An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

A simple approach for improving the hybrid MMVB force field: application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

KINETICS OF SUSPENDED EMULSION POLYMERIZATION OF METHYL METHACRYLATE

The kinetics of suspended emulsion polymerization of methyl methacrylate (MMA), in which water acted as the dispersed phase and the mixture of MMA and cyclohexane as the continuous phase, was investigated. It showed that the initial polymerization rate (Rp0) and steady-state polymerization rate (Rp) were proportional to the mass ratio between water and oil phase, and increased as the polymerization temperature, the potassium persulphate concentration ([I]) and the Tween20 emulsifier concentration ([S]) increased. The relationships between the polymerization rate and [I] and [S] were obtained as follows: Rp0 ∝ [I]0.73[S]0.32 and Rp ∝ [I]0.71[S]0.23. The above exponents were close to those obtained from normal MMA emulsion polymerization. It also showed that the average molecular weight of the resulting poly(methyl methacrylate) decreased as the polymerization temperature, [I] and [S] increased. Thus, MMA suspended emulsion polymerization could be considered as a combination of many miniature emulsion polymerizations proceeding in water drops and obeyed the classical kinetics of MMA emulsion polymerization.     

环己烷催化氧化制取顺酐和醋酸的催化剂研究

为研究气态环己烷催化氧化制取顺酐及醋酸的新反应，采取不同的方法制备了系列固体VPO催化剂.借助XRD、FT-IR对催化剂进行了主体晶相确定，用氧化还原滴定方法测定了不同晶相催化剂中钒的平均氧化数.结合催化反应的活性评价，发现催化剂主体晶相、结晶度、活化气氛和催化剂的V4＋/V5＋比均对目标反应的催化活性产生影响，5种催化剂中以(VO)2P2O7晶相催化剂的活性为最高.     

Hamiltonian graphs of given order and minimum algebraic connectivity

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs on n vertices.     

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown.     

On the construction of periodic solutions of kaplan-yorke type for some differential delay equations

In this paper we point out the main idea to yield periodic solutions of Kaplan-Yorke type of differential delay equations. Some new sufficient conditions for the existence of Kaplan-Yorke type periodic solutions have been given. Many interesting examples are also disscused.     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.