UNIFORM ESTIMATES OF THE RESOLVENT OF THE LAPLACE –BELTRAMI OPERATOR ON INFINITE VOLUME RIEMANNIAN MANIFOLDS WITH CUSPS

Abstract

In this article we extract characteristic points from scattering theories of the Lax–Phillips type and the Wilcox one, and in view of those points we show that the both settings can be translated into each other. Furthermore, we construct concrete translation representations of the Lax–Phillips type for the elastic equation in the half-space, in order to show the good selection from admitted constructions in the abstract arguments.     

用平移网络逼近函数及其导数

若Х（ｘ）∈Ｗ１Ｍ（Ｒ＾ｄ）,利用Х构造出具体的平移网络逼近Ｓｏｂｏｌｅｖ空间中的函数并给出逼近阶的估计。     

强平均解与概周期解的存在性

本文定义了概周期微分方程的强平均解,利用强平均解的性质,讨论了强平均解与概周期解的关系,从而建立了概周期解存在的若干定理。     

Albert's Construction for Semifields of Even Order

Albert's construction for commutative semifields of order 2 ⁿ , n odd, is presented. It avoids the construction of a presemifield and, in the case that n is prime, allows us to determine automorphism groups and the isomorphism classes. If n is a prime greater than three, the semifields are strictly not associative. These semifields are new for all n greater than three, differing from the binary semifields in that each admits only the trivial automorphism.

The authors present an explicit construction of an isotope of the 2⁵-element semifield that contains a subsemifield of order 2².     

Fiber Hamiltonians in non-relativistic quantum electrodynamics

A translation invariant Hamiltonian H of non-relativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum PT:

     

FSDB: a frameshift signal database

Programmed frameshifting is a recoding event in which a ribosome shifts reading frame by one or more nucleotides at a specific mRNA signal between overlapping genes. Programmed frameshifting is involved in the expression of many genes in a wide range of organisms, especially in viruses and bacteria. The mechanism of programmed frameshifting is not fully understood despite many studies, and there are few databases available for detailed information on programmed frameshifting. We have developed a database called FSDB (Frameshift Signal Database), which is a comprehensive compilation of experimentally known or computationally predicted data about programmed ribosomal frameshifting. FSDB provides a graphical view of frameshift signals and the genes using programmed frameshifting for their expression. It also allows the user himself/herself to find programmed frameshift sites in genomic sequences using a program called FSFinder (http://wilab.inha.ac.kr/fsfinder2). We believe FSDB will be a valuable resource for scientists studying programmed ribosomal frameshifting. FSDB is freely accessible at http://wilab.inha.ac.kr/fsdb/.     

Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces

This is a continuation of the investigation into the theory of wavelet frames for general affine subspaces. The main focus of this paper is on the structural properties of affine subspaces. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces, while every reducing subspace (with respect to the dilation and translation operators) is the orthogonal direct sum of two purely non-reducing ones. This result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine. Motivated by the fundamental question as to whether every affine subspace is singly-generated, and by a recent result that every singly generated purely non-reducing subspace admits a singly generated wavelet frame, we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of “small size”. As a consequence we establish a connection between the above mentioned two questions.     

Why ultra high performance liquid chromatography produces more tailing peaks than high performance liquid chromatography, why it does not matter and how it can be addressed

The purpose of this study is to demonstrate, with experiments and with computer simulations based on a firm chromatographic theory, that the wide spread perception of that the United States Pharmacopeia tailing factor must be lower than 2 (T(f)<2) is questionable when using the latest generation of LC equipment. It is shown that highly efficient LC separations like those obtained with sub-2 μm porous and 2.7 μm superficially porous particles (UHPLC) produce significantly higher T(f)-values than the corresponding separation based on 3 μm porous particles (HPLC) when the same amount of sample is injected. Still UHPLC separations provide a better resolution to adjacent peaks. Expressions have been derived that describe how the T(f)-value changes with particle size or number of theoretical plates. Expressions have also been derived that can be used to scale the injection volume based on particle size or number of theoretical plates to maintain the T(f)-value when translating a HPLC separation to the corresponding UHPLC separation. An aspect that has been ignored in previous publications. Finally, data obtained from columns with different age/condition indicate that T(f)-values should be complemented by a peak width measure to provide a more objective quality measure.     

Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

Regular left-continuous t-norms

A left-continuous (l.-c.) t-norm ⊙ is called regular if there is an n<ω such that the map x ↦ x⊙a has, for any a∈[0,1], at most n discontinuity points, and if the function mapping every a∈[0,1] to the set behaves in a specifically simple way. The t-norm algebras based on regular l.-c. t-norms generate the variety of MTL-algebras. With each regular l.-c. t-norm, we associate certain characteristic data, which in particular specifies a finite number of constituents, each of which belongs to one out of six different types. The characteristic data determines the t-norm to a high extent; we focus on those t-norms which are actually completely determined by it. Most of the commonly known l.-c. t-norms are included in the discussion. Our main tool of analysis is the translation semigroup of the totally ordered monoid ([0,1];≤,⊙,0,1), which consists of commuting functions from the real unit interval to itself.