In this largely expository note we give some homological properties of algebraic maps of complex algebraic varieties which are rather surprising from the topological point of view. These include a generalisation to higher dimension of the invariant cycle theorem for maps to curves. These properties are all corollaries of a recent deep theorem of Deligne, Gabber, Beilinson, and Bernstein which i...

The multiplicative order convergence was studied and investigated on Riesz algebras. This paper deals with algebras different topologies them. In this paper, we investigate which define various kinds of continuities. We give the relation between them under certain specific conditions. show some relations among locally full, convex solid Also, introduce notions topological continuity algebraic m...

We study the class of Bernstein algebras that are algebraic, in sense each element generates a finite-dimensional subalgebra. Every algebra has maximal algebraic ideal, and quotient is zero-multiplication algebra. Several equivalent conditions for to be given. In particular, known characterizations train terms nilpotency generalized case locally algebras. Along way, we show if Banach (respectiv...

this is a survey article on centralizers of finite‎ ‎subgroups in locally finite‎, ‎simple groups or lfs-groups as we‎ ‎will call them‎. ‎we mention some of the open problems about‎ ‎centralizers of subgroups in lfs-groups and applications of the‎ ‎known information about the centralizers of subgroups to the‎ ‎structure of the locally finite group‎. ‎we also prove the‎ ‎following‎: ‎let $g$ be...

In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

Locally Decodable codes(LDC) support decoding of any particular symbol of the input message by reading constant number of symbols of the codeword, even in presence of constant fraction of errors. In a recent breakthrough [9], Yekhanin constructed 3-query LDCs that hugely improve over earlier constructions. Specifically, for a Mersenne prime p = 2−1, binary LDCs of length 2O(n1/t) for infinitely...

1.1. Motivation. This paper is largely concerned with constructing quotients by étale equivalence relations. We are inspired by questions in classical rigid geometry, but to give satisfactory answers in that category we have to first solve quotient problems within the framework of Berkovich’s k-analytic spaces. One source of motivation is the relationship between algebraic spaces and analytic s...

Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg [14] first gave a breakthrough result in this topic by cleverly considering subcodes of Reed-Solomon codes. Thus, q-ary optimal locally repairable codes from subcodes of Reed-Solomon codes giv...

Following an active period of policy development and implementation in the 1990s,1 there have been two national great leaps forward that tackled geographical health inequalities in Australia in the new century. In 2000, in the context of growing disaffection in the rural electorate,2 the then health minister, Michael Wooldridge, was responsible for a federal Budget centrepiece of $562 million, ...