Uniqueness of normal forms (UN=) is an important property of term rewrite systems. UN= is decidable for ground (i.e., variable-free) systems and undecidable in general. Recently it was shown to be decidable for linear, shallow systems. We generalize this previous result and show that this property is decidable for shallow rewrite systems, in contrast to confluence, reachability and other proper...

background decrease in walking ability and balance disorders are common in multiple sclerosis patients. the aim of this study was to determine the effect of two different therapeutic methods on functional balance in people with multiple sclerosis. material and methods in this clinical trial study, 16 patients with multiple sclerosis (8male and 8 female with expanded disability status scale(edss...

Erythemal ultraviolet (UV)-radiation exposure to the right hand, mid-arm, shoulder, chin, nose and left and right sides of the face has been evaluated in a car from a large family class and a car from a small car class. In the small car, the site with highest exposure received 2.2 times more radiation than the site with the highest exposure in the larger car. In both cars, highest erythemal exp...

In a previous paper, the authors showed that the information complexity of the Fredholm problem of the second kind is essentially the same as that of the approximation problems over the spaces of kernels and right-hand sides. This allowed us to give necessary and sufficient conditions for the Fredholm problem to exhibit a particular level of tractability (for information complexity) over weight...

We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be saved and recombined through the eigenvectors of the tridiagonal projection matrix, which is equivalent theoretically to unrestarted Lanczos. Our algorithm capit...

Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial residuals must be collinear and this collinearity must be maintained at restart. Thus we cannot simultaneously solve shifted systems with unrelated right-hand si...

We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting.

We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.

We derive a differential inclusion governing the evolution of optimal trajectories to the Mayer problem. The value function is allowed to be discontinuous. This inclusion has convex compact right-hand sides.

The multiobjective problem with fuzzy goals (which may also represent fuzzy right hand sides of the constraints) is formulated as a fuzzy goal programming problem. A new approach and a new solution method are proposed.