An integrable SIS model

We provide a demonstration of the integrability of a classical model of an infectious disease which neither kills nor induces autoimmunity by means of the Painlevé analysis and use the Lie theory of transformation groups to present an explicit solution.     

泵浦统计,原子相干性及多单光子激光场光子数压缩效应

利用朗之万方程理论证明，在多单光子激光振荡的线性区域，泵浦统计、原子相干性及原子位相起伏可导致光子数压缩效应。     

Limits of commutative triangular systems on simply connected step 2-nilpotent Lie groups

We prove that on simply connected step 2-nilpotent Lie groupsG any limit of a commutative infinitesimals triangular system of probability measures which are either all symmetric or supported by some discrete subgroupH is infinitely divisible onG resp.H.     

Random creation and dispersion of mass

Consider evolution of density of a mass or a population, geographically situated in a compact region of space, assuming random creation-annihilation and migration, or dispersion of mass, so the evolution is a random measure. When the creation-annihilation and dispersion are diffusions the situation is described formally by a stochastic partial differential equation; ignoring dispersion make approximations to the initial density by atomic measures and if the corresponding discrete random measures converge “in law” to a unique random measure call it a solution. To account for dispersion Trotter's product formula is applied to semiflows corresponding to dispersion and creation-annihilation. Existence of solutions has been a conjecture for several years despite a claim in ([2], J. Multivariate Anal. 5, 1–52). We show that solutions exist and that non-deterministic solutions are “smeared” continuous-state branching diffusions.     

Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents

For infinitely multiple exponentials with two alternating exponents, we construct continuations to unbounded domains, so that these continuations are the limit functions of sequences of finitely multiple exponentials. We prove that, for different exponents, such a continuation is unique in the class of continuously differentiable functions. We extend the domain of existence of infinitely multiple exponentials. For exponents with the same signs, this domain remains bounded, while for exponents with different signs, it coincides with the number axis.     

Structural and electronic characteristics of perhydrogenated carbon nanotubes

The structural and electronic characteristics of fully hydrogenated armchair and zigzag carbon nanotubes have been determined by quantum chemical methods. With use of line group symmetries, the structures of nanotubes up to 10 nm in diameter could be optimized by periodic B3LYP calculations. “In–out” isomerism is shown to significantly stabilize perhydrogenated carbon nanotubes, the energetically most favorable structures being those with 1/3–1/2 of the carbon atoms endo-hydrogenated. In favored nanotubes the ratio of endo- to exo-hydrogens is 1:1, the stabilities increasing as a function of the diameter of the nanotube. The calculated band gaps indicate that the perhydrogenated carbon nanotubes are insulators.     

Many‐body energy decomposition analysis of cooperativity in hydrogen fluoride clusters

This article studies the cooperativity present in hydrogen fluoride clusters, (FH)_n, by means of a many‐body decomposition of the binding energy. With the aim of quantifying how the results depend on the calculation level, the partition was performed from dimer to hexamer at the RHF, MP2, and density functional (B3LYP) levels, and for the heptamer and octamer at the RHF and B3LYP levels, using a 6‐31++G(d, p) basis set in all cases. We obtain that, for a proper representation of the cooperative effects in hydrogen fluoride, at least the inclusion of the three‐body terms is fundamental. The contributions are found to be underestimated at the RHF level and overestimated at the B3LYP level, with respect to the MP2 results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Symmetries and Conservation Laws of the System: ux= vwx, vy= u wy, uv+wxx+wyy=0

After a short exposition of the theory of local and nonlocal symmetries and conservation laws for systems of PDEs, results on these and the recursion operator are listed for the system of PDEs u_x=vw_x, v_y=uw_y, uv+w_xx+w_yy=0. In between the methods of computation are explained.     

Extended Hartree-Fock (EHF) theory in chemical reactions

The roles of orbital, spin and permutation symmetries in the extended Hartree-Fock (EHF) wavefunction are investigated in relation to the applications of group theory to chemical reactions. The utility of the magnetically ordered set for an extended HF calculation is pointed out. The relative stabilities among linear Hückel and Möbius three-center three-electron (3,3) systems are investigated by the generalized Hartree-Fock (GHF) and EHF methods in order to confirm the reliability of the valence-bond (VB) selection rule for free radical reactions.