1,385 Results Found

The S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e.,...

We study $L_2$-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters ${\gamma }_j$ and ${\alpha }_j$ for $j\in \mathbb{N}$. W...

In life testing and reliability studies, most researchers have used the maximum likelihood estimation method to estimate unknown parameters, even though it has been proven that the maximum product of spacing method has properties as good as the maxim...

In this work, we first establish a new connection between adjoint Bernoulli’s polynomials and gamma function as a new sequence of linear positive operators denoted by ${\mathfrak{S}}_{r,\varsigma ,\lambda }(.;.)$. Further, convergence results for these sequences o...

We study the $g_E$-approximation property for the Banach space $E={\mathcal{\ell }}_q({\mathcal{\ell }}_p)$, which is an extension of Saphar’s p-approximation property. We establish some characterizations of the $g_E$-approximation property using the space of E-summing oper...

In rough set theory, there are many covering approximation spaces, so how to classify covering approximation spaces has become a hot issue. In this paper, we propose the concepts of a covering approximation $T_1$-space, F-symmetry, covering rough contin...

Some properties on Banach spaces, such as the Radon–Riesz, Dunford–Pettis and approximation properties, allow us to better understand the naive details about the structure of space and the robust inhomogeneities and symmetries in space. I...

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson’s ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law sha...

Intuitionistic Fuzzy Sets ($IF{S}_s$) and rough sets depending on covering are important theories for dealing with uncertainty and inexact problems. We think the neighborhood of an element is more realistic than any cluster in the processes of classificat...

This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry. The paper di...

In this work, we characterize the boundedness of t-generalized composition operators from $F(p,q,s)$ spaces to iterated weighted-type Banach space. We also provide estimates of the norm and the essential norm of t-generalized composition op...

In this paper, we prove the theorems on the simultaneous approximation of a pair of analytic functions by discrete shifts $(\zeta (s+ik{h}_1),\zeta (s+ik{h}_2,\alpha ))$, $h_1>0$, $h_2>0$ of the Riemann zeta function $\zeta \left(s\right)$ and Hurwitz zeta function $\mathrm{\&zeta}$...

Müntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces M_Λ,p of L_p functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, th...

Considered herein is the Cauchy problem of the two-component Novikov system. In the periodic case, we first constructed an approximate solution sequence that possesses the nonuniform dependence property; then, by applying the energy methods, we manag...

This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various funct...

In this article, we give the sharp bounds of probabilistic Kolmogorov $\left(N,\delta \right)$-widths and probabilistic linear $\left(N,\delta \right)$-widths of the multivariate Sobolev space $W_2^A$ with common smoothness on a $S_q$ norm equipped with the Gaussian measure $\mu$, where...

The aim of this paper is to apply polynomial approximation by sums of squares in several real variables to the multidimensional moment problem. The general idea is to approximate any element of the positive cone of the involved function space with su...

Our paper is devoted to indicating a way of generalizing Mann’s iteration algorithm and a series of fixed point results in the framework of b-metric spaces. First, the concept of a convex b-metric space by means of a convex structure is introdu...

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...

Visualization of the chemical space is useful in many aspects of chemistry, including compound library design, diversity analysis, and exploring structure–property relationships, to name a few. Examples of notable research areas where the visua...

The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimizat...

In this paper, the uniform approximation of continuous functions on $[0,1]$ by rational functions with prescribed poles and bounded multiplicities is studied. A classical theorem of Fichera characterizes density in $C\left(\right[0,1\left]\right)$ through the divergence of a...

The paper is devoted to Epstein zeta-function ${\zeta }_3\left(s\right)$, $s=\sigma +it$, of a quadratic form of three variables. We obtain a probabilistic characterization of the function ${\zeta }_3\left(s\right)$ in terms of weak convergence of probability measures in the space of...

The spontaneous scalarization of Schwarzscild-AdS is investigated in the Einstein-scalar-Gauss–Bonnet (ESGB) theory. Firstly, we construct scalarized AdS black holes numerically. Secondly, making use of the homotopy analysis method (HAM), we ob...

Pathological examination by endoscopic ultrasound–fine needle aspiration is not possible in approximately 10% of pancreatic tumor cases. Pancreatic juice cytology (PJC) is considered an alternative diagnostic method. However, its diagnostic cap...

In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of t...

The existence, uniqueness, and Carath$\acute{\mathrm{e}}$odory’s successive approximation of the fractional neutral stochastic differential equation (FNSDE) in Hilbert space are considered in this paper. First, we give the Carath$\acute{\mathrm{e}}$odory’s appro...

Using the concept of category, we provide some insight into and prove an intrinsic property of the category AprS of approximation spaces and continuous functions. We also introduce rough closure and rough interior operators to characterize clopen top...

We consider impulsive stochastic delay differential equations with state-dependent impulse times, where the k-th impulse occurs at a time $\tau$ satisfying $\tau ={\tau }_k\left(u\left({\tau }^{-}\right)\right)$. In generalized Lipschitz and growth conditions for coefficients, e...

The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense...

The goal of this paper is to consider a differential equation system written as an interesting equivalent form that has not been used before. Using Perov’s fixed point theorem in generalized metric spaces, the existence and uniqueness of the so...

The aim of this manuscript is to get the strong convergence theorems of the Moudafi’s viscosity approximation methods for an asymptotically nonexpansive nonself mapping in $CAT\left(0\right)$ spaces.

The thermal scattering law (TSL), i.e., S(α,β), represents the momentum and energy exchange phase space for a material. The incoherent and coherent components of the TSL correlate an atom’s trajectory with itself and/or with other atoms in the lattic...

Great attention has been paid to the propagation of electromagnetic (EM) waves across the sea surface due to its important applications. Most of the previous research, however, focuses on the half-space model illustrating the deep sea environment. In...

This paper is devoted to the approximation of a certain class of analytic functions by shifts $\mathcal{Z}(s+i\tau )$, $\tau \in \mathbb{R}$, of the modified Mellin transform $\mathcal{Z}\left(s\right)$ of the square of the Riemann zeta-function $\zeta (1/2+it)$. More precisely, we prove the exi...

The increasing complexity of urban structures has significantly elevated the risk and severity of façade fires in high-rise buildings. Unlike traditional models assuming continuous fuel beds, real-world fire scenarios often involve discrete co...

We study the multivariate $L_2$-approximation problem ${\mathrm{APP}}_d$ defined over a Banach space in the average case setting. The space is equipped with a zero-mean Gaussian measure with a weighted covariance kernel, which depends on parameter sequences $\mathit{\alpha }={\{}_{}$...

This article primarily examines the approximation properties of a weighted Sobolev space $W_{2,\kappa }^r$ defined on a sphere ${\mathbb{S}}^{d-1}$ equipped with Gaussian measures. Specifically, this study focuses on both the average case and probabilistic case sett...

We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to $\mu$-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost opti...

Spacing design for group cable bolt systems remains largely empirical and rarely considers stress interaction and displacement overlap together. This study develops a dual-index interaction framework for two representative cable bolt configurations i...

The distribution of word probabilities in the monkey model of Zipf’s law is associated with two universality properties: (1) the exponent in the approximate power law approaches −1...

Trajectory planning for parallel manipulators in dynamic environments entails high computational costs, as geometric collision checks must be repeated whenever the environment changes. This paper proposes a trajectory planning method that shifts the...

We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.

Ship route planning is a crucial activity that must consider not only the safety of the ship but also the safe passage of nearby ships in the same space and time. This study aims to provide general route-planning guidance to shipping traffic by impro...

This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces. The analysis is carried out using a generalized version of D...

We describe the construction of an optical-space, cylindrical black hole induced by high pressure in a dense fluid. Using an approximate analogy between curved spacetime and optics in moving dielectric media, we derive the mass of the black hole thus...

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki’s generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further...

Developing short-term forecasting models for global atmospheric temperature and wind in near space is crucial for understanding atmospheric dynamics and supporting human activities in this region. While numerical models have been extensively develope...

To provide a ground-based experimental reference for free-space optical time–frequency synchronization in future space applications, this paper investigates the impact of beam drift and dynamic link-state variations on free-space laser links. A...

In this paper, we propose a semi-implicit difference scheme for solving one-dimensional nonlinear space-fractional diffusion equations. The method is first-order accurate in time and second-order accurate in space. It uses a fractional central differ...