Consider a stationary ergodic sequence of random variables X = (Xn)n≥1 with values in a finite alphabet X = {0, ..., dx − 1} of size dx ≥ 2. Denote by pn(x), x = (x1, ..., xn) ∈ X the function pn(x) = P(X1 = x1, ..., Xn = xn) and let X be the vector with the entries X1, ..., Xn. As is well known, the entropy of X : H(X) = −E log pn(X) is the minimal number of bits on average, needed to encode a...

We investigate the minimal graded free resolutions of ideals of at most n + 1 fat points in general position in Pn. Our main theorem is that these ideals are componentwise linear. This result yields a number of corollaries, including the multiplicity conjecture of Herzog, Huneke, and Srinivasan in this case. On the computational side, using an iterated mapping cone process, we compute formulas ...

For graphs G and H , the Ramsey number R(G,H) is the smallest positive integer n such that every graph F of order n contains G or the complement of F contains H . For the path Pn and the wheel Wm, it is proved that R(Pn,Wm) = 2n − 1 if m is even, m 4, and n (m/2)(m − 2), and R(Pn,Wm)= 3n− 2 if m is odd, m 5, and n (m− 1/2)(m− 3). © 2005 Elsevier B.V. All rights reserved.

The problem treated is the evaluation of Pn(a, m)t the probability that a determinant of order n having integral elements be congruent to a modulo m. By "probability" is meant the fraction obtained by dividing the number of favorable cases by the number of possible cases: let each element of the determinant range over the values 1, 2, • • • , m; among the ra" possible determinants let g be the ...

increasing patch edges in natural habitats, as a result of habitat fragmentation, are a major threat for wildlife populations, especially avifaunal communities. habitat edges provide different conditions compared to the core area which can directly or indirectly cause changes in species number, population and composition. this fact will demand a dissimilar management strategy. this study was co...

In this paper, we study certain Fuchsian groups H (p1, . . . , pn) , called generalized Hecke groups. These groups are isomorphic to ∏∗ n j=1Zpj . Let Γ be a subgroup of finite index in H (p1, . . . , pn) . By Kurosh’s theorem, Γ is isomorphic to Fr ∗ ∏∗ k i=1Zmi , where Fr is a free group of rank r , and each mi divides some pj . Moreover, H/Γ is Riemann surface. The numbers m1, . . . , mk are...

PURPOSE To assess the treatment outcome of pT1a renal tumors, comparing overall survival (OS) in patients treated with radical nephrectomy (RN) and partial nephrectomy (PN), and to examine the rate of utilization of PN in a tertiary institution in Serbia. METHODS Included were patients treated for pT1a kidney tumors with open RN or open PN during 1996-2013. The inclusion criterion was the pat...

BACKGROUND Parenteral nutrition (PN) has been a life-saving treatment in infants intolerant of enteral feedings. However, PN is associated with liver injury (PN Associated Liver Injury: PNALI) in a significant number of PN-dependent infants. We have previously reported a novel PNALI mouse model in which PN infusion combined with intestinal injury results in liver injury. In this model, lipopoly...

A spanning tree in a connected graph G is a subgraph that contains every vertex of G and is itself a tree. Clearly, if G is a tree then it has only one spanning tree. Every connected graph contains at least one spanning tree: iteratively remove an edge from any cycle that is present until the graph contains no cycles. Counting spanning trees is a very natural problem. Following Lyons [5] we wil...