Three kinds of fragile points methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up the previous study original FPM symmetric Galerkin weak-form. The trial function piecewise-continuous, written as local Taylor expansions at points. A modified radial basis function-based differential qua...

We study the Cauchy problem for integrable nonlocal focusing nonlinear Schr\"odinger (NNLS) equation $ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 with step-like initial data close to ``shifted step function'' $\chi_R(x)=AH(x-R)$, where $H(x)$ is Heaviside function, and $A>0$ $R>0$ are arbitrary constants. Our main aim large-$t$ behavior of solution this problem. show that $R\in\left(\f...

*Correspondence: [email protected] Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan Abstract In this paper, we aim to investigate q-analogues of the natural transform on various elementary functions of special type. We obtain results associated with classes of q-convolution products, Heaviside functions, q-exponential...

Fractional order theory was used to characterize the accelerated creep phase of a nonlinear model. To accurately describe each stage anthracite model, “gyroscope” unit introduced by combining Heaviside function and damage definition. The effect on determined designing completing three-axis graded-separation loading tests anthracite. test curves were combined classify into five stages: transient...

In this article, we prove the existence of solutions to a nonlinear nonlocal elliptic problem with singualrity and discontinuous critical nonlinearity which is given as follows. \begin{align} \begin{split}\label{main_prob} (-\Delta)_p^su&=\mu g(x,u)+\frac{\lambda}{u^\gamma}+H(u-\alpha)u^{p_s^*-1},~\text{in}~\Omega u&>0,~\text{in}~\Omega, u&=0,~\text{in}~\mathbb{R}^N\setminus\Omega, \end{split} ...

This artcile is concerned with thermal buckling and thermal induced free vibration analyses of PCPs (perforated composite plates) with simply supported edges applying a mathematical model. The stiffness and density of PCP are defined locally using Heaviside distribution functions. The governing equations are derived based on CLPT. The present solution gives reasonable results in comparison with...

It is shown that cartesian product and pointwise-sum with a fixed compact set preserve various approximation-theoretic properties. Results for pointwise-sum are proved for F -spaces and so hold for any normed linear space, while the other results hold in general metric spaces. Applications are given to approximation of Lp-functions on the d-dimensional cube, 1 ≤ p < ∞, by linear combinations of...

Ground-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps and calls on variance. The latter leads to an ill-posed problem that we solve using regularization t...