On the quintuple product identity

In this note we present a new proof of the quintuple product identity which is based on our study of order theta functions with characteristics and the identities they satisfy. In this context the quintuple product identity is another example of an identity which when phrased in terms of theta functions, rather than infinite products and sums, has a simpler form and is much less mysterious.

     

New type of spherical pore Al alloy foam with low porosity and high strength

The Ultra Light Metal Structure with variouskinds of pores (open, close) realizes the lightness andmultifunction of structural material. The functionsinclude lightness (ρ < 1), high specific strength, highenergy absorption, sound insulation, heat insulationand electromagnetism shield. It is one of the hotspotsin material research nowadays[1— . The requirements 6]of high speed movement and high technology make Alalloy foam, which has higher specific st…     

Surface Extension in Layered Structures with the Use of Metal Meshes for Heat-Transfer Enhancement

The properties of multilayer metal-fiber coverings superimposed on plane base layers, which consist of various combinations of a copper mesh and different-length copper wires, are examined. Coverings from discrete copper microwires, two-layer coverings including a mesh and microwires, and three-layer coverings consisting of a mesh and two layers of microwire are investigated. The contacts between the fibers, the copper mesh, and the base layer are analyzed by using the metallography technique. Quantitative estimates for these contacts are presented. The side effects connected with the hydrogen disease of copper are discussed. The thermal properties of the porous structures are analyzed with the use of a termographic chamber. It is shown that the porous metal-fiber structures have good mechanical and heat-transfer properties.     

Standard Envelopes of Commutative Triple Systems

Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals).     

Lattice tensor products. III - Congruences

G. Grätzer and F. Wehrung introduced the lattice tensor product, A?B, of the lattices Aand B. In Part I of this paper, we showed that for any finite lattice A, we can "coordinatize" A?B, that is, represent A?,B as a subset A of B ^A, and provide an effective criteria to recognize the A-tuples of elements of B that occur in this representation. To show the utility of this coordinatization, we prove, for a finite lattice A and a bounded lattice B, the isomorphism Con A ≌ (Con A)B>, which is a special case of a recent result of G. Grätzer and F. Wehrung and a generalization of a 1981 result of G. Grätzer, H. Lakser, and R.W. Quackenbush.     

Porosity of ill-posed problems

We prove that in several classes of optimization problems, including the setting of smooth variational principles, the complement of the set of well-posed problems is -porous.

     

末态电子的关联在氢原子(e,2e)反应中的影响(英文)

在共面非对称几何条件下,利用双势公式解析计算了电子碰撞电离氢原子的三重微分截面.对快电子采用平面波近似,跃迁矩阵元可以表示成两个因子乘积的形式,即结构散射因子和出射道两电子的关联因子.在计算过程中对关联因子采取了最简单的近似,当入射能量为150 eV和54.4 eV时,计算结果与实验结果的符合说明对于这些入射能量该关联近似是有效的;而对于入射能量为27.2 eV时,计算结果与实验结果的较大差异说明这种关联近似是无效的.     

Assignment of phycocyanobilin in HMPT using triple resonance experiments

A complete assignment of all resonances of a small organic molecule is a prerequisite for a structure determination using NMR spectroscopy. This is conventionally obtained using a well‐established strategy based on COSY, HMQC and HMBC spectra. In case of phycocyanobilin (PCB) in HMPT this strategy was unsuccessful due to the symmetry of the molecule and extreme signal overlap. Since ¹³C and ¹⁵N labeled material was available, an alternative strategy for resonance assignment was used. Triple resonance experiments derived from experiments conventionally performed for proteins are sensitive and easy to analyze. Their application led to a complete and unambiguous assignment using three types of experiments. Copyright © 2011 John Wiley & Sons, Ltd.