amonge other things we give sufficient and necessary conditions for the lau product of banachalgebras to be biflat or biprojective.

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

Amonge other things we give sufficient and necessary conditions for the Lau product of Banachalgebras to be biflat or biprojective.

In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed ...

Treatment o f C[B(OMe)J4 with four equivalents o f a (rerr-phosphine)gold(I) chloride LAuCl with L = P (oC 6H n)3 or (2-MeC6H4)3P in the presence o f CsF in hexamethylphosphoric triamide (HMPT) affords the first complexes o f the type (LAu)4C. The product is formed to­ gether with salts (LAu)5C +BF4_ as the by-product for L = tricyclohexylphosphine, from which it can be separated by fractional ...

4 Dobromir Rahnev, Peter Kok, Moniek Munneke, Linda Bahdo, Floris P. de Lange, 5 Hakwan Lau 6 7 1 Columbia University, Department of Psychology, New York, USA 8 2 Radboud University Nijmegen, Donders Institute for Brain, Cognition and Behavior, 9 Netherlands 10 11 12 Abbreviated title: Theta burst TMS reduces resting state connectivity 13 14 Manuscript information: This manuscript contains 216 ...

in this paper we study the relation between module amenability of θ - lau product a×θb and that of banach algebras a, b. we also discuss module biprojectivity of a×θb. as a consequent we will see that for an inverse semigroup s, l 1 (s) ×θ l 1 (s) is module amenable if and only if s is amenable.