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in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

Previously we introduced the Uniform Cramér-Rao (CR) Bound as a lower bound on the variance of biased estimators, along with the concept of the delta-sigma tradeoff curve. For estimators whose variance lie on this curve, lower variance can only be achieved at the price of increased estimator bias gradient norm, and vice versa. However, for single pixel estimation, one can specify a variety of d...

‎let $r$ be a $*$-prime ring with center‎ ‎$z(r)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $r$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $r$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎suppose that $u$ is an ideal of $r$ such that $u^*=u$‎, ‎and $c_{sigma,tau}={cin‎ ‎r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ in the present paper‎, ‎it is shown that...

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Hückel equation), configurational entropy of mixing (Flory-Huggins relation)...

Starting with a Lie algebroid A over a space M we lift its action to the canonical transformations on the affine bundle R over the cotangent bundle T * M. Such lifts are classified by the first cohomology H 1 (A). The resulting object is a Hamiltonian algebroid A H over R with the anchor map from Γ(A H) to Hamiltonians of canonical transformations. Hamiltonian algebroids generalize Lie algebras...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group G. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundl...

The theory of crystal bases introduced by Kashiwara in [4] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [5] he define...