Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

The boundary conditions for canonical vacuum general relativity is investigated at the quasi-local level. It is shown that fixing the area element on the 2-surface S (rather than the induced 2-metric) is enough to have a well defined constraint algebra, and a well defined Poisson algebra of basic Hamiltonians parameterized by shifts that are tangent to and divergence free on S. The evolution eq...

We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators f...

we prove that rs-bl-algebras are mv-algebras.

let $mathcal{r}$ be a  commutative ring with identity, let $a$ and $b$ be two $mathcal{r}$-algebras and $varphi:blongrightarrow a$ be an $mathcal{r}$-additive algebra homomorphism. we introduce a new algebra $atimes_varphi b$, and give some basic properties of this algebra. generalized $2$-cocycle derivations on $atimes_varphi b$ are studied. accordingly, $atimes_varphi b$ is considered from th...

We discuss the rôle of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov transformations in terms of operators of the quantum Weyl-Heisenberg algebra. The quantum parameter acts as a label for the unitarily inequivalent representati...

Nakajima (2003) introduced a t-deformation of q-characters, (q, t)-characters for short, and their twisted multiplication through the geometry of quiver varieties. The Nakajima (q, t)-characters of Kirillov-Reshetikhin modules satisfy a t-deformed T -system. The T -system is a discrete dynamical system that can be interpreted as a mutation relation in a cluster algebra in two different ways, de...

This paper presents a multi-threaded BLAS library for dual SMP Intel computer running Linux. We present simple techniques to obtain parallelism for BLAS call transparently from the client program. We discuss some synchronization methods available under Linux, show performances results for a representative set of BLAS and for a high level linear algebra kernel. We then explain some key points on...

First we briefly describe the link between the Virasoro algebra and the free scalar field on a two-dimensional space-time given as a standard commutative cylinder, and in the Euclidean version on a complex plane. The field-theoretical model generalized then to the noncommutative cylinder leads to discrete time-evolution. Its Euclidean version is shown to be equivalent to a model on a complex q-...