Hochschild (co)homology of exterior algebras using algebraic Morse theory

In [1 Han, Y., Xu, Y. (2007). Hochschild (co)homology of exterior algebras. Comm. Algebra 35(1):115–131.[Web of Science ®] , [Google Scholar]], the authors computed the additive and multiplicative structure of HH*(A;A), where A is the n-th exterior algebra over a field. In this paper, we derive all their results using a different method (AMT) as well as calculate the additive structure of HH_k(A;A) and HH^k(A;A) over ?. We provide concise presentations of algebras HH_?(A;A) and HH*(A;A) as well as determine their generators in the Hochschild complex. Finally, we compute an explicit free resolution (spanned by multisets) of the A^e-module A and describe the homotopy equivalence to its bar resolution.     

On the classifying space of Artin monoids

A theorem proved by Dobrinskaya [9 Dobrinskaya, N. E. (2006). Configuration spaces of labeled particles and finite Eilenberg-MacLane complexes. Proc. Steklov Inst. Math. 252(1):30–46.[Crossref] , [Google Scholar]] shows that there is a strong connection between the K(π,1) conjecture for Artin groups and the classifying spaces of Artin monoids. More recently Ozornova obtained a different proof of Dobrinskaya’s theorem based on the application of discrete Morse theory to the standard CW model of the classifying space of an Artin monoid. In Ozornova’s work, there are hints at some deeper connections between the above-mentioned CW model and the Salvetti complex, a CW complex which arises in the combinatorial study of Artin groups. In this work we show that such connections actually exist, and as a consequence, we derive yet another proof of Dobrinskaya’s theorem.     

Liouville theorems for the weighted Lane–Emden equation with finite Morse indices

In this paper, we study the nonexistence result for the weighted Lane–Emden equation: (0.1) and the weighted Lane–Emden equation with nonlinear Neumann boundary condition: (0.2) where f(|x|) and g(|x|) are the radial and continuously differential functions, is an upper half space in , and . Using the method of energy estimation and the Pohozaev identity of solution, we prove the nonexistence of the nontrivial solutions to problems 0.1 and 0.2 under appropriate assumptions on f(|x|) and g(|x|). Copyright © 2017 John Wiley & Sons, Ltd.     

Morse Decomposition of Semiflows on Topological Spaces

This paper studies Morse decompositions of discrete and continuous-time semiflows on compact Hausdorff topological spaces. We extend two classical results which are well-known facts for flows on compact metric spaces: the characterization of the Morse decompositions through increasing sequences of attractors and the existence of Lyapunov functions.     

一维Morse势的Dirac方程的束缚态

在标量型和矢量型Morse势相等的条件下,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解.并且在求精确解时,运用一种新的自变量变换方法,使方程求解变得比较简单.     

MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW （I）

The spectral flow for paths of admissible operators in arbitrary Banarch space is deflned andsome properties of the spectral Itow is studied.     

MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW （II）

1.IntroductionandMainResultsStartingfromthepioneeringworks[5,61ofH.AmannandE.Zehnderin1980,C.ConleyandE.Zehnderestablishedanindextheoryin1984intheircelebratedwork[if]fornondegeneratepathsinSp(Zn)startedfromtheidentitymatrixwithn22.Thisindextheorywasextendedtothenondegeneratecaseofn~1byE.Zehnderandthefirstauthorin[28]of1990.ThisindextheoryforthedegenerateHamiltoniansystemswasestablishedbythefirstauthorin[21]of1990andC.Viterboin[34]of1990viadifferentmethods,andthenextendedtoalldegenerates…     

关于Norton问题

本文证明了ＮｏｒｔｏｎＡ．所提出的猜测．在映射具有适当可微性的假设下,对 秩为ｒ的集合,刻画了它的像的Ｈａｕｓｄｏｒｆｆ测度．     

BN、BH分子辐射带系的Franck-Condon因子计算

在双原子分子核运动的波动方程中,计入分子的振转相互作用项,在Morse势近似下,得出的波函数除与振动量子数有关外,还与转动量子数有关。用该波函数编程计算了BN分子A³Π-X³Π辐射带系及BH分子A¹Π-X¹∑⁺带系的Franck-Condon因子。计算中转动量子数取值由J=0至J=180,结果适用于低温、高温和强激波条件。     

Infinitely many solutions for double hamonic perturbed problem

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