5,887 Results Found

Several iterative integro-differential formulations for two-point, second- and third-order, nonlinear, boundary-value problems of ordinary differential equations based on Green’s functions and the method of variation of parameters are presented...

This paper provides several illustrations of the numerous remarkable properties of the lambda extensions of the two-point correlation functions of the Ising model, shedding some light on the non-linear ODEs of the Painlevé type they satisfy. W...

As convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadam...

Volume fraction, or one-point statistics, is commonly used to homogenize composites. However, it contains no geometric information regarding the spatial distribution of the phases. The spatial distribution can be characterized using higher-order stat...

This paper provides results on the sign of the Green function (and its partial derivatives) of an n-th order boundary value problem subject to a wide set of homogeneous two-point boundary conditions. The dependence of the absolute value of the Green...

It is shown that a class of symmetric solutions of scalar non-linear functional differential equations can be investigated by using the theory of boundary value problems. We reduce the question to a two-point boundary value problem on a bounded inter...

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives...

In this paper, we obtain new estimates for the error function of the Hermitian interpolating polynomial for functions in $C^n[a,b]$. Specifically, explicit and sharp estimates are derived over the $L_p$ norms (for $1\le p\le \infty$) of the n-th derivative,...

Green’s functions for linear two-point boundary-value problems subject to non-homogeneous Neumann’s boundary conditions are derived. It is shown that, for the differential operator $L\left(y\right)=y^{″}+ky$ with $k\ne n\pi /L$ where n is a natural n...

Pores, voids and cracks widely exist in rock materials, and the microstructural characteristics of rock are key to understanding its macroscopic behaviour because they strongly influence its mechanical behaviour in rock mass engineering. Owing to the...

The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated...

In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions...

This manuscript introduces the first hp-adaptive mesh refinement algorithm for the Theory of Functional Connections (TFC) to solve hypersensitive two-point boundary-value problems (TPBVPs). The TFC is a mathematical framework that analytically satisf...

In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spa...

We study the two-point problem $-u^{\prime \prime }\left(t\right)=w\left(t\right)f(t,u\left(t\right))$, $a<t<b$, $u\left(a\right)=M_1$, $u\left(b\right)=M_2$, where the weight w is positive and integrable on $(a,b)$ but may be unbounded near one or both endpoints. We prove that the problem has exactly one s...

We consider the second-order impulsive differential equation with impulses in derivative and without the damping term. Sufficient conditions that a nontrivial solution of the homogeneous equation having a zero of its derivative does not have a zero i...

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we con...

The two-point force-velocity model allows the assessment of the muscle mechanical capacities in fast, almost fatigue-free conditions. The aim of this study was to investigate the concurrent validity of the two-point parameters with directly measured...

This paper proposes an iterative algorithm for the search for common fixed points of two mappings. The properties of approximation and convergence of the method are analyzed in the context of Banach spaces. In particular, this article provides suffic...

Making use of the Boyd-Wong fixed point theorem, we establish a new existence and uniqueness result and an approximation process of the fixed point for the product of two nonlinear operators in Banach algebras. This provides an adequate tool for deri...

Gamma-ray bursts (GRBs) are the most luminous objects known: they outshine their host galaxies, making them ideal candidates for probing large-scale structure. Our aim is to determine the Spatial Two-Point Correlation Function of the GRBs with spectr...

In this paper, a two-point step-size gradient technique is proposed by which the approximate solutions of a non-linear system are found. The two-point step-size includes two types of parameters deterministic and random. A new adaptive backtracking li...

In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points He...

In this article, we use the applications of special functions in the form of Chebyshev polynomials to find the approximate solution of hyperbolic partial differential equations (PDEs) arising in the mathematical modeling of transmission line subject...

In this paper, a multi-objective optimization method is proposed to determine trade-off between conflicting operation objectives of wind farm (WF) systems, i.e., maximizing the output power and minimizing the output power fluctuation of the WF system...

Based on the geometry of a radial function, a sequence of approximations for arcsine, arccosine and arctangent are detailed. The approximations for arcsine and arccosine are sharp at the points zero and one. Convergence of the approximations is prove...

We study change-point estimation for absolutely continuous independent and identically distributed random variables from a nonparametric point of view. We define a sequence of processes and estimators based on U-statistics, whose kernel function has...

This is the second in a series of papers investigating the formulation of the simplified Dark Matter models with graviton mediators in cosmological backgrounds. We address here the crucial problem of the fundamental observable of interest, namely the...

In this paper, we obtain the explicit expression of the Green’s function related to a general n-th order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, an n dimensional parameter dependence is also...

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral...

The primary focus of this article is on applying specific generalized Jacobi polynomials (GJPs) as basis functions to obtain the solution of linear and non-linear even-order two-point BVPs. These GJPs are orthogonal polynomials that are expressed as...

Neuropathologic changes may occur in the nervous system due to long-term substance use, leading to functional disability with altering of balance. We know little about substance-related mechanisms that can cause movement disorders. This study investi...

This paper establishes some links between Sturm–Liouville problems and the well-known controllability property in linear dynamic systems, together with a control law design that allows any prefixed arbitrary final state finite value to be reach...

The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible, it is necessary to go beyond two-point statistics. Rather than going to highe...

We investigate the lateral dynamics in a purely viscous lipid membrane which is supported by a thin polymer sheet (polymer-supported membrane). The generalized frequency-dependent mobility tensor of the polymer-supported membrane is obtained by takin...

The therapeutic drug monitoring (TDM) of vancomycin (VCM) in critically ill patients often results in the estimated area being under the concentration–time curve (AUC) values that deviate from individual observations. In this study, we investig...

This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n-th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on the selection of a particular type...

In this paper, an optimal higher-order iterative technique to approximate the multiple roots of a nonlinear equation has been presented. The proposed technique has special properties: a two-point method that does not involve any derivatives, has an o...

In this work, we study the key role of generic Effective Field Theory (EFT) framework to quantify the correlation functions in a quasi de Sitter background for an arbitrary initial choice of the quantum vacuum state. We perform the computation in uni...

This article establishes a comparison principle for the nabla fractional difference operator ${\nabla }_{\rho \left(a\right)}^{\nu }$, $1<\nu <2$. For this purpose, we consider a two-point nabla fractional boundary value problem with separated boundary conditions and...

The objective of this study was to investigate the effectiveness of buccinator myomucosal island flaps for tongue reconstruction following malignant tumor resections. A retrospective study was performed on 52 patients who underwent tongue reconstruct...

(1) Background: Chorda tympani (CT) manipulation during stapes surgery affects its functions. We hypothesized that this alters tongue morphology and sensory functions. (2) Methods: Patients undergoing stapes surgery were tested 1 day preoperatively,...

In this paper, a new definition for the fractional order operator called the Caputo-Fabrizio (CF) fractional derivative operator without singular kernel has been numerically approximated using the two-point finite forward difference formula for the c...

The contribution presents a modified method of stochastic reconstruction of two porous stainless-steel filters. The description of their microstructures was based on a combination of the two-point probability function for the void phase and the linea...

In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo...

A universal method for modeling and characterizing non-circular particles is developed. The n-point correlation functions (n = 1, 2 and 3) are efficiently computed with a GPU parallel computing procedure. An algorithm for dynamic packing of impenetra...

With the substantial growth of the smart textiles market, electrical properties are becoming a basic requirement for most of the advanced textiles used in the development of wearable solutions and other textile-based smart applications. Depending on...

Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the ${\phi }_4^4$-scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- a...

The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary c...

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This method is based on cubic B-spline basis functions with a new approximation for the second-order derivative.&nbs...