This study proposes a decoupling approach based on first-order exponential function approximation for reliability-based optimization. It establishes an explicit relationship between the failure probability and design parameters within only one implem...
Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation ef...
In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series appro...
The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has...
For the calculation of thermal processes of canned food, the original formula method of Ball is still widely used for its accuracy and safety. However, it requires the consultation of tables that Ball prepared and the relative interpolation of the da...
We develop a shared denominator Carathéodory–Fejér (CF) method for efficiently evaluating linear combinations of
We examine a Szász–Mirakyan–Durrmeyer type operator that reproduces the functions 1 and
In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval
The Hurwitz zeta-function
In this paper, we introduce
In this paper, we construct a new variant of the classical Szász–Mirakyan operators,
The practical use of computational thermo-fluid dynamics (CFD) for food thermal process calculations still appears very premature due to both the high costs and the inhomogeneity and anisotropy of foods. Therefore, the traditional formula method with...
There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, w...
In this paper we study approximation properties of exponential-type operators for functions from exponential weighted spaces. We focus on some modifications of these operators and we derive a new example of such operators. A probabilistic approach fo...
The main contribution of the paper is the simplification of the computational process of fuzzy control of a mobile robot controlled by a microcontroller. We present a way to implement this control method with a reduced computation time of control act...
This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known...
We consider the optimal order quantity problem for exponentially deteriorating items where the opportunity cost is based on compound interest and backorders are allowed. Our objectives in this research are to develop a model that accurately models de...
We study
We present three new approximation properties of the Balázs–Szabados operators. Firstly, we prove that, in certain cases, these operators approximate some super-exponential functions on compact intervals. Next, we provide a new estimate of the error...
This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U,...
In this paper, we consider the modified Mellin transform of the product of the square of the Riemann zeta function and the exponentially decreasing function, and we discuss its probabilistic and approximation properties. It turns out that this Mellin...
The exact perimeter of an ellipse involves the complete elliptic integral of the second kind, which lacks a closed-form expression in elementary functions. As a result, analytical approximations have been proposed for applications requiring fast and...
Distributed-order, space-fractional diffusion equations are used to describe physical processes that lack power-law scaling. A fourth-order-accurate, A-stable time-stepping method was developed, analyzed, and implemented to solve inhomogeneous parabo...
Some inventory items deteriorate and lose their useful life while in storage due to evaporation, spoilage, pilferage, and chemical or mechanical breakdown. Some examples of this phenomenon are the inventories of fresh food, batteries, electronic item...
This paper presents modified Lagrange–Jacobi functions derived from the sine, exponential, and hyperbolic tangent coordinate transformations. The resulting Lagrange–Jacobi functions and their respective matrix elements for observables can...
Padé approximations are approximations of holomorphic functions by rational functions. The application of Padé approximations to Diophantine approximations has a long history dating back to Hermite. In this paper, we use the Maier&ndash...
This paper analyzes the exponential convergence properties of Symmetric Stochastic Bernstein Polynomials (SSBPs), a novel approximation framework that combines the deterministic precision of classical Bernstein polynomials (BPs) with the adaptive nod...
Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express t...
In this paper, we generalize a sequence of positive linear operators introduced by Ismail and May and we study some of their approximation properties for different classes of continuous functions. First, we estimate the error of approximation in term...
In this paper, the time-fractional wave equation associated with the space-fractional Fokker–Planck operator and with the time-fractional-damped term is studied. The concept of the Green function is implemented to drive the analytic solution of the t...
In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for...
In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength relia...
This study investigates the use of the bisection algorithm in inventory models to obtain an approximated optimal solution for the economic manufacturing quantity (EMQ) problem under imperfect production conditions. The objectives are threefold. First...
In cryptography, techniques and tools developed in the subfield of linear cryptanalysis have previously successfully been used to allow attackers to break many sophisticated cryptographic ciphers. Since these linear cryptanalytic techniques require e...
In this paper, we present splitting approaches for stochastic/deterministic coupled differential equations, which play an important role in many applications for modelling stochastic phenomena, e.g., finance, dynamics in physical applications, popula...
The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the appro...
In any Bayesian computations, the first step is to derive the joint distribution of all the unknown variables given the observed data. Then, we have to do the computations. There are four general methods for performing computations: Joint MAP optimiz...
This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exp...
The purpose of this study is to offer a systematic, unified approach to the Mellin-Barnes integrals and associated special functions as Fox H, Aleph ℵ, and Saxena I function, encompassing the fundamental features and important conclusions und...
In this paper, we introduce q-cosine and q-sine Euler polynomials and determine identities for these polynomials. From these polynomials, we obtain some special properties using a power series of q-trigonometric functions, properties of q-exponential...
This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expect...
We apply known special functions from the literature (and these include the Fox
For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points. The adaptive approach, which uses Poly-Sinc interpolation to achieve a...
The paper investigates an algorithm for the numerical solution of a parametric eigenvalue problem for the Helmholtz equation on the plane specially tailored for the accurate mathematical modeling of lasing modes of microring lasers. The original prob...
In non-equilibrium plasmas, the temperature cannot be uniquely determined unless the energy-distribution function is approximated as a Maxwell–Boltzmann distribution. To overcome this problem, we applied Tsallis statistics to determine the temp...
The exponential function
This work presents the modified Lagrange interpolating polynomial (MLIP) method, which aims to provide a straightforward procedure for deriving accurate analytical approximations of a given function. The method introduces an exponential function with...
In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from resea...
This study considers the Fourier component in the basic Rankine–Fourier decomposition of the flows created by pulsating sources and dipoles (with time-harmonic strength) uniformly distributed over a general flat triangle that steadily advances...
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