In this paper, we examine the linear codes with respect to Hamming metric from incidence matrices of zero-divisor graphs vertex set consisting all non-zero zero- divisors ring ℤn and two distinct vertices being adjacent if their product is zero over ℤn. The main parameters are obtained.

A nowhere-zero k-flow on a graph G is an assignment of a direction and a non-zero integer in absolute value smaller than k to each edge of G in such a way that, for each vertex, the sum of incoming values equals the sum of outgoing values. Nowhere-zero flow problems evolved from flowcolouring duality to a theory which has a central role in graph theory. There are many important flow problems wh...

Japanese dialogue containing zero pronouns is analyzed for the purpose of automatic Japanese-Engl ish conversation translation. Topic-driven Discourse Structure is formalized which ident i f ies ma in ly non -human zero pronouns as a by-product. Other zero pronouns are handled us ing cogni t ive and soc io l ingu i s t i c i n fo rma t ion in honorific, deictic, speech-act and mental predicates...

We suggest practical sub-linear size zero-knowledge arguments for statements involving linear algebra. Given commitments to matrices over a finite field, we give a sub-linear size zero-knowledge argument that one committed matrix is the product of two other committed matrices. We also offer a sub-linear size zero-knowledge argument for a committed matrix being equal to the Hadamard product of t...

We investigate non-unique factorization of polynomials in Zpn [x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Zpn [x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Zpn [x]...

Let V be a real unitary space. A real unitary space is said to be a subspace of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the zero of it = the zero of V , (iii) the addition of it = (the addition of V )↾[: the carrier of it, the carrier of it :], (iv) the external multiplication of it = (the external multiplication of V )↾[: R, the carrie...

The product of two zero mean correlated normal random variables, and more generally the sum independent copies such has received much attention in statistics literature appears many application areas. However, important distributional properties are yet to be recorded. This review paper fills this gap by providing basic theory for variables. Properties covered include probability cumulative dis...

Demand for product characteristics is examined within the context of models that allow for both corner and interior solutions corresponding to zero and non-zero demand. Product attribute information is associated with marginal utility and curvature (satiation) parameters of various utility functions. Empirical applications demonstrate the need for incorporating characteristics in a fairly gener...