李color三系的Frattini子系的性质

给出了李color三系的Frattini子系的定义,得到了李color三系的Frattini子系的一些性质·特别的,证明了李color三系T有分解T=T_1⊕T_2⊕…⊕T_m,则φ(T)有分解φ(T)=φ(T_1)⊕φ(T_2)⊕…⊕φ(T_m).     

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

We present the software package MO VI PAC for calculations of vibrational spectra, namely infrared, Raman, and Raman Optical Activity (ROA) spectra, in a massively parallelized fashion. MO VI PAC unites the latest versions of the programs SNF and AKIRA alongside with a range of helpful add‐ons to analyze and interpret the data obtained in the calculations. With its efficient parallelization and meta‐program design, MO VI PAC focuses in particular on the calculation of vibrational spectra of very large molecules containing on the order of a hundred atoms. For this purpose, it also offers different subsystem approaches such as Mode‐ and Intensity‐Tracking to selectively calculate specific features of the full spectrum. Furthermore, an approximation to the entire spectrum can be obtained using the Cartesian Tensor Transfer Method. We illustrate these capabilities using the example of a large π‐helix consisting of 20 (S)‐alanine residues. In particular, we investigate the ROA spectrum of this structure and compare it to the spectra of α‐ and 3₁₀‐helical analogs. © 2012 Wiley Periodicals, Inc.     

Is it worthwhile to go beyond the local-density approximation in subsystem density functional theory?

Frozen density embedding (FDE) theory is one of the major techniques aiming to bring modeling of extended chemical systems into the realm of high accuracy calculations. To improve its accuracy it is of interest to develop kinetic energy density functional approximations specifically for FDE applications. In the study reported here we focused on optimizing parameters of a generalized gradient approximation-like kinetic energy functional with the purpose of better describing electron excitation energies. We found that our optimized parametrizations, named excPBE and excPBE-3 (as these are derived from a Perdew-Burke-Ernzerhof-like parametrization), could not yield improvements over available functionals when applied on a test set of systems designed to probe solvatochromic shifts. Moreover, as several different functionals yielded very similar errors to the simple local-density approximation (LDA), it is questionable whether it is worthwhile to go beyond the LDA in this context.     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

大型动态规划的分解算法

An approach about large dynamic programming based on discrete linear system with a quadratic index function is proposed by importing two Lagrange multipliers.     

The impulse influence function for de-centralized control

Impulse influence matrix function is introduced based on that the de-centralized control analysis is analogous to the sub-structural analysis in structural mechanics. The static sub-structural analysis is analogous to the usual de-centralized control, whereas the dynamic sub-structural analysis corresponds to the de-centralized control theory. The re-     

Weakest bound electron potential model theory

Differing from the self‐consistent field (SCF) method, in which an N‐electron atom problem is treated as a one‐electron problem with the use of a basic assumption of average potential, we develop a unified weakest bound electron potential model (WBEPM) theory. The relativistic form of the theory is given for the first time and is combined with the nonrelativistic form introduced in previous work to arrive at the unified WBEPM theory. The theory has two main ideas. First, from consideration of viewpoints of the dynamic successive ionization and the choice of zero of energy in quantum mechanics, an N‐electron atom system can be subdivided into N subsystems only containing a weakest bound electron (WBE) in each of subsystems. For each subsystem by separation of WBE and non‐weakest bound electrons (NWBE), WBE is believed to move in an approximate potential field provided by a “core” consisting of NWBEs and the nucleus. Thus, a complicated N‐electron problem is reduced to a simple analytical one‐electron problem of WBE. Second, the properties of an atom, such as total wave function, total energy, atomic energy levels, and transition between energy levels, can be investigated through the behaviors of a WBE or several WBEs, or up to all WBEs. Several excellent illustrative results show that the theory is capable of attaining very good computational accuracy. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.     

Products of operators of multidimensional structured model of systems

The author has previously defined the concept of a general system in terms of operators and operands. An operand is a mapping defined on a subset of an m-fold Cartesian product instead of the usual set and collection of k-ary relations on it. An operator is a kind of mapping between two collections of operands. Here subsystems, extensions, and the notion of P-semiexactness is studied. In particular we derive conditions such that P-semiexactness of a composition of operators, and of one factor, implies P-semiexactness of the other factor.