In this paper we introduce the uniqueness and completeness problems of array comprehensions. An array comprehension has the uniqueness property if it deenes each array element at most once. Uniqueness is a necessary condition for correctness in single assignment languages such as Haskell, Id, and Sisal. The uniqueness problem can be stated as a data dependence problem, which in itself can be re...

Introduction [1] There is an ongoing debate in the field of religion and film studies about whether or not film makes a unique contribution to our understanding of religion. Since most religion and film scholars are concerned about the representation of religion on the silver screen, only a few scholars who are interested in something more than how religion is portrayed in the movies carry out ...

We consider the system of m linear equations in n integer variables Ax = d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1,1}n by reformulating the problem as a linear program. Uniqueness characterizations of ordinary linear programming solutions are utilized to obtain sufficient uniqueness conditions such as the intersection of the kernel of A and the dual con...

Unique object references have many important applications in object-oriented programming. For instance, with su cient encapsulation properties they enable safe and e cient transfer of message objects between concurrent processes. However, it is a long-standing challenge to integrate unique references into practical object-oriented programming languages. This paper introduces a new approach to e...

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

Numerical examples demonstrated that a prescribed positive Jacobian determinant alone can not uniquely determine a diffeomorphism. It is conjectured that the uniqueness of a transformation can be assured by its Jacobian determinant and the curl-vector. In this work, we study the uniqueness problem analytically and propose an approach to the proof of the uniqueness of a transformation with presc...