A cyclic sum S(x) ■ T.x¡/(xj+i + x, + 2) 's formed with the N components of a vector x, where xN+l « JCj, xN+2 =• x2, and where all denominators are positive and all numerators are nonnegative. It is known that there exist vectors x for which S(x) < N/2 if N > 14 and even, and if N > 25. It has been proved that the inequality S(\) > N/2 holds for N ^ 12. Although it has been conjectured repeate...

18] V. Ramachandran. Parallel open ear decomposition with applications to graph biconnectivity and triconnectivity. A linear-time algorithm for a special case of disjoint set union. Transitive com-paction in parallel via branchings. 47 sequence L(u) (see preprocessing stage) of endpoints of edges of C in T H and the preorder numbers of the children of u in T H , this can be done in time O(jCj +...

New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n = 12 and n = 15. In many cases one can construct a code C containing at least d2=ne codewords. It is known that a code with jCj d2=(n + 1)e can be easily obtained. It should be noted that the proposed codes for n = 12 and n = 15 are also t...

Proof. To convert T into the canonical form with respect to variable x, we need to find an atomic constraint A which can equivalently represent all the subset constraints over x in T. Such an A can be obtained by enforcing that x belongs to the set difference of a) intersection of the subsets Ci’s such that there is a constraint of the form x ∈ Ci in T And b) union of the subsets Cj’s such that...

An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies the relation $JCJ=C$, where $J$ counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively in literature. Many results for centrosymmetric generalized wider classes of arise wide variety disciplines. In this paper, we obtain interesting spectral properties nonnegative...

This paper deals with polynomials orthogonal with respect to a Sobolev type inner product hf ; gi 1⁄4 Z p p f ðeÞgðeihÞdlðeÞ þ fðcÞA 1⁄2gðcÞ H ; where l is a positive Borel measure supported on 1⁄2 p; pÞ, A is a nonsingular matrix and jcj > 1. We denote fðcÞ 1⁄4 ðf ðcÞ; f 0ðcÞ; . . . ; f ðpÞðcÞÞ and vH the transposed conjugate of the vector v. We establish the connection of such polynomials wit...

We prove a generalization of an old conjecture of Pillai (now a theorem of Stroeker and Tijdeman) to the effect that the Diophantine equation 3 2 1⁄4 c has, for jcj > 13; at most one solution in positive integers x and y: In fact, we show that if N and c are positive integers with NX2; then the equation jðN þ 1Þ Nj 1⁄4 c has at most one solution in positive integers x and y; unless ðN; cÞAfð2; ...