On the action of the Iwahori–Hecke algebra on modular invariants

We compute the action of the modular Iwahori–Hecke algebra on the ring of invariants of the mod p cohomology of elementary p-groups under Borel subgroup of the general linear group. Applications include a direct proof of the structure of the universal Steenrod algebra and a new proof of a key result on the structure of the Takayasu modules.     

Location of hot spots in thin curved strips

The maxima and minima of Neumann eigenfunctions of thin tubular neighbourhoods of curves on surfaces are located in terms of the maxima and minima of Neumann eigenfunctions of the underlying curves. In particular, the hot spots conjecture for a new large class of domains (possibly non-convex and non-Euclidean) is proved.     

Optimization of Polynomial Fractional Functions

A new approach is proposed for optimizing a polynomial fractional function under polynomial constraints, or more generally, a synomial fractional function under synomial constraints. The approach is based on reformulating the problem as the optimization of an increasing function under monotonic constraints.     

Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings

Supported by a grant from the Centre de Recerca Matematica, Institut d'Estudis Catalans (Spain)     

Variations in the structure of aromatic solvents under the influence of dissolved fullerene C70

Dilute solutions of the C₇₀ fullerene (at concentrations from 0.0001–0.0005% to a few hundredths of a percent) in benzene, toluene, and p-xylene are investigated using small-angle and wide-angle X-ray diffraction. It is revealed that an increase in the C₇₀ fullerene concentration leads to a nonmonotonic shift of the small-angle X-ray diffraction patterns along the intensity axis: the intensity first decreases, reaches a minimum, and then increases. The wide-angle X-ray diffraction patterns of all the solutions under investigation exhibit two halos: as the fullerene concentration in the solution increases, the intensity of the first halo increases, whereas the intensity of the second halo decreases. The variations observed in the X-ray diffraction patterns of the fullerene solutions are interpreted in terms of structuring of the solvents, i.e., the formation of a specific order on the molecular and supramolecular levels. The X-ray diffraction data are in good agreement with the nonmonotonic concentration dependences of the density of the fullerene solutions in aromatic solvents. A structural interpretation of the initial decrease in the density of the fullerene solutions is proposed.     

非对称信息下供应商-零售商供应链的批量折扣决策

在供应链管理的文献中,许多工作研究供应商如何使用激励手段,如数量折扣,去影响零售商的订货行为以增加供应商的利润(与整个供应链的利润).多种形式的激励策略模型已有许多,但通常有一个关键的假设,即,供应商关于零售商的成本结构具有完全信息.本文研究了在非对称信息下供应商的最优数量折扣决策问题,得到了最优策略,并与完全信息的情形进行了比较.     

铕离子对tRNAPhe结构影响的NMR研究

采用NMR波谱方法研究了溶液中铕离子对酵母苯丙氨酸转移核糖核酸(phenylalanine transfer ribonucleic acid,简称tRNA^Phe)结构和构象变化的影响.Eu³⁺离子对tRNA^Phe亚胺质子范围的¹H NMR谱具有特殊的影响,酵母tRNA^Phe亚胺质子谱作为Eu³⁺浓度函数的研究表明位于扩大二氢尿嘧啶螺旋(D-螺旋)的端梢三级碱基对G₁₅·C₄₈明显地受加入Eu³⁺的影响(向低场位移0.85);堆积在G₁₅·C₄₈上的U₈·A₁₄碱基对在存有1~2个Mg²⁺离子下亦受加入Eu³⁺的影响.酵母tRNA^Phe中可能受到Eu³⁺影响的另一亚胺质子为G₁₉·C₅₆三级碱基对,由于G₁₉·C₅₆的亚胺质子共振位于高度叠加的12.6与12.2之间,其归属仅供参考.该碱基对有助于D-环对TΨC环的联接.配位Eu³⁺引起tRNA分子构象的变化并且导致一些谱峰向高场或低场位移.     

A Mössbauer study on TiBaCa3(Cu1−xFex)3O8.5 superconductors

Two main superconducting phases, 1223 and 2223 in TiBaCa₃Cu₃O_8.5 superconductor, are identified by powder x-ray analysis and⁵⁷Fe Mössbauer spectroscopy analysis. The Mössbauer fitting results shown that iron atoms in the lattice substitute two inequivalent sites of copper atoms for each main phase. The temperature dependence of Mössbauer parameters are obtained, and several problems are discussed which relate to the electric charge transfer which takes place around the superconducting transition temperature, the lattice dynamics and the effect on oxygen deficiency at different temperatures.     

On monomial k-Buchsbaum curves in ℙ3

Using the theory of affine semigroup rings we describe all strictly 2-Buchsbaum monomial curves in ℙ³.