We construct a surface hopping semigroup, which asymptotically describes nuclear propagation through crossings of electron energy levels. The underlying time-dependent Schrödinger equation has a matrix-valued potential, whose eigenvalue surfaces have a generic intersection of codimension two, three or five in Hagedorn’s classification. Using microlocal normal forms reminiscent of the Landau-Zen...

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

Abstract We extend to matrix-valued stochastic processes, some well-known relations between realvalued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and martingale polynomials. In particular, joint semigroup densities of the eigenvalue processes of the generalized matrix-valued Ornstein-Uhlenbeck and squared OrnsteinUhlenbeck processes are ...

Given that the supply of several rare earth elements (REEs) is sometimes limited, recycling REEs used in various advanced materials, such as Nd magnets, is important for realizing efficient use of REE resources. In the present work, the feasibility of using DNA for REE recovery and separation was examined, along with the identification of the binding site of REEs in DNA. In particular, a DNA-...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

Recently, the worldwide supply of rare earth element (REE) resources will be severely restricted. On the other hand, coal fly ash particles emitted from coal-fired electric power plants contain relatively high concentrations of REEs. The contents of REEs in coal fly ash are regularly several hundreds of ppmw. In order to extract and recover REEs from coal fly ash particles, as a first step, we ...

In the present study, bioaccumulation of REEs in Zea mays L. (corn plant) has been analyzed. The role of Rare Earth Element (REEs) in physiology and biochemistry of corn plant have been studied. Physiological characters like peroxidase (POD) and superoxide dismutase (SOD) activities, biochemical analysis of chlorophyll, carotenoids and phenol contents have also been carried out. The plant growt...

We present a new shorter and simplified proof for the undecidability of the mortality problem in matrix semigroups, originally proved by Paterson in 1970. We use the clever coding technique introduced by Paterson to achieve also a new result, the undecidability of the vanishing (left) upper corner. Since our proof for the undecidability of the mortality problem uses only 8 matrices, a new bound...