A grounded M -Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most M along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their typical value at the root v0 of the tree. We prove that the probability that the value of a uniformly chosen random function at v0 is more than M + t is doubly...

The vertex boundary-width problem (for short VBWP) is to determine the value of vbw(G)=max1 |V |minS⊆V,|S|= |N(S)| for a given graph G= (V ,E), where N(S)= {v / ∈ S|v is a neighbor of u for some u ∈ S}. In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees. © 2007 Elsevier B.V. All rights reserved.

In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matr...

Two alternative exact characterizations of the minimum error probability of Bayesian M -ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness...

In coding theory, Plotkin’s upper bound on the maximal cadinality of a code with minimum distance at least d is well known. He presented it for binary codes where Hamming and Lee metric coincide. After a brief discussion of the generalization to q-ary codes preserved with the Hamming metric, the application of the Plotkin bound to q-ary codes preserved with the Lee metric due to Wyner and Graha...

In this paper, we propose a construction of fullrank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of fullrank binary 1-perfect codes (1994). Properties of i-components of q-ary Hamming codes are investigated and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1...

in this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. we also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Open answer set programming combines the strengths of logic programming (a rule-based presentation and a nonmonotonic semantics) and description logics (open domains). Reasoning under an open answer set semantics is undecidable in general, but decidability can be obtained for particular classes of logic programs, e.g., for bound guarded programs. In this paper, we show how bound guarded program...

Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd integer. In this paper, two new families of p-ary sequences of period N = p −1 2 are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d = 4 and d = (p +1)/2 = N +1. The upper bound on the magnitude of correlation values of two sequences in the family is derived using Weil bound. Their upper bound is derived as 3 √ ...