We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...

This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in...

Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm. Mots clés : Arbres couvrants de poids minimum, sécurisation des réseaux.

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular function or minimize a nonincreasing supermodular function in the setting of bounded total curvature c. In the case of submodular maximization with curvature ...

We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and the elementary sorting operators acting on permutations. The two others are the monoid algebras of nondecreasing functions and nondecreasing parking functions....

Proof of the Paper’s Theorem 4: As in the proof of Theorem 1 in the paper, we apply a theorem by Koopmans (1960, Section 14). First note that by the fact that each ui is nondecreasing and increasing in some dimension on [0, 1] and V satisfies unanimity, his postulates 2 and 5 are satisfied. Next, his postulate 1 follows from continuity (in fact, differentiability) of V under the metric d(C,C ′)...

We present results that allow the researcher in certain cases to determine the direction of the bias that arises when control for confounding is inadequate. The results are given within the context of the directed acyclic graph causal framework and are stated in terms of signed edges. Rigorous definitions for signed edges are provided. We describe cases in which intuition concerning signed edge...

In a quadratic number field Q(V~D), D a squarefree integer, with class number 1, any algebraic integer can be decomposed uniquely into primes, but for only 21 domains Euclidean algorithms are known. It was shown by Cohn [5] that for D < —19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs. We extend this result by showing that there does no...

In this paper, a special class of boundary value problems, −▵u=λuq+ur,inΩ,u&gt;0, inΩ,n·∇u+g(u)u=0,on∂Ω, where 0&lt;q&lt;1&lt;r&lt;N+2N−2 and g:[0,∞)→(0,∞) is nondecreasing C1 function. Here, Ω⊂RN(N≥3) bounded domain with smooth ∂Ω λ&gt;0 parameter. The existence the solution verified via sub- super-solutions method. addition, influences parameters on minimum are also discussed. second positive...

In the case of proportional allocation goods and burdens, shares all agents with respect to their values are equal, i.e., they form a constant sequence. degressively this sequence is nondecreasing when increasingly ordered according values. The division performed principle ambiguous, its selection requires many negotiations among participants. aim paper limit range such problem complex, set fea...