The Lie algebra of a nuclear group is a locally convex nuclear vector space. Mathematics Subject Classification (2000): 22B05, 22E65, 46Axx 1. The Lie Algebra of Abelian Topological Groups Let G be an abelian topological group. The set of all one–parameter–subgroups L(G) := {λ : R→ G : λ is a continuous homomorphism} is called the Lie algebra of G . We define addition pointwise and scalar multi...

The global holomorphic invariant αG(X) introduced by Tian [?], Tian and Yau [?] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau [?] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

A comparative analysis of the features UV-stimulated emission (SE) various disordered active materials based on ZnO crystallites for a random laser (RL) was carried out. The superlinear increase in intensity UV photoluminescence (PL) band polydisperse nano-micro-crystalline (PNMC) powder at wavelength λ = 387 nm and some narrowing its halfwidth range 20 ÷ 15 with increasing pump indicates lasin...

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region has strong fluctuation whose modulus is compatible with that of the color diagonal ghost propagator. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboratio...

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, αG in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r − 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon’s algorithm). This paper re...

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, αG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r − 1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI. This paper shows our experimental results of Cheon’s al...

The global holomorphic invariant αG(M) introduced by Tian[14], Tian and Yau[13] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau[19] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

For an element x of the Cuntz algebra ON , define the isotropy subgroup Gx ≡ {g ∈ U(N) : αg(x) = x} of the unitary group U(N) with respect to the canonical action α of U(N) on ON . We have irreducible representations of the crossed product ONoGx by extending irreducible generalized permutative representations of ON and irreducible representation of Gx. ¿From this, the Peter-Weyl theorem for Gx ...

The special case of 4D string-like theory proposed early is investigated. Regge trajectories in the developed model are non-linear for the small masses and the values of spin and have the different asymptotical slopes αp. The value αp just as the form of the trajectory depends from the quantum state of some ”internal“ (relativistic invariant) variables. It is also shown that some trajectories h...