Presentations for S and S/? from a Given Presentation for ?

Stochastic Mean-Field Dynamics For Nuclear Collisions

“…In order to develop a stochastic description, we need to evolve an ensemble of single-particle densities associated with the ensemble of Slater determinants, and write a member of singleparticle density matrix in the form, 0 Here />• • are time-independent elements of density matrix which are determined by the initial conditions. The main assumption of the approach is that each matrix 0 element is a Gaussian random number specified by a mean value p^-= Sip , • and a variance [8],…”

“…For example, in the induced fission dynamics, relevant collective variables can be taken as relative distance of fragments, mass-asymmetry and neck parameter. Here, we consider a single collective variable q(t) and introduce the quasi-static single-particle representation, h{q)Wj{r,q) = £j{q)Wj(r;q) (8) where h(q) = h[p(q)] denotes the mean-field Hamiltonian as a function of collective variable q(t). We expand the single-particle density in terms of the quasi-particle representation, /?…”

Semigroup Presentations for Congruences on Groups

“…An extension of a group H by a group N is a group G having N as a normal subgroup and G/N ∼ = H. It is known that if H and N are both finitely presented groups, then the extension of them is finitely presented (see [7,Corollary 10.2]). Recently, it is proved in [3] that, for given a semigroup S and a congruence ρ on S, if ρ is finitely presented as a subsemigroup of the direct product S × S, then S and S/ρ are finitely presented. In [3] finite presentability of ρ on a finitely presented infinite semigroup is an open problem.…”

“…Recently, it is proved in [3] that, for given a semigroup S and a congruence ρ on S, if ρ is finitely presented as a subsemigroup of the direct product S × S, then S and S/ρ are finitely presented. In [3] finite presentability of ρ on a finitely presented infinite semigroup is an open problem. More recently, for inverse semigroups S and T , and for a surjective homomorphism π : S → T with kernel K which is a congruence on S, it is showed in [4] that how to the obtain a presentation for K from a given a presentation for S and vice versa.…”

Shape fluctuations in a Fermi system with nonlinear dissipativity

“…The damping in cold nuclei was intensively investigated in both the quantum (RPA like) [1,2,3,4,5] and the semiclassical (kinetic theory) approaches [6,7,8,9,10,11,12]. The collisional damping is due to the coupling of particle-hole excitations to more complicated states.…”