Dependent types have been proposed for functional programming languages as a means of expressing semantically rich properties as types. In this paper, we consider the problem of bringing semantic programming based on dependent types to an object-oriented language. A type-theoretically light extension to Java (with generics) is proposed, called property types. These are types indexed not by othe...

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

We derive multiplicative updates for solving the nonnegative quadratic programming problem in support vector machines (SVMs). The updates have a simple closed form, and we prove that they converge monotonically to the solution of the maximum margin hyperplane. The updates optimize the traditionally proposed objective function for SVMs. They do not involve any heuristics such as choosing a learn...

The geometric programming problem (GP) is to minimize a posynomial g(t) = I ∑

We consider a multiobjective linear program and the coefficients of the multiobjective function are subject to some uncertainties. Let x be an efficient point. We propose a procedure to compute an additive and multiplicative (percentage) tolerance in which all the objective function coefficients may simultaneously and independently vary while preserving the efficiency of x. Although the toleran...

Wepropose a generic dynamic programming algorithm for computing the inverses of a multiplicative function. We illustrate our algorithm with Euler’s totient function and the sum of k-th powers of divisors. Our approach can be further adapted for computing certain functions of the inverses, such as their quantity, the smallest/largest inverse, which may be computed faster than the inverses themse...

The nucleon is introduced as a new allocation concept for non-negative cooperative n-person transferable utility games. The nucleon may be viewed as the multiplicative analogue of Schmeidler's nucleolus. It is shown that the nucleon of (not necessarily bipartite) matching games can be computed in polynomial time. 9 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. e term calculus is proved complete for a semantics in linearly distributive categories with additives. It is also shown that proof equivalence is decidable by showing that the cut elimination rewrites supply a conžuent rewriting system modul...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.