Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be ac...

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...

For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the resulting 4-velocity is seemingly due to a complex electromagnetic field. This work shows that this is not due to some complex formalism used (such as Clifford a...

We outline a formalism used for a construction of two-loop flavor singlet exclusive evolution kernels in the MS scheme. The approach is based on the known pattern of conformal symmetry breaking in MS as well as constraints arising from the superconformal algebra of the N = 1 super Yang-Mills theory. Talk given at the 8th International Workshop on Deep Inelastic Scattering and QCD Liverpool, Apr...

The “Ocean SAmpling MObile Network” (SAMON) Project is a simulation testbed for Web-based interaction among oceanographers and simulation based design of Ocean Sampling missions. In this paper, the current implementation of SAMON is presented, along with a formal model based on process algebra. Flexible optimization handles planning, mobility, evolution, and learning. A generic behavior message...

In the paraxial regime of three-dimensional optics, two evolution Hamiltonians are equivalent when one can be transformed to the other modulo scale by similarity through an optical system. To determine the equivalence sets of paraxial optical Hamiltonians one requires the orbit analysis of the algebra sp(4, R) of 4 x 4 real Hamiltonian matrices. Our strategy uses instead the isomorphic algebra ...

The term algebra usually denotes various kinds of mathematical ideas and techniques, more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. The notion that in mathematics there is such a separate sub-discipline, as well as the very use of the term “algebra” to denote it, are themselves the outcome of historical evolution o...

In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP, and we use them to describe invariant evolutions of projective N -gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N -gon invariant evolutions a...

‎let $omega$ be a class of unital‎ ‎$c^*$-algebras‎. ‎we introduce the notion of a local tracial $omega$-algebra‎. ‎let $a$ be an $alpha$-simple unital local tracial $omega$-algebra‎. ‎suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$‎ ‎which has a certain non-simple tracial rokhlin property‎. ‎then the crossed product algebra‎ ‎$c^*(g,a,alpha)$ is a unital local traci...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...