Jordan Journal of Mathematics and Statistics

A Novel Logarithmic-Exponential Cum Ratio-Type Estimator Under Simple Random Sampling

2025-12-03T10:32:21+03:00

In sample surveys, the use of auxiliary variables to estimate the population mean has become crucial for improving the efficiency of the estimators, including traditional ratio, product and regression estimators. This paper introduces a new logarithmic-exponential cum ratio-type estimator for the elevated estimation of population mean under simple random sampling. We have obtained the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation and identified the situations in which it performs more efficiently than existing estimators. To verify the theoretical results, we have conducted numerical study based on eight real data sets belonging from the clinical, agricultural and business fields. Their performances have also been evaluated through simulation study that utilized two artificially generated datasets. A sensitivity analysis based on the sample estimates has been investigated to reassert the behaviours of proposed estimators.

Keywords: Study variable; Auxiliary variable; Population mean; Mean squared error; Percent Relative Efficiency.

2010 Mathematics Subject Classification. 62D05

Effect of Cyclotron Frequency on Vibrational Partition Function and Enthalpy for Hellmann Potential

2025-12-03T10:38:00+03:00

This study presents a comparative analysis of the eigenvalues, vibrational partition function, and vibrational enthalpy of the Hellmann potential under different quantum states, cyclotron frequencies, and temperatures. The study reveals that the eigenvalue at higher quantum states exhibit less negativity values, with the present method consistently yielding lower eigenvalues than the NU and AP methods. The effect of cyclotron frequency on eigenvalues indicates an upward energy shift with increasing frequency, while spacing between successive energy levels increases at higher quantum numbers. The vibrational partition function exhibits temperature-dependent behaviour, increasing steadily in some cases while showing fluctuations and saturation effects at specific values of cyclotron
frequency. Similarly, the vibrational enthalpy trends suggest stabilization at higher temperatures, with variations in magnitude and rate of change depending on cyclotron frequency. These findings highlight the complex interplay between quantum state, cyclotron frequency, and thermal effects on the Hellmann potential system.

Keywords: Bound state; Wave equation; Eigensolutions; Thermodynamic properties; Potential model.

2010 Mathematics Subject Classification. 26A25; 26A35

Adaptive Hybrid Progressive Censoring in m-Component Reliability Model and Generalized Inverse Weibull Distribution

2025-12-03T10:48:02+03:00

In thispaper, the authors investigate the Bayesian inference of the m-component stress-strength parameter for the generalized inverse Weibull distribution under an adaptive hybrid progressive censoring scheme. The study considers three cases. In the first step, the paper employs the MCMC method to derive a Bayesian estimate of the m-component stress-strength parameter when both the common parameters for strengths and stress variables are unknown. Secondly, assuming that the common parameters are known, two approximation methods are employed: namely, the MCMC method and Lindley’s approximation. Finally, in a broader scenario where all parameters are distinct and undisclosed, the paper employs MCMC simulation to calculate a Bayesian estimate of the m-component stress-strength parameter. To evaluate and compare these methods’ performance, one Monte Carlo simulation is conducted.
Additionally, a real data set is used to implement theoretical methods proposed in this study.

Keywords: m-component stress-strength reliability; Lindley’s approximation; MCMC method; Adaptive hybrid progressive censoring
scheme.

2010 Mathematics Subject Classification. 62N05; 62F15

On Coherent Filters of Pseudo-Complemented Almost Distributive Lattices

2025-12-03T10:52:48+03:00

In a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL), the notions of coherent filters, strongly coherent filters, ♦-closed filters are introduced and their properties are studied. A set of equivalent conditions for any filter of a pseudo- complemented ADL to become a coherent filter is given. Also, the concept of median filters is introduced and a set of equivalent conditions for any maximal filter of a pseudo-complemented ADL to become a median filter is derived which leads to the characterization of a stone ADL.

Keywords: strongly coherent filter; median filter;minimal prime filter; maximal filter; stone ADL.

2010 Mathematics Subject Classification. 06D99; 06D15

Modified Conformable Self Adjoint Equation and Sturm Liouville Problems with Applications

2025-12-03T11:06:17+03:00

Within this research, we introduce a new modified conformable operator and study its properties in detail. Furthermore, we investigate the self-adjoint modified conformable equation and its connection to modified conformable initial value problems.
Additionally, we analyze the modified conformable Sturm–Liouville problem, determining its eigenvalues and corresponding eigenfunctions, while establishing results on orthogonality and dependence. Finally, illustrative examples are provided to demonstrate
the applicability of our findings.

Keywords: Modified conformable derivative; Modified conformable integral; Modified conformable Sturm Liouville problem; Modified conformable self adjoint equation; Orthogonality; Dependence.

2010 Mathematics Subject Classification. 34B24; 26A33

Geometry of Paracontact Manifolds Admitting Conformal Ricci-Yamabe Solitons

2025-12-03T11:16:47+03:00

This study investigates the classification of conformal Ricci-Yamabe solitons within the framework of paracontact geometry. In particular, we analyze the structural properties of para-Kenmotsu manifolds that satisfy the conditions for conformal Ricci-Yamabe solitons, with special attention to three-dimensional cases exhibiting conformal gradient Ricci-Yamabe solitons. In addition, we provide a comprehensive classification of para-Sasakian and para-cosymplectic manifolds that admit conformal Ricci-Yamabe solitons and its gradient form conformal gradient Ricci-Yamabe solitons. To substantiate the theoretical findings, an explicit example is constructed and discussed in detail.

Keywords: Paracontact manifolds; self-similar solution; conformal Ricci-Yamabe solitons; Einstein manifolds.

2010 Mathematics Subject Classification. 53B30; 53C21; 53C25

Some Classes Related to the Set of Generalized Drazin Invertible Linear Relations

2025-12-03T11:23:50+03:00

In this paper, we introduce and investigate several classes of linear relations on Banach spaces related to generalized Drazin invertibility. First, we focus on a subclass of the generalized Drazin invertible linear relations, namely the class of generalized strongly Drazin invertible linear relations. In particular, we derive two distinct characterizations: one in terms of a bounded projection and a quasi-nilpotent operator, and another based on a specific relationship between T and T². This, in turn, leads us to the definition and study of the class of Hirano invertible linear relations. We then introduce the concept of weakly generalized Drazin invertibility and establish a connection between this notion and invertibility in the sense of Hirano. As an application, we present new criteria ensuring the existence of a generalized Drazin inverse for a given linear relation T.

Keywords: Linear relation; Generalized inverse; Drazin inverse; Hirano inverse.

2010 Mathematics Subject Classification. 47A06; 16U90

An Interplay between Quadratic-Phase Fourier Transform and Octonion Algebra

2025-12-03T11:29:31+03:00

The quadratic-phase Fourier transform (QPFT) has emerged as a versatile five-parameter integral transform, unifying a wide range of unitary transformations, from the classical Fourier transform to the more recent special affine Fourier transform. However, its limitations become evident when applied to the precise representation of non-transient octonion-valued signals. To address this, we introduce the octonion quadratic-phase Fourier transform-a distinct integral transform specifically designed for such signals. In this study, we investigate its fundamental properties, including the energy-preserving relation and the inversion formula. Furthermore, we establish a set of uncertainty principles, such as Heisenberg’s and logarithmic uncertainty principles, providing deeper insights into the intricate interplay between octonion algebra and the quadratic-phase Fourier transform.

Keywords: Quadratic-phase Fourier transform; Quaternion Fourier transform; Octonion Fourier transform; Uncertainty principles.

2010 Mathematics Subject Classification. 42A38; 42C20; 11R52; 26D10; SDG9

Improper Injective Coloring Parameters of Certain Cycle-Related Graphs

2025-12-03T12:16:06+03:00

Any vertex coloring of a graph can be viewed as a random experiment of assigning colors to the vertices, whose random variable is defined based on the number of vertices assigned a particular color in that coloring. Based on this, the statistical parameters of mean and variance have been extended to chromatic mean and chromatic variance for various vertex colorings of graphs in the literature. In this article, the ideas of chromatic mean and chromatic variance of cycle-related graphs with respect to their improper injective coloring are investigated.

Keywords: Improper coloring; injective coloring; chromatic sum; chromatic mean; chromatic variance.

2010 Mathematics Subject Classification. 05C15, 05C38, 62A01

New Results of Itˆo’s Formula Using q-Calculus

2025-12-03T12:21:20+03:00

In this paper, we extend the classical Itˆo formula by employing the framework of quantum calculus to derive its q-analogue, applicable to both classical Brownian motion and q-Itˆo processes via the quantum Taylor expansion. We also determine the q-infinitesimal generators associated with stochastic q-differential equations. To illustrate the applicability of our results, we present the q-Black-Scholes equation as a concrete example. Throughout the study, we assume 0 < q < 1, and we show that the classical results of Itˆo calculus are recovered in the limit as q → 1.

Keywords: q-calculus; Itˆo calculus; semigroup; stochastic differential equations.

2010 Mathematics Subject Classification. 05A30; 60H05; 60H10; 60J65

Kumaraswamy Sine Inverted Rayleigh Distribution: Properties and Application to Bladder Cancer Data

2025-12-03T12:57:41+03:00

In this work, we introduce the Kumaraswamy Sine Inverted Rayleigh (KWSIR) distribution as an extension of the classical Inverse Rayleigh distribution, offering greater flexibility in modeling real-world data. The KWSIR distribution combines the Kumaraswamy and Sine Inverted Rayleigh distributions, resulting in a unimodal, right-skewed probability density function and an increasing or J-shaped hazard rate function. We explore key statistical properties, including the probability density function, cumulative distribution function, quantile function, moments, incomplete moments, entropy measures, and order statistics. Parameter estimation is conducted using the maximum likelihood method. To illustrate its applicability, we analyze a real-world dataset on bladder cancer, demonstrating the superior fitting performance of the KWSIR distribution.

Keywords: Probability distribution; maximum likelihood estimation; moments, moment generating function.

2010 Mathematics Subject Classification. 26A25; 26A35

An Extension of Caputo’s k-Fractional Derivative Operator and its Applications

2025-12-03T13:02:46+03:00

This research introduces a novel extension of the Caputo fractional derivative operator, characterized by a new parameter k >0. We establish several properties of the Caputo k-fractional derivative operator and present a series of results related to its application. Additionally, we extend the concept of k-hypergeometric functions and derive their integral representations utilizing the k-fractional derivative operator. Our work further includes the development of linear and bilinear generating relations for the extended k-hypergeometric functions, as well as the Mellin transform of selected extended k-fractional derivatives.

Keywords: Caputo fractional derivative operator; k-fractional derivative operator; k-hypergeometric functions; linear generating relations; mellin transform; extended k-fractional derivatives.

2010 Mathematics Subject Classification. 26A30; 26A45; 26A48

Effects of Relaxation Times and Inclined Angles on a Material with Corrugation under Magneto-Thermal Stress

2025-12-03T13:15:37+03:00

The current research deals with the Mathematical solutions for the thermo-mechanical response of surface waves on a half-space with an inclined mechanical load on the corrugated-impedance surface influenced by magnetic field and thermal stress. We utilized the harmonic approach for wave analysis in determining the solution of the model. Using Green and Lindsay theory of thermoelasticity, the distribution fields of the system such as the thermal, normal and shear stresses, and the displacement components were analytically derived. Also, the behavior of the two times relaxation constants, special angles of various inclinations and the effect of magnetism, etc., on the distributions are graphically presented using MATHEMATICA 11 software. Our computational results show that an increase in the inclined angles (special and non-special angles) produces a corresponding increase in the distribution profiles of the surface wave. Also, increase in one of the thermal relaxation constants exhibited decreasing effects on the distribution profiles whilst the temperature profile increases in modulation. Thus, our result holds true for the thermal assumptions of the temperature distribution under the considered thermo-elasticity model. Also, researchers working in the area of non-destructive material testing and evaluation would find this investigation useful; owing to the grooved-impedance coloration of the material surface and the model in its entirety.

Keywords: Relaxation times, impedance boundary, special angle of inclination, grooved boundary, magneto-thermal effects.

2010 Mathematics Subject Classification. 26A25; 26A35