics Subject Classification. 26A25; 26A35

Some Inequalities Involving Csisz´ar Divergence Using a Montgomery Identity and Green Function Via Diamond integrals

Muhammad Bilal — 2025-04-09

In the present paper, some results involving Csisz´ar divergence are formulated via diamond integrals by using Montgomery ´identity and Green function. By selecting various kinds of convex functions, bound of different entropies and divergence measures are obtained. Further, new bounds of different divergence measures are deduced.

Keywords: divergence measures; Montgomery identity; diamond integral; Green’s function.

2010 Mathematics Subject Classification. 39B62; 26A33; 05A30

On the Well-Posedness for the Incompressible Hall-Magnetohydrodynamic System in Critical Fourier-Besov-Morrey Spaces

Fatima Ouidirne — 2025-04-09

In this work, we establish the local well-posedness of the incompressible Hall- magnetohydrodynamic system in critical framework Fourier-Besov-Morrey spaces, which can be seen as a complement to the corresponding results of the Hall-magnetohydrodynamics equations in Fourier-Besov spaces.

Keywords: Well-posedness; Hall-magnetohydrodynamic system; Fourier-Besov-Morrey spaces.

2010 Mathematics Subject Classification. 60H15, 76D05, 42B37

Study of Bipolar Fuzzy Soft Hypervector Spaces

O. R. Dehghan — 2025-04-09

In this paper, three topics in bipolar fuzzy soft hypervector spaces are investigated. At first, four equivalent conditions for the definition of a bipolar fuzzy soft hypervector space are presented, from different points of view. Then some new bipolar fuzzy soft hypervector spaces are constructed using the notions of subhyperspace, level subset, generated subhyperspace, and previous bipolar fuzzy soft hypervector spaces. Finally, normal bipolar fuzzy soft hypervector spaces are studied as a special kind of bipolar fuzzy soft hypervector spaces. All concepts are supported by interesting examples.

Keywords: Hypervector space; Level subset; Bipolar fuzzy soft hypervector space; Subhyperspace; Normal bipolar fuzzy soft hypervector space.

2010 Mathematics Subject Classification. 06D72; 20N20; 08A72

Stochastic Analysis of Repairable System Comprised Two Subsystems With k-out-of-n: G Operational Policy and Copula Repair Approach

Umesh Chand — 2025-04-09

The finest performable systems are needed everywhere. The present paper deals with system performance assessment consisting of two subsystems in a series arrangement. The first subsystem follows the k-out-of-n: G work policy, and the second subsystem consists of three units and operates under the 2-out-of-4: G scheme. The failure rates are considered constants and obey negative exponential distribution. Two types of repair, general repair, and copula, are employed for repairing the models partial failure and complete breakdown states. Supplementary variable and Laplace transformation methods were used to study the traditional reliability measures for different values of system parameters.
The probabilistic estimates, like system availability and reliability analysis, MTTF, and profit analysis, have been computed with Maple software.

Keywords: System Availability; MTTF; System Reliability; Cost Analysis; Gumbel-Hougaard family copula.

On Reformulated Geometric-Harmonic Index of Graphs

Goutam Veerapur — 2025-04-09

In theoretical chemistry, the topological indices are mostly used to explore/develop QSAR and QSPR analyses of molecular graphs. The edge variant of the Geometric-Harmonic index is one type of topological indices it is described as (equation), where dG (t) is the degree of a vertex t in G . In this paper, using several molecular structural parameters, we establish some new bounds on the the edge variant of Geometric-Harmonic index EGH(G ). Also, we connect these indices to a number of well-known molecular descriptors.

Keywords: Reformulated Zagreb indices; edge degree; vertex degree; platt number; order and size.

2020 Mathematics Subject Classification. 05C09, 05C92

Extropy and Entropy Estimation Based on Uniformly and Log-Normal Distributed Data

Huda H. Qubbaj — 2025-04-09

This paper proposes non-parametric estimates for the two information measures extropy and entropy when a progressively Type-I interval censored data is available. Different non-parametric approaches are used for deriving the estimates; namely Moments, Linear, Kernel and differential Approximation methods. Some properties of the proposed estimates are studied. The performance of the proposed estimates is studied under various censoring schemes via simulation studies considering the parent distributions of the data; namely Uniform and Log-Normal distributions. The results indicate that Moments Approximation (J₁ and H₁) and Linear
Approximation (J₂ and H₂) estimates for the extropy and entropy have a smaller mean squared error than competing estimates. A real data set is presented and analysed.

Keywords: Entropy; Extropy; Mean Square Error; Non-parametric statistics; Monte Carlo simulation; Type-I Interval Censoring.

2010 Mathematics Subject Classification. 26A25; 26A35

On the Possibility of Mikusinski’s Operational Calculus for the Fractional Laplacian

Ibrahim Abdullahi Saleh — 2025-04-09

We try to adapt the framework of Mikusi ´nski’s operational calculus in order to apply it to differential equations involving the fractional Laplacian.We find a fundamental theorem of calculus which connects the fractional Laplacian with its inverse in general, even when no decay conditions are imposed. Ultimately, we discover that no suitable function space exists satisfying all the required conditions, and so the method of Mikusinski, in the sense that it has previously been used for fractional operators, cannot be applied to the fractional Laplacian.

Keywords: fractional Laplacian; Mikusinski’s operational calculus; fundamental theorem of fractional calculus.
2010 Mathematics Subject Classification. 44A40; 26A33

Clairaut Convolution Differential Equation

Sami H. Altoum — 2025-04-09

The Clairaut convolution differential equation, a variant of the more general Clairaut equation, has been a subject of considerable interest in the realm of mathematical analysis. Based on an infinite dimensional test space of holomorphic functions, the purposes of this work are to investigate the convolution calculus in white noise theory to introduce and study the solution of the analogue of the Clairaut equation, called Clairaut convolution differential equation (CCDE). We study the Clairaut convolution differential equation as a natural counterpart of the classical Clairaut differential equation and give its general and singular solutions.

Keywords: Clairaut equation; Convolution derivative; Convolution differential equation.

2010 Mathematics Subject Classification. 54C40; 14E20; 46E25; 20C20

On Some Fundamental Subclasses of Analytic Bi-univalent Functions

Oqlah Al-Refai — 2025-04-09

The aim of the current paper is to establish a general coecient estimations for fundamental subclasses of bi-univalent functions. These subclasses encompass bi-starlike, bi-convex, strongly bi-starlike, and strongly bi-convex functions. Some new estimates are sharp and other findings involve several enhancements and extensions of well-known results.

Keywords: Bi-univalent functions; Coefficient estimates; Bi-starlike functions; Bi-convex functions; Strongly bi-starlike functions; Strongly bi-convex functions.

2010 Mathematics Subject Classification. 30C50; 30C45; 30C55