Bounded rewriting for linear term rewriting systems has been defined in (I. Durand, G. Sénizergues, M. Sylvestre. Termination of linear bounded term rewriting systems. Proceedings of the 21st International Conference on Rewriting Techniques and Applications) as a restriction of the usual notion of rewriting. We extend here this notion to the whole class of left-linear term rewriting systems, an...

In [2] a clever term rewriting characterization of the polytime functions is given by de ning a set RB′ of feasible rewrite rules for predicative recursion. It is shown that the derivation length function (DlRB′ ,f ) of RB′ for f is bounded by a monotone polynomial in the length of the inputs. We give a simpli ed proof of this result. As a consequence we obtain the stronger result that DlRB′ ,f...

x until it reaches a xed point. In order to determine whether an argument is a xed point, f x is compared with x. In the case of grammar analysis problems, the rst components of the elements of the grammar analysis problems are always the nonterminals of the given grammar. It follows that the rst components of the elements of f x and x are always equal, and that equality depends just on the sec...

This 2-year project description is part of the Digital Design Derivation Project of the Hardware Methods Laboratory, Computer Science Department, Indiana University. Participating researchers, students, and staff include Prof. Steven D. Johnson, Prof. David E. Winkel, Bhaskar Bose, Zheng Zhu, Kamlesh Rath, Esen Tuna, C. David Boyer, and Willie Hunt. The 2-year project investigates sequential de...

and Applied Analysis 3 The role of “compact operators” is replaced by that of “minimal one-sided ideals”. The proof of our results relies on the quasispatiality of the derivation and Banach algebra techniques. This paper is a continuation of 5 . Some definitions and notations can be found in 5 . 2. Preliminaries Throughout this paper, X is a complex Banach space, and X∗ is the topological dual ...

Abstract In the 1950s, the Nobel Prize winner John F. Nash has shown that under certain conditions, the best solution to the bargaining problem is when the product of the (increase in) utilities is the largest. Nash’s derivation assumed that we are looking for strategies that assign a single situation to each bargaining situation. In this paper, we propose a simplified derivation of Nash bargai...

Let R be a ring. An additive mapping F : ? is called generalized derivation if there exists d of such that F(xy) = F(x)y + xd(y) for all x,y R. The main purpose this paper to characterize some specific classes derivations rings. Precisely, we describe the structure noncommutative prime rings with involution belong particular class derivations. Consequently, recent results in line investigation ...

A classical theorem of S. Bochner states that a function f : R → C is the Fourier transform of a finite Borel measure if and only if f is positive definite. In 1938, I. Schoenberg found a beautiful converse to Bochner’s theorem. We present a non-technical derivation of of Schoenberg’s theorem that relies chiefly on the law of large numbers of classical probability theory.

A. Derivation of the proximal operation for the smoothed hinge loss By the definition of the smoothed hinge loss, we have that, for −1 ≤ y i v ≤ 0, f * i (v) = sup u∈R {uv − f i (u)} = sup u∈R uv − 1 2 (1 − y i u)

Let k[X] be the algebra of polynomials in n variables over a field k of characteristic zero, and let f ∈ k[X] r k. We present a construction of a derivation d of k[X] whose ring of constants is equal to the integral closure of k[f ] in k[X]. A similar construction for fields of rational functions is also given.