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...

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...

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...

2 An Interesting Tiling Problem We will work with a simply connected subset R ⊆ Z (thought of as a union of unit cubes). Usually we will think of R as being a hyper-rectangle, but it doesn’t have to be. Let ui denote the unit vector in the ith coordinate and let u∗ = (1, 1, . . . , 1). Let RL = {x ∈ R | ∃i ∈ [k], x− ui 6∈ R} denote the lower boundary of R. A subset S ⊆ R is a downset if RL ⊆ S ...

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...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...

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...

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

We derive a lower bound for energies of harmonic maps of convex polyhedra in R 3 to the unit sphere S, with tangent boundary conditions on the faces. We also establish that C maps, satisfying tangent boundary conditions, are dense with respect to the Sobolev norm, in the space of continuous tangent maps of finite energy. Mathematics Subject Classifications (2000). 58E20, 35J55.

Recently it was found that in the lead-free (1-x)BaZr0.2Ti0.8O3-xBa0.7Ca0.3TiO3 (BZT-xBCT) system, the highest piezoelectric d33 coefficient appears at the tetragonal (T) - orthorhombic (O) phase boundary rather than the O - rhombohedral (R) phase boundary, but the physical origin of it is still unclear. In this work we construct the phase diagram of the BZT-xBCT system using a generic sixth-or...