The stationary solution of Smoluchowski’s coagulation equation with injection is found analytically with different exponentially decaying source terms. The latter involve a factor in the form of a power law function that plays a decisive role i...
Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of...
An exponential-type function was discovered to transform known difference formulas by involving a shifted parameter
In many Bayesian computations, we first obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining the marginals for each vari...
The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental fun...
In this paper, we prove that the Taylor expansions of analytic functions appearing in the linearization of quadratic maps at hyperbolic fixed points do not successfully approximate invariant manifolds, such as stable and unstable manifolds, when high...
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical app...
In this paper, we define the
We approximate the solution of a generalized form of the Bagley–Torvik equation using Taylor’s expansions in fractional powers. Then, we study the fractional Laguerre-type logistic equation by considering the fractional exponential functi...
A non-linear filtering algorithm based on the alpha-divergence is proposed, which uses the exponential family distribution to approximate the actual state distribution and the alpha-divergence to measure the approximation degree between the two distr...
This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convex...
In this work, we build upon our previous finding that hydrodynamic porosity is an exponential function of pore-scale flow velocity (or interstitial Reynolds number). We previously discovered this relationship for media with a square cavity geometry&m...
In this paper, we focus on the computation of Caputo-type fractional differential equations. A high-order predictor–corrector method is derived by applying the quadratic interpolation polynomial approximation for the integral function. In order...
This paper addresses the stabilization problem of hybrid stochastic McKean–Vlasov differential equations via a discrete-time state observation feedback control strategy. Utilizing the coupling method and particle system approximation, Itô...
We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis of acute viral infections without solving a full virus load...
This paper studies optimal dividend and capital injection strategies with active exit options under a jump-diffusion model. We introduce a piecewise terminal payoff function to capture stop-loss exits (for deficits) and profit-taking exits (for surpl...
This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Wei...
This paper is devoted to the experimental study of the integral approximation method in entropy optimization problems arising from the application of the Randomized Machine Learning method. Entropy-optimal probability density functions contain normal...
The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an alg...
Optimization methods, namely, gradient optimization methods, are a key part of neural network training. In this paper, we propose a new gradient optimization method using exponential decay and the adaptive learning rate using a discrete second-order...
In this study, time-course of the recovery from the inactivation of ionic currents which have inactivation in cerebellar Purkinje cell is examined. Kinetics of the ionic currents are expressed with Hodgkin-Huxley equations. Peak value function of the...
In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of...
This paper aims to consider approximation-estimation tests for decision-making by machine-learning methods, and integral-estimation tests are defined, which is a generalization for the continuous case. Approximation-estimation tests are measurable sa...
Empirical studies suggest that asset price fluctuations exhibit “long memory”, “volatility smile”, “volatility clustering” and asset prices present “jump”. To fit the above empirical characteristics of...
Softmax is a step in transformer computation during which the internal buffer size grows rapidly because of the use of the exponential function. Softmax is a fundamental yet computationally expensive operation in vision transformer attention, posing...
Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is...
The Z-function is the real function given by
The aim of this research is to estimate the parameters of the modified Frechet-exponential (MFE) distribution using different methods when applied to progressive type-II censored samples. These methods include using the maximum likelihood technique a...
In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions...
This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is applied to solve this model, where the approximate sol...
The complexity of drug–disease interactions is a process that has been explained in terms of the need for new drugs and the increasing cost of drug development, among other factors. Over the last years, diverse approaches have been explored to unders...
In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in mor...
The problem of recovering the relaxation spectrum of the process described by the stretched exponential Kohlrausch–Williams–Watts (KWW) model is considered using the Post–Widder Laplace transform inversion rule. Based on the specifi...
When simulating cohesive cracks in the XFEM framework, specific enrichment schemes are designed for the non-singular near-tip field and an iteration procedure is used to solve the nonlinearity problem. This paper focuses on convergence and accuracy a...
This report bridges fundamental ideas from introductory calculus to advanced concepts in quantum mechanics and nonlinear dynamics. Beginning with the behavior of second derivatives in oscillatory and exponential functions, it introduces the Airy equa...
The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation...
As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis fu...
In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic pr...
We present analytical estimates for the maximum line strength in a transition array, as well as for the numbers of strong and weak lines. For that purpose, two main assumptions are used as concerns the line strength distribution. The first one, due t...
In this paper, we develop an accurate technique via the use of the Adomian decomposition method (ADM) to solve analytically a
Here, classical and quantum field theory of dipolar, axisymmetric quadrupolar and octupolar Bose gases is considered within a general approach. Dipole, axisymmetric quadrupole and octupole interaction potentials in the momentum representation are cal...
A new two-parameter weighted-exponential (WE) distribution, as a beneficial competitor model to other lifetime distributions, namely: generalized exponential, gamma, and Weibull distributions, is studied in the presence of adaptive progressive Type-I...
In this article, a new one parameter survival model is proposed using the Kavya–Manoharan (KM) transformation family and the inverse length biased exponential (ILBE) distribution. Statistical properties are obtained: quantiles, moments, incompl...
Transformer-based models have achieved remarkable success across various AI tasks, but their growing complexity has led to significant computational and memory demands. While most optimization efforts have focused on linear operations such as matrix...
A solution of the governing equation representing the drawdown in a horizontal confined aquifer, where groundwater flow is unsteady, was first provided by Theis and is famously known as the Theis solution. This solution was given in terms of an expon...
We shall discuss the numerical solution of the Cauchy problem for the fully fractional Fokker-Planck (fFP) equation in connection with Sinc convolution methods. The numerical approximation is based on Caputo and Riesz-Feller fractional derivatives. T...
The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introd...
A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (...
This study addresses the important problem of estimating sensitive study variables when respondents may be reluctant to provide truthful answers due to privacy concerns. In such situations, scrambled response techniques are widely used because they p...
Load frequency control (LFC) is essential for maintaining frequency stability and regulating tie-line power in interconnected power systems. Conventional fixed-order PI and PID controllers offer limited tuning flexibility for complex multi-area syste...
of 9