Critical behaviour of Raman frequency shifts for translational modes near the melting point of ammonia solid I based on Pippard relations

A correlation between thermal expansivity α _p and frequency shifts (1/ν) (?ν/?P) _T was established for the ammonia solid I near its melting point. For this correlation, calculated frequencies for the translational modes of ν _T (100?cm^?1) and ν _T (130?cm^?1) were used to acquire the Raman frequency shifts at pressures of 0, 1.93 and 3.07?kbar in ammonia solid I. In this crystalline system, values of the slope dP_m /dT were deduced for the fixed pressures from linear plots of α _p vs. (1/ν) (?ν/?P) _T . Slope values at zero pressure are in very good agreement with those obtained experimentally. It is also shown that the spectroscopic modification of the Pippard relations applies satisfactorily to ammonia solid I.     

HANKEL OPERATORS AND HANKEL ALGEBRAS

ＨＡＮＫＥＬＯＰＥＲＡＴＯＲＳＡＮＤＨＡＮＫＥＬＡＬＧＥＢＲＡＳＹＡＮＳＨＡＯＺＯＮＧＣＨＥＮＸＩＡＯＭＡＮＧＵＯＫＵＮＹＵＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｎｅ２３，１９９５．ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｆｕｄａ...     

半群的i-v Fuzzy理想

在半群上引入i-v Fuzzy理想的概念.研究了半群的i-v Fuzzy理想的若干性质,特别是给出了半群的i-v Fuzzy子集成为理想的若干特征性质.     

STABLE AND UNSTABLE IDEAL PLANE FLOWS

IntroductionWe COnsider SOllltlollS     

Extremal Betti Numbers of Some Cohen-Macaulay Binomial Edge Ideals

We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs.     

高能重离子碰撞中产生的末态粒子的横质量谱(英文)

基于多源理想气体模型, 用两个方程分别描述了高能重离子中心碰撞中产生的p, K±和π±的横质量分布。在忽略末态粒子的相对论效应的情况下, 除π±外, 计算结果可近似地描述实验结果。考虑了源的次级样本后, 发现计算结果与高能Au-Au和Pb-Pb中心碰撞的实验结果符合得较好。 Based on the multisource ideal gas model, which do not consider the dynamic mechanism of particles, two formulae are given to describe the transverse mass distributions of protons, kaons and pions produced in central heavy ion collisions at high energies. In the case of neglecting the relativistic effect, our calculated results approximately describe the experimental data, except for pions. By considering the sub samples of the sources, it is found that our calculated results are in good agreement with the experimental data in the central Au Au and Pb Pb collisions at high energies.     

Virtually semisimple modules and a generalization of the Wedderburn-Artin theorem

A widely used result of Wedderburn and Artin states that “every left ideal of a ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct product of matrix rings over division rings.” Motivated by this, we call a module M virtually semisimple if every submodule of M is isomorphic to a direct summand of M and M is called completely virtually semisimple if every submodule of M is virtually semisimple. We show that the left R-module R is completely virtually semisimple if and only if R has a unique decomposition as a finite direct product of matrix rings over principal left ideal domains. This shows that R is completely virtually semisimple on both sides if and only if every finitely generated (left and right) R-module is a direct sum of a singular module and a projective virtually semisimple module. The Wedderburn-Artin theorem follows as a corollary from our result.     

半群的次极大理想与次极小理想

在半群中引入次极大理想和次极小理想的概念，研究了它们的基本性质．证明了次极大理想的存在性，并得到如下定理，半群中每个理想可以分解成一些次极大理想的交，特别地，在满足理想降链条件的半群中，每个理想可以分解成有限个次极大理想的交，对于次极小理想．可以得到对偶的结果．