In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matr...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the firstpassage time density and provide an upper bound for this function. In the cas...

In this work, we study the blow-up and global solutions for a quasilinear reaction–diffusion equation with a gradient term and nonlinear boundary condition:      (g(u)) t = ∆u + f (x, u, |∇u| 2 , t) in D × (0, T), ∂u ∂n = r(u) on ∂D × (0, T), u(x, 0) = u 0 (x) > 0 in D, where D ⊂ R N is a bounded domain with smooth boundary ∂D. Through constructing suitable auxiliary functions and using ma...

We consider a Schrödinger operator HD A with a non-vanishing radial magnetic field B = dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator. Under some assumptions on an additional radial potential V the operator HD A − V has a discrete negative spectrum and we ob...

We use the biorthogonal multiwavelets related by differentiation constructed in previous work to construct compactly supported biorthogonal multiwavelet bases for the space of vector fields on the upper half plane R+ such that the reconstruction wavelets are divergence-free and have vanishing normal components on the boundary of R+. Such wavelets are suitable to study the Navier–Stokes equation...

Keywords: Upper and lower solutions p-Laplacian operator Fractional differential equation Integral boundary condition Eigenvalue a b s t r a c t In this paper, we are concerned with the eigenvalue problem of a class of singular p-Lapla-cian fractional differential equations involving the Riemann–Stieltjes integral boundary condition. The conditions for the existence of at least one positive sol...

We present the theory of the multi-α-solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound Nu = 1+(1/6)R is between the bounds Nu = 1+0.152R for the case of a fluid ...

We consider the boundary value problem y(n)(t) = P (t, y), t ∈ (0, 1) y(ti) = 0, j = 0, . . . , ni − 1, i = 1, . . . , r, where r ≥ 2, ni ≥ 1 for i = 1, . . . , r, ∑r i=1 ni = n and 0 = t1 < t2 < · · · < tr = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for t...

Searching spatial data is an important operation for scientific simulations which are performed mostly with periodic boundary conditions. An R-Tree is a well known tree data structure used to contain spatial objects and it is capable of answering to spatial searching queries in an efficient way. In this paper, a novel method to construct an R-Tree considering periodic boundary conditions is pre...