Difference Discrete Variational Principle,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures II：Euler—Lagrange Cohomology

In this second papcr of a scries of papers, we explore the differcnce discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving propertiesin both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multi-parameter differential approach. In terns of the difference discrete Euler-Lagrange cohomological concepts, we show thatthe symplcctic or multisymplectic geometry and their difference discrete structure-preserving properties can always beestablished not only in thc solution spaces of the discrete Euler-Lagrange or canonical equations derived by the differencediscrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrangecohomological conditions are satisfied.

Difference Discrete Variational Principles,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures Ⅲ：Application to Symplectic and Multisymplectic Algorithms

In the previous papers I and II,we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach.We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the lagrangian and Hamiltonian formalisms.In this paper,we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms.We will show that either Hamiltonian schemes of Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied.

THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF

Let X be a compact complex manifold.Consider a small deformation π :X→B of X,the dimensions of the cohomology groups of tangent sheaf H q(X_t,T_X_t) may vary under this deformation.This article studies such phenomena by studying the obstructions to deform a class in H q(X,T X) with parameter t and gets a formula for the obstructions.

QUANTUM COHOMOLOGY OF BLOWUPS OF SURFACES AND ITS FUNCTORIALITY PROPERTY

在这篇文章，用 WDVV 方程，作者首先证明表面的发作的所有 Gromov-Witten invariants 能被一些递归的关系从自己的 Gromov-Witten invariants 计算。而且，它可以在发作上决定量产品。它也证明有为发作的大量 cohomology 的 functoriality 的某度。给词调音：量 cohomology；WDVV 方程；Gromov-Witten

COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

作者证明那是对一个可分离的 Hilbert 空格起作用的巢代数学 T (N) 的所有第 n 个完全围住的 cohomology 组当系数在包含巢代数学的任何极端微弱地关上的 T (N)-bimodule 躺着时，是小的。他们也为所有 n ≥证明那 1 并且有包含 A 的极端微弱地关上的 A-bimodule M 的 CSL 代数学 A。给词调音：嵌套代数学；CSL 代数学；完全围住的 cohomology

EXACT－VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE

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On the Cohomology of Associative Superalgebras

This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.

On 2 - 3 Matrix Chevalley Eilenberg Cohomology

The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra;which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 - 3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.

The Second Hochschild Cohomology Group for One-Parametric Self-Injective Algebras

In this paper, we determine the second Hochschild cohomology group for a class of self-injective algebras of tame representation type namely, which are standard one-parametric but not weakly symmetric. These were classified up to derived equivalence by Bocian, Holm and Skowroński in [1]. We connect this to the deformation of these algebras.

Discrete Exterior Calculus of Proteins and Their Cohomology

This paper proposes a novel application of cohomology to protein structure analysis. Since proteins interact each other by forming transient protein complexes, their shape (e.g., shape complementarity) plays an important role in their functions. In our mathematical toy models, proteins are represented as a loop of triangles (2D model) or tetrahedra (3D model), where their interactions are defined as fusion of loops. The purpose of this paper is to describe the conditions for loop fusion using the language of cohomology. In particular, this paper uses cohomology to describe the conditions for “allosteric regulation”, which has been attracted attention in safer drug discovery. I hope that this paper will provide a new perspective on the mechanism of allosteric regulation. Advantages of the model include its topological nature. That is, we can deform the shape of loops by deforming the shape of triangles (or tetrahedra) as long as their folded structures are preserved. Another advantage is the simplicity of the “allosteric regulation” mechanism of the model. Furthermore, the effect of the “post-translational modification” can be understood as a resolution of singularities of a flow of triangles (or tetrahedra). No prior knowledge of either protein science, exterior calculus, or cohomology theory is required. The author hopes that this paper will facilitate the interaction between mathematics and protein science.

Some Results for Formal Local Cohomology Modules

Let(R,m) be a commutative Noetherian local ring,I an ideal of R and M a finitely generated R-module.Let lim←nHim(M/InM) be the ith formal local cohomology module of M with respect to I.In this paper,we discuss some properties of formal local cohomology modules ←limnHim(M/InM),which are analogous to the finiteness and Artinianness of local cohomology modules of a finitely generated module.

Cofiniteness of Local Cohomology Modules with Respect to a Pair of Ideals

Let R be a commutative Noetherian ring,I and J be two ideals of R,and M be an R-module.We study the cofiniteness and finiteness of the local cohomology module H_(I,J)~i(M)and give some conditions for the finiteness of Hom_R(R/I,H_(I,J)~s(M))and Ext_R^1(R/I,H_(I,J)~s(M)).Also,we get some results on the attached primes of H_(I,J)^(dimM)(M).

Batalin-Vilkovisky Structure on Hochschild Cohomology of Self-Injective Quadratic Monomial Algebras

We give a complete description of the Batalin-Vilkovisky algebra structure on Hochschild cohomology of the self-injective quadratic monomial algebras.

Cohomology Complex Projective Space with Actions of G_5

Let M2n be a cohomology CPn and p a prime. S et Dp(M2n)={d＞0|M2n admits a smooth Gp action such tha t the fixed point set of the action contains a codimension-2 submanifold of deg ree d}, DEp(M2n)={(d; m1, m2, …, mμ)|M2n admits a GP action of Type Ⅱ0, having multiplicities m1, m2, …, mμ at the isolated fixed points, and m1+m2+…+mμ=n, d is the degree of the fixed codimension-2 submanifold}. In this paper, we prove that for n=5 or 7 , if D5(M2n)≠φ, then D5(M2n)={1}; if DE5(M2n )≠φ, then DE5(M2n)={(1; n, 0)}.

The Artinianness of Local Cohomology Modules

In this paper,let (R,m)be a Noetherian local ring,I(?)R an ideal, M and N be two finitely generated modules.Firstly,we study the properties of H_I^t(M),t=f-depth(I,M) and discuss the relationship between the Artinianness of H_I^i(M,N) and the Artinianness of H_I^i(N).Then,we get that H_I^d(M,N)is I-cofinite,if(R,m)is a d-dimensional Gorenstein local ring.

Cohomology of Weakly Reducible Maximal Triangular Algebras

In this paper, we introduce the concept of weakly reducible maxi mal triangular algebras S*!which form a large class of maximal t riangular algebras. Let B be a weakly closed algebra containing S, we prove that the cohomology spaces Hn(S , B) ( n≥1) are trivial.

具有高阶导子Lie-Yamaguti代数的上同调

研究具有高阶导子的Lie-Yamaguti代数,称之为LieYHDer对。首先给出LieYHDer对的上同调,然后研究了LieYHDer对的中心扩张,根据上同调考虑LieYHDer的形变。

Cohomology groups of a new class of Kadison-Singer algebras

Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and Q.We show that L is a Kadison-Singer lattice with the trivial commutant.Moreover,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.

Lie-Yamaguti代数的相对微分算子

本文研究Lie-Yamaguti代数的相对微分算子.首先给出Lie-Yamaguti代数上相对微分算子的概念并给出等价刻画.随后,引入Lie-Yamaguti代数上相对微分算子的上同调.最后,讨论Lie-Yamaguti代数上相对微分算子的无穷小形变.

带权罗-巴李超三系

给出带权罗-巴李超三系的表示和上同调。作为应用,引入和研究带权罗-巴李超三系的形式形变。