A New Method for Computing the 1-Dimensional Homology Group of a Given 2-Complex

In [3], a vector space associate with a graph G: 'its cycle space' was described over the two element field Z2. Here we generalize the theory to the ring Z to compute 1-dimensional homology group of a given 2-complex with a combination of algebraic and graph-theoretic method.

Vocal structure, behavior and partitioning of all 23 Pternistis spp. into homologous sound(and monophyletic) groups

The aims of this research were (1) to provide a description of spurfowl Pternistis spp. calls and their social context;(2) to describe the divergence of advertisement calls;and (3) to appropri-ate 23 spurfowl species to homologous sound groups which have been synthesized with recognized monophyletic groups within Pternistis spurfowls. Sound group partitioning was primarily based on male advertisement calls. A total of 218 recordings (rendering^300 identifiable calls) were analyzed covering 22 out of 23 spurfowl species in Africa. One species was assessed from written accounts. The repertoire size per spurfowl varies between 7 and 11 calls. Spurfowl calls were arranged into three broad categories including (1) advertisement calls;(2) maintenance calls including distress calls, juve-nile whining (“mews”), cheeps and comfort calls;and (3) male-female and female-offspring bonding calls. Spurfowl species were set out in eight sound groups of which five were more or less congruent with the monophyletic groups of Hall (1963), but sound groups produced more partitioning as Hall described only five groups relevant to Pternistis spp. The divergence of advertisement calls appar-ently minimizes hybridization between sympatric species but the“genetic distance”between spurfowl species is relatively small causing hybridization among spurfowl species. Despite the vocalizations of Hartlaub’s Spurfowl (P. hartlaubi) differing significantly from the rest of the spurfowls, sound analy-ses suggest that it remains within Pternistis.

MULTIPLE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC EQUATIONS INVOLVING NATURAL GROWTH TERM

In this article, under some conditions on the behaviors of the perturbed function f（x, s） or its primitive F（x,s） =∫so f（x,t）dt near infinity and near zero, a class of asymptotically linear elliptic equations involving natural growth term is studied. By computing the critical group, the existence of three nontrivial solutions is proved.

Color cyclic homology and Steinberg Lie color algebras

The present paper contains two interrelated developments. First, the basic properties of the construction theory over the Steinberg Lie color algebras are developed in analogy with Steinberg Lie algebra case. This is done on the example of the central closed of the Steinberg Lie color algebras. The second development is that we define the first ε-cyclic homology group HC1 （R, ε） of the F-graded associative algebra R （which could be seemed as the generalization of cyclic homology group and the Z/2Z-graded version of cyclic homology that was introduced by Kassel） to calculate the universal central extension of Steinberg Lie color algebras.

TOWARD A THEORY OF WEAK I SEQUENCES

The author introduces a notion of weakIsequences and characterizes such sequences by means of homological methods.This notion extends the notion of weakMsequences and thus extends the notions of generalized Cohen Macaulay modules and Buchsbaum modules to more general cases.

Cellular Chain Complex of Small Covers with Integer Coefficients and Its Application

Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn（λ） corresponding to the pair （Pn, λ） has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn（λ） with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ？n of this cellular chain complex and get that ？n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to （F, λF） is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ？k=0 or ±2 for 0 ≤ k 〈 n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn（λ）. Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion.

Geometric and topological rigidity for compact submanifolds of odd dimension

We investigate rigidity problems for odd-dimensional compact submanifolds.We show that if Mn（n 5） is an odd-dimensional compact submanifold with parallel mean curvature in Sn＋p,and if RicM ＆gt;（n- 2-1n）（1 ＋ H2） and H ＆lt; δn,where δn is an explicit positive constant depending only on n,then M is a totally umbilical sphere.Here H is the mean curvature of M.Moreover,we prove that if Mn（n 5） is an odd-dimensional compact submanifold in the space form Fn＋p（c） with c 0,and if RicM ＆gt;（n-2-εn）（c＋H2）,where εn is an explicit positive constant depending only on n,then M is homeomorphic to a sphere.

Overexpression of enhancer of zests homolog 2 in lymphoma

Objective This article aimed to review the biological characteristics of enhancer of zests homolog 2 （EZH2）, and the transcriptional repression mechanism of action of EZH2 in tumors, particularly in the progression of lymphoma. Data sources The data cited in this review were mainly obtained from the articles listed in PubMed and HighWare that were published from March 2004 to April 2012. The search terms were ＂enhancer of zests homolog 2＂, ＂polycomb group＂, and ＂lymphoma＂. Study selection Articles regarding the mechanism of EZH2 in post-transcriptional modification, functions of polycomb group proteins, and the roles of EZH2 in lymphoma were selected. Results EZH2 acts as oncogene and involved in many kinds of tumors. Moreover, it plays an important role in tumorigenesis and lymphomagenesis by promoting the proliferation and aggressiveness of neoplastic cells, facilitating malignant tumor cell diffusion, and mediating transcriptional silencing. Conclusion EZH2 mediated transcriptional repression through its methyltransferase activity at the chromatin level has certain influence on lymphoma, and there might exist a therapeutic window for the development of new agents and identification of novel diagnostic markers based on EZH2.

On Proper and Exact Relative Homological Dimensions

In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.