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.
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.
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.
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 L-2-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 CS of 75%, and an L-2-norm recovery of 99.946% when applied to a standard 474 & times; 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.
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 Gamma : Z(m)-> Z(n) 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 is an element of Z(+) and further to the case gcd(m, n) = p(1)(s1) .p(s2) (2) ... p(k)(st) , with distinct primes p(i )and s(i) is an element of Z(+), i = 1,2,. . .t. Our results contribute to a deeper understanding of the behavior of fuzzy modules under structural mappings between cyclic modules.
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.
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 is an element of N-k} such that the sum of their digits, s(g)(n), in base g >= 2 satisfies s(g)(n) equivalent to a mod b, where a is an element of Z and b >= 2.
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, ( root n )) given by O (root n/p log (n/epsilon))and O (n/p(3) log (n/epsilon)). 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(root n log(n)log ( n /epsilon)) for large update methods. This bound is consistent with epsilon 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.
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.
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.
We study 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.
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.
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.
In this paper, some results involving Csiszar f-divergence between two probability measures are presented with respect 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.
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.
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.
Liang and Bai proposed the notion of odd harmonious labeling of a graph in 2009. Since then, numerous papers have explored this topic. This study adds some new results to the existing literature. First, we provide a sufficient condition for an Eulerian graph to be an odd harmonious graph, which enhances the result from 2014. Furthermore, we identify several new classes of graphs that exhibit odd harmonious properties.
This paper introduces two biased estimators to avoid problems arising from multicollinearity in the logistic regression model. We investigated the theoretical excellence of the proposed estimators according to the mean square error matrix (MSE) and the scalar mean square error (MSE) criterion. We found that they have the superiority than some existing estimators. Moreover, we run the simulation study, which depended on the simulated MSE (SMSE), squared bias (SB) and generalized cross validation (GCV) as criteria to compare the estimators. The simulation results showed that the proposed estimators have the superiority than the estimators under comparison at several factors and at the same time, they work well at the high level of correlation. In addition, we investigated the behavior of the present estimators applying the real data. Under this trend, the results were consistent with the theoretical results.
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 (J(1) and H-1) and Linear Approximation (J(2) and H-2) estimates for the extropy and entropy have a smaller mean squared error than competing estimates. A real data set is presented and analysed.
The global crisis triggered by the COVID-19 pandemic necessitated precise data monitoring and rigorous analysis efforts from worldwide health authorities and governments, particularly during the pandemic's initial surge. This study employs Newcomb Benford's Law specifically to identify potential anomalies in the reporting of COVID-19 data during the pandemic's first wave. Our methodology encompasses the application of Newcomb Benford's Law to the first digit analysis focusing on three (3) key statistics [d*, alpha- statistic (alpha*) and w statistic (w*)] in conjunction with the Kolmogorov-Smirnov test to unveil possible inconsistencies within world continental COVID-19 data reportage. By evaluating the actual distribution of leading digits across various COVID-19 data categories such as cumulative confirmed cases, deaths, recoveries, and active cases against the theoretical distribution proposed by Newcomb Benford's Law, possible significant deviations were identified. We used the deviation from the Newcomb Benford's law of anomalous numbers as a proxy for data accuracy. The findings reveal that except for the Australia/Oceania continent which exhibited pronounced deviations due to its unique data structure, the COVID-19 data from all other continents maintained a possible high level of reliability during the initial outbreak. The study concludes that while Benford's Law is a valuable tool for anomaly detection in diverse data, its use in COVID-19 reportage data shows potential pitfalls. To enhance the effectiveness and reliability of detecting anomalies, the study advocates for integrating additional anomaly detection strategies, like density and boundary based approaches encompassing the local outlier factor and one-class SVM, alongside the Newcomb Benford analysis.
