Let A and B be bounded linear operators on a Hilbert space satisfying A ≥ B ≥ 0. The well-known Furuta inequality is given as follows: Let r ≥ 0 and p > 0; then A r 2 Amin{1,p}A r 2 ≥ (A r 2 BpA r 2 ) min{1,p}+r p+r . In order to give a self-contained proof of it, Furuta (1989) proved that if 1 ≥ r ≥ 0, p > p0 > 0 and 2p0 + r ≥ p > p0, then (A r 2 Bp0A r 2 ) p+r p0+r ≥ (A r 2 BpA r 2 ) p+r p+r ...

Suppose that S is the space of all summable sequences a wlth lla’S n>oSUp ajJl and J the space of all sequences 6 of bounded variation aJBl S "a"SllSl’J this inequality leads to e description of e dual space of S as J. It, related Inequalities, and their consequences are the content of this paper, In parttcular the Inequality cited above leads directly to the Stolz form of Abel’s theorem and pr...

where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a...

A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality. Logarithmic Sobolev inequalities capture the spirit of classical Sobolev inequalities with the logarithm function replacing powers, and they can be considered as limiting cases of...

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...

The critical number of G, denoted by c(G), is the smallest s such that Σ(S) = G for every subset S of G with cardinality s not containing 0. The parameter c(G) was first studied by Erdős and Heilbronn in [4]. They obtained the inequality c(Zp) ≤ 3 √ 6p. Olson proved in [13] that c(Zp) ≤ √ 4p− 3 + 1. The authors of [1] obtained the inequality c(Zp) ≤ √ 4p− 7. The evaluation of c(G) for groups wi...

In this paper I examine the sources of wage inequality changes among prime age male workers in Brazil during the 1980’s and 1990’s. Inequality increased in the 1980’s and decreased in the 1990’s. I begin by decomposing these changes into three effects. First, the effect due to changes in the skill distribution of the workers; second, the effect due to changes in skill prices and premiums; and t...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of Walsh (1978) on the local times of the stream W (s, •), near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of Khoshnevisan (1995a): as s → 0, the...

Abstract: One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of [20] on the local times of the stream W (s, •) near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of [10]: As s → 0, the local times of...