Probability inequalities are. obtained for the supremum of a weighted empirical process indexed. by a Vapnik-Cervonenkis class C of sets. These inequalities are particularly useful under the assumption P(ufC E: C : P(C) < t D -? 0 as t -? o. They are used to obtain almost sure bounds on the rate of growth of the process as the sample size approaches infinity, to find an asymptotic sample modulu...

In a well-known paper[5], Arora, Rao and Vazirani obtained an O( √ log n) approximation to the Balanced Separator problem and Uniform Sparsest Cut. At the heart of their result is a geometric statement about sets of points that satisfy triangle inequalities, which also underlies subsequent work on approximation algorithms and geometric embeddings. In this note, we give an equivalent formulation...

O F Degree theory for generalized variational inequalities and applications B.T. Kien , M.-M. Wong , N.C. Wong , J.C. Yao a,* Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan Department of Information and Technology, Hanoi University of Civil Engineering, 55 Giai Phong, Hanoi, Viet Nam Department of Information Management, Meiho Institute of Technology, ...

Abstract: In this paper, constraint rotation techniques are considered for preconditioning 0–1 knapsack problems. These techniques permit one to generate new inequalities by means of rotation of the original ones in order to approach the convex hull associated with the feasible integer points. The time and space complexities of Kianfar’s inequality rotation algorithm for combinatorial problems ...

if global trade were fair, it is argued, then international aid would be unnecessary and inequalities inherent to the economic system would be justifiable. here, we argue that while global trade is unfair, in part because richer countries set the rules, we believe that additional interventions must go beyond trade regulation and short-term aid to redress inequalities among countries that will p...

The minimum weight feedback vertex set problem (FVS) on series-parallel graphs can be solved in O(n) time by dynamic programming. This solution, however, does not provide a “nice” certificate of optimality. We prove a min-max relation for FVS on series-parallel graphs with no induced subdivision of K2,3 (a class of graphs containing the outerplanar graphs), thereby establishing the existence of...

The bulk scaling limit of eigenvalue distribution on the complex plane ${\mathbb{C}}$ Ginibre random matrices provides a determinantal point process (DPP). This is typical example disordered hyperuniform system characterized by an anomalous suppression large-scale density fluctuations. As extensions DPP, we consider family DPPs defined $D$-dimensional spaces ${\mathbb{C}}$, $D \in {\mathbb{N}}$...

Let P be a linear, elliptic second order symmetric operator, with an associated quadratic form q, and let W be a potential such that the Hardy inequality λ0 ∫ Ω Wu 2 ≤ q(u) holds with (non-negative) best constant λ0. We give sufficient conditions so that the spectrum of the operator 1 W P is [λ0,∞). In particular, we apply this to several well-known Hardy inequalities: (improved) Hardy inequali...

We find sufficient conditions for a probability measure μ to satisfy an inequality of the type ∫ Rd fF ( f ∫ Rd f 2 dμ ) dμ ≤ C ∫ Rd f2c∗ ( |∇f | |f | ) dμ + B ∫ Rd f dμ, where F is concave and c (a cost function) is convex. We show that under broad assumptions on c and F the above inequality holds if for some δ > 0 and ε > 0 one has ∫ ε 0 Φ ( δc [ tF ( 1t ) Iμ(t) ]) dt <∞, where Iμ is the isop...

Given an arbitrary Petri net structure which may have uncontrollable and unobservable transitions and may be unbounded, the procedure described in this paper generates a supervisor for liveness enforcement. The supervisor is specified as a conjunction of linear marking inequalities. For all initial markings satisfying the linear marking inequalities, the supervised Petri net is live. Moreover, ...