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Register a new user(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings
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We propose a new class of algebraic structure named as emph{$(m,n)$-semihyperring} which is a generalization of usual emph{semihyperring}. We define the basic properties of $(m,n)$-semihyperring like identity elements, weak distributive $(m,n)$-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient $(m,n)$-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient $(m,n)$-semihyperring, etc and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and $(m,n)$-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy $(m,n)$-semihyperrings and the relationship between fuzzy $(m,n)$-semihyperrings and the usual $(m,n)$-semihyperrings.
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We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism, ideals, etc., for (m,n)-semirings. Following earlier work by Rao, we consider a system as made up of several components whose failures may cause it to fail, and represent the set of systems algebraically as an (m,n)-semiring. Based on the characteristics of these components we present a formalism to compare the fault tolerance behaviour of two systems using our framework of a partially ordered (m,n)-semiring.
In this invited talk I discuss two recent applications of charmonium (Psi) decays to N Nbar m final states, where N is a nucleon and m is a light meson. There are several motivations for studying these decays: 1) They are useful for the study of N* spectroscopy; 2) they can be used to estimate cross sections for the associated charmonium production processes p pbar to Psi m, which PANDA plans to exploit in searches for charmonium hybrid exotics; and 3) they may allow the direct experimental measurement of NNm (meson-nucleon) strong couplings, which provide crucial input information for meson exchange models of the NN force. The latter two topics are considered in this talk, which will also compare results from a simple hadron pole model of these decays to recent experimental data.
We show how a recently proposed large $N$ duality in the context of type IIA strings with ${cal N}=1$ supersymmetry in 4 dimensions can be derived from purely geometric considerations by embedding type IIA strings in M-theory. The phase structure of M-theory on $G_2$ holonomy manifolds and an $S^3$ flop are the key ingredients in this derivation.
In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n+m, where n and m ($m eq 0$) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to $(n_1, ..., n_k | m_1, ..., m_s)$ (where $n_1+... +n_k=n, m_1+ ... + m_s=m$) for $n_1geq n-1$ and $(n_1, ..., n_k | m)$ were classified in works cite{FilSup}--cite{C-G-O-Kh1}. Here we prove that in the case of $(n_1, ..., n_k| m_1, ..., m_s)$, where $n_1leq n-2$ and $m_1 leq m-1$ the Leibniz superalgebras have nilindex less than n+m. Thus, we complete the classification of Leibniz superalgebras with nilindex n+m.
We introduce and define the quantum affine $(m|n)$-superspace (or say quantum Manin superspace) $A_q^{m|n}$ and its dual object, the quantum Grassmann superalgebra $Omega_q(m|n)$. Correspondingly, a quantum Weyl algebra $mathcal W_q(2(m|n))$ of $(m|n)$-type is introduced as the quantum differential operators (QDO for short) algebra $textrm{Diff}_q(Omega_q)$ defined over $Omega_q(m|n)$, which is a smash product of the quantum differential Hopf algebra $mathfrak D_q(m|n)$ (isomorphic to the bosonization of the quantum Manin superspace) and the quantum Grassmann superalgebra $Omega_q(m|n)$. An interested point of this approach here is that even though $mathcal W_q(2(m|n))$ itself is in general no longer a Hopf algebra, so are some interesting sub-quotients existed inside. This point of view gives us one of main expected results, that is, the quantum (restricted) Grassmann superalgebra $Omega_q$ is made into the $mathcal U_q(mathfrak g)$-module (super)algebra structure,$Omega_q=Omega_q(m|n)$ for $q$ generic, or $Omega_q(m|n, bold 1)$ for $q$ root of unity, and $mathfrak g=mathfrak{gl}(m|n)$ or $mathfrak {sl}(m|n)$, the general or special linear Lie superalgebra. This QDO approach provides us with explicit realization models for some simple $mathcal U_q(mathfrak g)$-modules, together with the concrete information on their dimensions. Similar results hold for the quantum dual Grassmann superalgebra $Omega_q^!$ as $mathcal U_q(mathfrak g)$-module algebra.In the paper some examples of pointed Hopf algebras can arise from the QDOs, whose idea is an expansion of the spirit noted by Manin in cite{Ma}, & cite{Ma1}.
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