Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Diphenylmethane transformations over boron trifluoride modified alumina and silica-alumina

Transformations of diphenylmethane were investigated in a flow system in the presence of alumina and silica-alumina modified with boron trifluoride at atmospheric pressure and elevated temperatures. Hydrogen transfer reaction was observed on addition of tetralin to the substrate stream. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

The adsorption of toluene on V-Sb oxides. Theoretical aspects

Toluene adsorption reactions on the (1 1 0) surface of VSbO₄ have been analyzed following the changes in the electronic structure of the hydrocarbon molecule and metal cation sites of the oxide using the Just Another Extended Hückel Molecular Orbital Program (JAEHMOP) code. The bonding character of these interactions has also been studied in the same theoretical framework. The calculations indicate that the exothermic hydrocarbon parallel interaction on Sb-V sites results in the weakening of one of the C-H bonds of the methyl fragment. This leads to a H-abstraction that involves the participation of a Sb-cation. Both methyl and phenyl fragments decrease their electronic population and so does the V-cation site. Most of these electrons are transferred to other V atoms in the bulk solid. As a result the LUMO of the toluene-oxide system fully populates. The analysis reveals that methyl-Sb bonding interactions mainly involve C_2px and H_1s orbitals with Sb_5s orbital, while non-bonding phenyl-V interactions involve C_2px orbitals with V_3dx²−y² orbital. This last interaction facilitates the desorption of the benzyl species after H-abstraction.     

声表面波32位MSK抽头延迟线

介绍了扩频通信有效的ＭＳＫ信号特点及声表面波ＭＳＫ抽头延迟线构成方式，给出了声表面波３２位ＭＳＫ抽头延迟线的实验结果。     

An easy and fast way to determine the enantiomeric purity of substituted cyclanones

The determination of the enantiomeric purity of 2 or 3-substituted cyclanones, particularly cyclohexanones, is conveniently achieved by derivatisation into cyclic aminals with commercially available (R, R)-1,2-diphenylethylenediamine. The derivatisation procedure is directly done into the NMR tube, instantaneously, and ¹³C NMR allows an accurate measure of the ee.     

The analysis of arbitrarily shaped aperture-coupled patch antennasvia a mixed-potential integral equation

A mixed-potential integral equation (MPIE) is formulated for the electric and magnetic currents on a multilayered aperture-coupled patch antenna. The integral equation is solved via the method of moments (MoM) using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes. The input impedance and radiation efficiency of various aperture-coupled elements are calculated using the proposed technique and compared to measured results. The advantages and disadvantages of several aperture and patch configurations are discussed, and six methods of numerically de-embedding the element's input impedance are compared     

Some characterisations of supported algebras

We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L₀ and R₀ which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules.