For the elliptic equation −∇ · (p(x)∇v) + λq(x)v = f, x ∈ Ω ⊂ R, the problem of determining when one or more of the coefficient functions p, q, and f are defined uniquely by a knowledge of one or more of the solution functions v = vp,q,f,λ is considered.

1 . I N T R O D U C T I O N During the last two decades or so, inverse scattering problems for the Helmholtz equation have enjoyed a remarkable degree of popularity, both in pure and applied contexts (see the monograph [1] and the references therein). One of the most important theoretical considerations in inverse scattering problems is uniqueness. Different approaches have been proposed [2-10]...

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

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...