Jordan Journal of Mathematics and Statistics

New Extension of Weibull Distribution: Theory, Properties, and Applications of Water Runoff Data

Wed, 15 Apr 2026 00:00:00 +0300

Probability distribution theory offers flexibility in modeling for different categories of data sets. That flexibility of the models makes it suitable for quantifying risks and uncertainties in extreme events. This ia also valuable for decision-making. This study proposed new model as extension of Weibull model, known as exponentiated power alpha index generalized Weibull (EPAIGW).
Graphical study of densities and reliability functions are given for EPAIGW model. Several statistical properties of the new model are derived. For parameters estimation, maximum likelihood method is used. Simulation study is done for EPAIGW model. EPAIGW model is compared with other competitive models to check model performance using water runoff data. This leads to more precise risk assessment, and more solid and economical decisions. It also offers a methodical approach to estimate the probability of unfavourable occurrences and bolstering plans to lesson their effects in fields of epidemiology, climate science, economics and reliability engineering.

Keywords: Weibull; exponentiated; hazard; alpha; simulation; likelihood; runoff; extreme; empirical.

2010 Mathematics Subject Classification. 60E05; 62E15

On Proximity and Fixed Point Theorem for Semi Contractions of E-Metric Space

Sharifa Al-Sharif, Ameina Nuseir, Hamza Hamadneh — Wed, 15 Apr 2026 00:00:00 +0300

In this paper, we investigate some theorems on the existence and convergence of best proximity point for a semi-cyclic contraction pair (S,T) in the setting of non solid cone E-metric space with empty interior containing semi-interior points which poses larger class of metric spaces. further we apply our finding results in the E-cone metric space to prove the existence of the solution of certain integral equation.

Keywords: Positive non solid cone; semi-interior point; fixed point; best proximity point.

2010 Mathematics Subject Classification. 47H10; 46B40; 54H25

A Comparative Investigation of Disease Detection in Jamun (Syzygium cumini): A Study on the YOLOv3 and Gaussian YOLOv3Models

M. Haripriya, A. Radhika, J. Jeslin — Wed, 15 Apr 2026 00:00:00 +0300

Leaf disease detection is a critical task in precision agriculture, aiming to monitor and control the spread of plant diseases for sustainable crop management. Object detection models have shown promise in accurately identifying and localizing diseases on plant leaves in recent years. This paper explores the effectiveness of YOLOv3 (You Only Look Once) and a variant known as Gaussian YOLOv3 in the context of leaf disease detection. YOLOv3 is known for its real-time object detection capabilities and high accuracy.
However, it may face challenges in accurately localizing subtle disease patterns and handling uncertainties in complex leaf images.
To address these challenges, Gaussian YOLOv3 incorporates Gaussian components to model uncertainty and improves localization accuracy. The comparative analysis involves evaluating the performance of YOLOv3 and Gaussian YOLOv3 in terms of localization accuracy, speed, adaptability to diverse conditions, and training requirements. Experiments are conducted using a dataset comprising various leaf diseases under different environmental conditions. They enable timely interventions and agricultural decision-making, reducing crop losses and ensuring effective disease management.

Keywords: Leaf disease detection, YOLOv3, multi-scale prediction, K-means cluster, Gaussian YOLOv3, Uncertainty.

2010 Mathematics Subject Classification. 26A25; 26A35

A Boolean Lattice of Isotone Derivations

Mourad Yettou, Ali Jaballah — Wed, 15 Apr 2026 00:00:00 +0300

Westudy the set of derivations that are isotone on a Boolean lattice. To that end, new properties of derivations on an arbitrary Boolean lattice are established. The complement of an isotone derivation is detected. In addition, a Boolean structure for the lattice of isotone derivations is introduced and characterized. As well as, a strong negation for this Boolean lattice is provided. Finally, we prove that their fixed sets form also a Boolean lattice.

Keywords: Boolean lattice, derivation, isotone derivation, fixed point, fixed set.

2010 Mathematics Subject Classification. 06B05; 06E05

Numerical Solutions of Linear and Nonlinear Fredholm Integro-Differential Equations by Using the Weighted Integral Mean Value Methods

Samir Lemita, Abdelkrim Arbia — Wed, 15 Apr 2026 00:00:00 +0300

In this work, we present a numerical algorithm for approaching the solutions of a specific form of linear and nonlinear Fredholm integro-differential equations. This algorithm is constructed by applying the weighted integral mean value methods, which allow us to convert the proposed equations into a system of algebraic equations, then by solving this system we obtain the approximate solutions. Moreover, we provide some illustrative examples to show the effectiveness and simplicity of the algorithm.

Keywords: Fredholm equations; Integro-differential equations; Degenerate kernels; Weighted integral mean value theorem.

2010 Mathematics Subject Classification. 45B05; 65R20; 26A24

A New Parametric Kernel Function Based on p-generalized Sigmoid Function for the Primal-dual Interior Point Method of Linear Optimization

Fateh Merahi, Amrane Houas — Wed, 15 Apr 2026 00:00:00 +0300

For the purpose of linear optimization, we propose a novel parametric kernel function situated within the context of the primal-dual interior point methodology. This function incorporates a logarithmic barrier term and a p-generalized sigmoid function. To evaluate the complexity associated with iterations of the algorithm, we consider various simple cases and mild conditions. The results show that the iteration bounds for the small- and large-update interior point methods constructed with these functions are, respectively, given by O (√n/p log (n/ε)) andO (n/p3 log (n/ε)). By selecting a specific parameter p, the primal-dual interior point methods based on this kernel function can achieve an optimal iteration bound of O(√nlog(n)log (n/ε)) for large update methods. This bound is consistent with the known complexity results for linear and semidefinite optimization problems obtained from self-regular kernel functions. In order to demonstrate the effectiveness of the new kernel function, we present numerical results from several test problems, which confirm that the optimal number of iterations has been achieved.

Keywords: kernel function, interior-point algorithms, linear optimization, primal-dual methods.

2010 Mathematics Subject Classification. 90C51; 90C05

Estimations of Divergence Measures and Shannon Entropy Via Generalized Majorization Theorem Using Taylor’s Formula and Green Functions

Awais Rasheed, Khuram Ali Khan, Josip Peˇcari´c, Ðilda Peˇcari´c — Wed, 15 Apr 2026 00:00:00 +0300

In this paper, some results involving Csisz´ar f-divergence between two probability measures are presented with respect to generalized majorization theorem via Taylor’s formula and Green functions. In seek of applications, the special cases of obtained results are deduced in terms of Shannon entropy, Kullback-Leibler divergence, Bhattacharyya coefficient, Jeffrey’s distance and Triangular discrimination.

Keywords: Csisz´ar f-divergence; Shannon entropy; Kullback–Leibler distance; Taylor’s formula.

2010 Mathematics Subject Classification. 26D15; 26D20; 94A17; 94A20

The Level Cardinality of Fuzzy Module Under Z-Module Homomorphism on Zm Into Zn Where gcd(m,n) is Product of Powers of Primes

Manju Varghese, Shery Fernandez — Wed, 15 Apr 2026 00:00:00 +0300

The homomorphic image of a fuzzy module over an R-module is itself a fuzzy module, yet explicit bounds on level cardinalities under specific structural constraints remain largely unexplored. In prior work, such bounds were established for Z-module homomorphisms Γ : Zm →Zn when gcd(m,n) is either a prime or the product of two distinct primes, getting maxima of 3 and 4 respectively. In this paper, we extend these results to the cases gcd(m,n) = p^s, where p is a prime and s ∈ Z+ and further to the case gcd(m,n) = p^s1₁ .p^s2₂ ... p^st_k , with distinct primes p_i and s_i ∈ Z+, i = 1,2,...t. Our results contribute to a deeper understanding of the behavior of fuzzy modules under structural mappings between cyclic modules.

Keywords: Fuzzy module homomorphism; level cardinality.

2010 Mathematics Subject Classification. 20K30; 08A72

Reachability of Linear Systems over the Symmetrized Max-Plus Algebra

Suroto, Diah Junia Eksi Palupi, Ari Suparwanto — Wed, 15 Apr 2026 00:00:00 +0300

The criteria of reachability [resp. observability] of max-plus algebraic linear system is determined using asticity of columns or rows of reachability [resp. observability] matrix. In this paper, we determine the criteria of reachability [resp. observability] of symmetrized max-plus algebraic linear system. The determination of these criteria is carried out using rank of reachability [resp. observability] matrix. The linear system is reachable [resp. observable] when the reachability [resp. observability] matrix is full row or column rank in balance sense.

Keywords: Linear Systems; Observability; Reachability; Rank; Symmetrized Max-Plus Algebra.

2010 Mathematics Subject Classification. 93C05; 15A03; 15A80

A New Extension of b-Metric Spaces in BC Frameworks with an Application to Integral Equations

Wed, 15 Apr 2026 00:00:00 +0300

In this paper, the term ”Bicomplex valued extended b-metric spaces” or briefly ”BC-valued extended b-metric spaces” refers to a new extension of bicomplex valued b-metric spaces that we introduce in this study. Using this novel class of metric spaces, we extend numerous findings from literature and establish fixed point theorems with the aid of illustrative examples. Moreover, as an application of our results, we show that a unique solution of the Urysohn integral exists.

Keywords: BC numbers; Metric spaces; BC- b-metric spaces; Fixed point.

2010 Mathematics Subject Classification. 54H25, 47H10, 54D99

A Note on the Distribution of k-Full Integers in Arithmetic Progressions

Nadia Ayachi, Walid Wannes — Wed, 15 Apr 2026 00:00:00 +0300

A k−full integer (k ≥ 2) is a positive integer n such that p^k divides n whenever p is a prime divisor of n. Let N_k be the set of such integers. For a real x ≥ 1, we present an asymptotic formula for the number of natural numbers {n ≤ x, n ∈ N_k} such that the sum of their digits, s_g(n), in base g ≥ 2 satisfies s_g(n) ≡ a mod b, where a ∈ Z and b ≥ 2.

Keywords: Exponential sums, K-full integers, Sum of digits function.

2020 Mathematics Subject Classification. 11A63, 11L03, 11N69

A Computational Study of Fuzzy Fractional Sharma-Tasso-Olver Equation Via Analytical Method

Shreya Mukherjee, Amit Kumar, Nikhil Khanna, Gopal Datt — Wed, 15 Apr 2026 00:00:00 +0300

In this article, we obtain the numerical solution of the fuzzy form of the fractional Sharma-Tasso-Olver equation using the Homotopy Analysis Transform Method. This method combines two powerful and well-known methods: the Homotopy Analysis Method and the Laplace Transform Method. Two approximate solutions of the fuzzy fractional Sharma-Tasso-Olver equation are obtained using this approach. Comparisons are made between the results obtained by the proposed method and the exact solution available in the open literature. All the obtained numerical computations justify that the proposed method is highly reliable, simple, efficient, and effective for handling fuzzy fractional-order equations like the Sharma-Tasso-Olver equation.

Keywords: Laplace transform method; Caputo derivative; Homotopy analysis transform method; Fractional Sharma-Tasso-Olver equation.

2010 Mathematics Subject Classification. 26A33; 34A08; 34A34; 60G22

Enhanced Image Compression Via an Optimized Wavelet Thresholding Approach

A. M. Jarrah, Abisha V., Ch Karam Nawaz, Pankaj Sharma — Wed, 15 Apr 2026 00:00:00 +0300

Image compression is crucial for reducing the size of digital images, particularly in applications such as medical imaging and satellite communication. Discrete Wavelet Transform (DWT) has emerged as a powerful tool for image compression due to its multiresolution analysis capabilities. In this study, we propose a novel thresholding technique for selecting optimal threshold values to enhance image compression using DWT. We evaluate the performance of our approach using different wavelets, including Haar, db2, db5, sym2, and coif1, and analyze key metrics such as Peak Signal-to-Noise Ratio (PSNR), Compression Score (CS), and L₂-norm recovery. Here, we show that for first level of decomposition using db2 wavelet, our proposed technique achieves a PSNR of 35.79 dB, a CSof 75%, and an L2-norm recovery of 99.946% when applied to a standard 474 × 474 image of Srinivasa Ramanujan. Our method not only maintains image quality but reduces computational time compared to existing thresholding techniques. This work contributes to the advancement of efficient image compression techniques in various domains.

Keywords: Image Compression; Discrete Wavelet Transform (DWT); Thresholding; Multiresolution Analysis (MRA).

2010 Mathematics Subject Classification. 41A30; 42C15; 42C40

Impact of Inclined Magnetic Field on the Dynamics of Two Immiscible Viscous Fluids Flow in an Inclined Channel with Variable Permeability Porous Medium: A Finite Difference Approach

Angad Prasad, P. K. Singh — Thu, 16 Apr 2026 00:00:00 +0300

This paper utilizes the finite difference method to numerically analyze the fluid flow in an inclined channel filled with a porous medium and containing two immiscible, viscous, incompressible, and electrically conducting fluids. These fluids have different viscosities and are arranged in two equal-width separate layers within the channel. The channel experiences a magnetic field that is inclined, and the permeability of the porous material changes across the width of the channel. The upper layer’s fluid has lower viscosity than the lower layer’s fluid. The Brinkman equation is employed to characterize the flow within the porous material. The paper presents numerical expressions for velocity and volumetric flow rate using the finite difference method, incorporating no-slip boundary conditions at the top and bottom plates and continuity of velocity with shear stress continuity at the interface. The effects of key parameters, such as the Hartmann number, Gravitational parameter and the permeability parameter, etc on the velocity distribution and volumetric flow rate are investigated. The results are graphically represented and thoroughly discussed.

Keywords: Brinkman equation; Variable Permeability; Hartmann number; viscosity ratio parameter; Finite difference method.

2020 Mathematics Subject Classification. 76S05; 76W05; 76M20