Length-biased distributions are special cases of weighted distributions.We used this idea in this paper to propose a generalization of a one-parameter linear exponential distribution.The various characteristics of the recommended distribution are deduced and explored in detail.Numerical studies show that it is right-skewed and it is a leptokurtic distribution.Additionally, the mean waiting time and residual life functions are studied.To estimate the distribution's parameters, six methods of estimation are employed.A simulation study indicates that the resulting estimators are approximately unbiased and consistent.The practical utility of the distribution is demonstrated using three real-world financial data sets, representing earnings per share from the financial, industrial, and service sectors listed on the Amman Stock Exchange.They show that the suggested distribution has the best fit for these data sets compared to some competence distributions.

This paper improves the rate of convergence of the half Bernstein polynomial of positive and linear operators H n,2k (g; x) by applying the technique of iterative combination (Micchelli combination).It turns out that this method improves the order of approximations to O(n -k ).Next, using this sequence, we investigate the Voronovskaja asymptotic expression in both ordinary and instantaneous approximating for smooth functions.The mistake caused by this approximation is then estimated by means of the modulus for continuity.Next, in order for approximation assessment functions, we provide numerical illustrations via this iterative combination of the sequence H n,2k (g; x).Lastly, we contrast the repeated combination's outcomes with the numerical outcomes obtained from the sequence H n,2k (g; x) without iterative combination.

This paper presents mathematical models for predicting the durability of materials intended for use in the manufacturing of nanosatellites, considering both simple and complex stress states.The material damage process is examined in two phases.In the first phase, analytical formulas for the incubation period (latent damage) are derived using a criterion-based approach, considering fixed, exponential, and Abel kernels for the damage operator.In the second phase, an integral equation of the Volterra type, characterizing the failure process, is derived and solved based on the classical strength criterion, accounting for hereditary-type damaged materials.Time dependence graphs of the damage process were constructed using the obtained results and comparisons were made.The research determined that for the exponential case of the damage operator kernel, the incubation period constitutes 12.5% and 5.6% of the total failure time for mechanical memory coefficients of 0.3 and 0.2, respectively.

In graph theory, domination is an important concept with many practical applications.Different types of domination have been defined based on the structure of dominating sets.In this study, we propose a new domination parameter by focusing on the edges of a graph, inspired by the concept of Modern Roman domination, which models defense strategies.This new concept, called the Edge Modern Roman domination, assigns labels to the edges of a graph in such a way that each edge without defense is supported by neighboring edges that provide protection.We calculate the minimum sum of these assigned labels, called the Edge Modern Roman domination number, for some standard and known graphs.Furthermore, we investigate the behavior of this parameter under some certain graph operations such as the corona product and the Cartesian product.

In this paper, the damping effects of vegetation are investigated in shallow water model. Wave dissipation due to the inertia and drag force induced by vegetation is implemented based on Morison’s formulation. The dissipation term is added in momentum equation. The non-linear model is then solved numerically using momentum conservative scheme on staggered grid domain. To validate the numerical scheme, simulations of solitary wave propagation without vegetation are conducted and compared to the exact solution and laboratory experiment. Besides, several simulations of solitary wave with vegetation on sloping beach are also conducted with varying plant stem density. The numerical results reveal that vegetation significantly reduces the velocity of wave propagation. Additionally, an increase in vegetation stem density correlates with a decrease in solitary wave run-up.

Artificial sampling is one of the main approaches to dealing with imbalanced data. However, despite a vast amount of research on sampling techniques, there is little known about the choice of the optimal sampling ratio which can significantly improve the classification accuracy. In this paper, we attempt to fill the gap in the literature by conducting both mathematical and numerical analysis. Concretely, we conduct a large-scale empirical study on the relationship between the sampling ratio and classification accuracy. In addition, we investigate the theoretical sampling ratio using the Bayesian approach and obtain the optimal ratio of √1 e ≈ 0.6065 which is in line with the results of the numerical experiments. We find that while factors such as the original imbalance ratio or the number of features do not play a discernible role in determining the optimal ratio, the number of samples in the dataset may have a tangible effect. We hope that the insights revealed in this study will help researchers and practitioners select the optimal sampling ratio when dealing with imbalanced data.

An evolution equation is a partial diferential equation that describes the time evolution of a physical system starting from given initial data. Evolution equations arise from many areas of applied and engineering sciences. To this end, this article investigates the analytical studies of a generalized geophysical Korteweg-de Vries equation in ocean physics. The examination of this model is conducted via the Lie group theory of diferential equations. In the first place, point symmetries, which are constituent elements of a four-dimensional Lie algebra, are systematically computed. Thereafter, one-parameter transformation groups for the algebra are calculated. Besides, going forward, a one-dimensional optimal system of subalgebras is derived in a procedural manner. Sequel to this, the subalgebras and combination of the achieved symmetries are invoked in the reduction proces which enables the derivation of nonlinear ordinary diferential equations associated with the generalized geophysical Korteweg-de Vries equation under study. Most of the achieved nonlinear ordinary diferential equations are further solved either via direct integration or using a power series approach. Furthermore, travelling wave solutions are initially obtained. This is attained via direct integration and the use of Jacobi elliptic function approach. These techniques enable the attainment of various exact soliton solutions, including non-topological soliton solutions as well as general periodic function solutions of note, such as cosine amplitude, sine amplitude, and delta amplitude solutions of the model. Furthermore, numerical simulations of the solutions are invoked to gain a gross knowledge of the physical phenomena represented by the under-study generalized geophysical Korteweg-de Vries equation in ocean physics. In the end, the investigation further gives attention to the calculation of conserved vectors for the model using Ibragimov's theorem for conservation laws, as well as Noether's theorem.

In this paper, our aim is to compute exact solutions for the generalized (3+1)-dimensional KadomtsevPetviashvili Benjamin-Bona–Mahony (gnKP-BBM) equation by invoking an effective method, namely the Lie symmetry technique. Firstly, we derive the infinitesimals and write down the Lie symmetries. Using these symmetries the gnKP-BBM equation is reduced to various nonlinear ordinary differential equations (NLODEs). Thereafter, solutions of the NLODEs are derived by using the Jacobi elliptic cosine method, the (G 0 /G)-expansion method, the simplest equation technique and Kudryashov’s method. Conclusively, we derive conservation laws of the gnKP-BBM equation by using the Ibragimov’s method.

In this article, we explore the exterior penalty fuzzy valued function method for Fuzzy Nonlinear Programming Problems (FNLPP). We present methods of penalty fuzzy valued function for solving constrained optimization problems by converting to unconstrained optimization problems. Triangular fuzzy numbers are used to represent the problem’s decision variables and coefficients. Using a new fuzzy arithmetic and fuzzy ranking method on the parametric form of triangular fuzzy numbers, the optimal solution of the FNLPP is found by applying the exterior penalty fuzzy valued function method without changing to its equivalent crisp form. We present a numerical example of the suggested method and compare the results to those produced by existing methods