in this paper, we consider the finitely presented groups $g_{m}$ and $k(s,l)$ as follows;$$g_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$k(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.

We revisit the singular IIB supergravity solution describing M fractional 3branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevantN = 1 SUSY SU(N+M)×SU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N → N −M . Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep...

We find new solutions to 11-dimensional supergravity describing M5-branes wrapped on holomorphic 2-cycles embedded in C. These solutions preserve N = 1 supersymmetry in four dimensions. They are dual to N = 1 gauge theories in four dimensions by Maldacena’s duality. USITP-00-19 DTP/00/111 hep-th/0012194 email: [email protected] email: [email protected] email: [email protected] email: Douglas.Smith...

We motivate and summarize our analysis of hep-th/0610276 in which we consider D7-brane probe embeddings in the Polchinski-Strassler background with N = 2 supersymmetry. The corresponding dual gauge theory is given by the N = 2 theory with fundamental matter. Based on a talk given by C. Sieg at the RTN Workshop 2006, Napoli. ∗[email protected], [email protected], [email protected], [email protected]...

This paper presents a dual-objective facility programming model for a green supply chain network. The main objectives of the presented model are minimizing overall expenditure and negative environmental impacts of the supply chain. This study contributes to the existing literature by incorporating uncertainty in customer demand, suppliers, production, and casting capacity. An industrial case st...

We find new solutions to 11-dimensional supergravity describing M5-branes wrapped on holomorphic 2-cycles embedded in C. These solutions preserve N = 1 supersymmetry in four dimensions. They are dual to N = 1 gauge theories in four dimensions by Maldacena’s duality. USITP-00-19 DTP/00/111 hep-th/0012194 email: [email protected] email: [email protected] email: [email protected] email: Douglas.Smith...

In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

We study SL(3, R) deformations of a type IIB background based on D5 branes that is conjectured to be dual to N = 1 SYM. We argue that this deformation of the geometry correspond to turning on a dipole deformation in the field theory on the D5 branes. We give evidence that this deformation only affects the KK-sector of the dual field theory and helps decoupling the KK dynamics from the pure gaug...