Hara [Ha3] and Smith [Sm2] independently proved that in a normal Q-Gorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R,∆) of a normal ring R and an effective Q-Weil divisor ∆ on SpecR. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.

Let K n denote a regular n-gon with unit side length. For two regular polygons K n and K m let the relative Newton number N(K n ; K m) of K n and K m be the maximum number of congruent copies of K m that can touch K n without having interior points in common. In this paper we determine the exact value of N(K n ; K m) for various pairs (n; m).

The low level acoustico-visual association reported by Yehia et al. (Speech Comm., 26(1):23-43, 1998) is exploited for audio-visual speech enhancement with natural video sequences. The aim of this study is to demonstrate that the redundant components of AV speech are extractible with a suitable representation which does not involve any categorization process. A comparative study is achieved bet...

The statistical Machine Translation Model has two components: a language model and a translation model. This paper describes how to improve the quality of the translation model by using the common word pairs extracted by two asymmetric learning approaches. One set of word pairs is extracted by Viterbi alignment using a translation model, the other set is extracted by Viterbi alignment using ano...

The celebrated Regularity Lemma of Szemerédi asserts that every sufficiently large graph G can be partitioned in such a way that most pairs of the partition sets span -regular subgraphs. In applications, however, the graph G has to be dense and the partition sets are typically very small. If only one -regular pair is needed, a much bigger one can be found, even if the original graph is sparse. ...

Kepler (1619) and Croft (1980) have considered largest homothetic copies of one regular polytope contained in another regular polytope. For arbitrary pairs of polytopes we propose to model this as a quadratically constrained optimization problem. These problems can then be solved numerically; in case the optimal solutions are algebraic, exact optima can be recovered by solving systems of equati...

The central concept in Szemerédi’s powerful regularity lemma is the so-called ε-regular pair. A useful statement of Alon et al. essentially equates the notion of an ε-regular pair with degree uniformity of vertices and pairs of vertices. The known proof of this characterization uses a clever matrix argument. This paper gives a simple proof of the characterization without appealing to the matrix...

Motivated by questions in the study of relative trace formulae, we construct a generalization Grothendieck's simultaneous resolution over regular locus certain symmetric pairs. We use this space to prove version results Donagi and Gaitsgory about automorphism sheaf stabilizers. also obtain partial toward applications Springer theory for spaces.

In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of families forms. this article, we prove the existence pairs representing same integers which not in Kaplansky's list.

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.