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1.
F.P. Temme 《Journal of mathematical chemistry》1997,21(4):373-384
On existence of limiting
‐module decompositional sets for weak
‐branching at high n; on Voronoi polyhedral dual as geometric analogues to Cayley’s SU2
embedding theorem; and on SU
dual group with retention of self‐associacy over subduced irrep set, as being the sufficient further condition to ensure
the determinacy of SU
embeddings.
In the context of structures arising from nuclear permutation (NP) or NMR dual‐group spin algebras, the first conjecture sets
out the high‐index n, and thus weak‐branching limit (WBL), aspects of
module decompositions as giving rise to a set of numerical values for the associated Kostka coefficients which are invariant
to further incrementation in the
index; the existence of such combinatorial limit properties, implicit in sst
tableaux enumerations, has not been addressed in the mathematics literature to date. Conjectures 2 and 3 are concerned with
the questions of geometric and sufficient algebraic realisations of the determinacy of natural finite group embeddings in
specific SU
permutation groups. In conjecture 2, the Voronoi dual‐structures to the regular polyhedra for NP/NMR automorphic SU2
embedded spin symmetries hold the key to physical insight. Specifically, they provide a novel combinatorial geometric view
of Cayley’s theorem; the mid‐face intersecting
‐axes of the initial NMR automorphic solids become (vertex) body‐diagonal axes of the specific‐dual Voronoi polyhedra, where
a distinctness condition from the spin‐sites gives raise to a geometric statement of Cayley’s theorem. Conjecture 3 is concerned
with SU
embeddings for which the simple Cayley criterion alone is an insufficient condition to guarantee determinacy. The
self‐associacy property and its retention over the subduced irrep‐subset(s) (i.e., comparable to studies of
system‐invariants via Yamanouchi–Gel’fand subduction chains) is now seen as indicative of retention of determinacy for such
SU
group embeddings through the above sufficiency condition.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Ljupčo Pejov Gjorgji Ivanovski Vladimir M. Petruševski 《Journal of mathematical chemistry》1999,26(4):317-326
A perturbation theoretical method is proposed that allows determination of the function describing the dependence of the intramolecular
XH(D) potential on the hydrogen bond strength. Treating the XH(D) oscillators as mixed cubic–quartic oscillators in which
the stretch–stretch couplings of the ν(X–H(D)) mode with the internal modes of the radical X may be neglected, and introducing
the hydrogen bonding influence through the changes in the harmonic diagonal force constants (as proposed by Sceats and Rice
[41]), it is possible to extract the analytical form of the function
) from the experimental
versus
correlations. The other parameters obtained by the empirical correlations, within this model, also have an exact physical
meaning. The method is applicable to weak hydrogen bonds as well as to hydrogen bonds of intermediate strength, and, strictly
speaking, to linear X–
systems. However, extension to arbitrary geometry may be easily done.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number
of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers
of sites of D lying on the symmetry elements
for G. 相似文献
4.
A second-order method is developed for the numerical solution of the initial-value problems
,
,
and
,
,
, in which the functions
and
, where A and B are positive real constants, are the reaction terms arising from the mathematical modelling of chemical systems such as in
enzymatic reactions and plasma and laser physics in multiple coupling between modes. The method is based on three first-order
methods for solving u and v, respectively. In addition to being second-order accurate in space and time, the method is seen to converge to the correct
fixed point (
, V* = A/B) provided
. The approach adopted is extended to solve a class of non-linear reaction–diffusion equations in two-space dimensions known
as the “Brusselator” system. The algorithm is implemented in parallel using two processors, each solving a linear algebraic
system as opposed to solving non-linear systems, which is often required when integrating non-linear partial differential
equations (PDEs).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
István Szalkai 《Journal of mathematical chemistry》1999,25(1):31-46
The phases of multicomponent systems (mixtures, states, etc.) containing the compounds
are
, where
and
. For
(quaternary or higher dimensional systems), the displaying methods and visual investigations in the
dimensional Euclidean space
are tangentially or not at all described in the literature. In this paper we first develop the theoretical (both mathematical and computational) background in any dimension in
. We focus not only on the important points, lines, surfaces of these systems, and computing method of the states of some processes in such systems, but also on the approximating methods of the above mentioned lines and surfaces, and, finally, on the question which is the region where a state (a point) falls into. Using the above results a computer program for PC's was created for evaluating and displaying the approximated surfaces. This program is described in I. Szalkai, SALT3DIM.exe – A program for handling 4 component mixtures, Preprint No. 047, University of Veszprém (1996), and the computing results are planned to be published in a forthcoming paper (I. Szalkai, Handling multicomponent systems in
. II: Computational results, J. Chem. Inf. Comput. Sci., submitted). 相似文献
6.
By analyzing the topological structures of the three types of icosahedral fullerenes: (1)
, (2)
and (3)
k,\;h,k = 1,2,...} \right)$$
" align="middle" border="0">
, we have obtained theoretically the 13C NMR spectra with natural abundance for 13C of all the icosahedral (Ih and I) fullerenes. 相似文献
7.
Analytical expressions for the calculation of both orbital and total moments of diatomic molecules using Gaussian‐type orbitals
are formulated. Moments
with
are computed for the ground state of 35 diatomic molecules at equilibrium bond length using 6‐311G(d,p) basis sets. In order to test our expressions, these expectation momentum values are compared with the values calculated
using self‐consistent‐field wave functions of Hartree–Fock quality, which give Hartree–Fock limit energies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
The dependencies of the relative permittivity of over 50 liquids on the pressure P, as
, and of some 40 liquids on the (square of the) electric field E at ambient conditions, as
were obtained from literature data. The function
was fitted to a simple expression in and the compressibility, T. These data were used to obtain the limiting slope for the partial molar volumes and the electrostriction of electrolytes in various solvents. 相似文献
9.
We study a first‐order exothermic chemical reaction in a continuous stirred‐tank reactor modelled by a 3‐parameter family
of vector fields in
. We prove that there exist regions in
which contain points that depend on parameters such that the chemical reaction has 0, 1, 2, or 3 small amplitude limit cycles
that surround the origin. We conclude that this model can reach two stable small amplitude limit cycles. Finally, we show
that one of these regions contains the point in the parameter space considered by Gurel and Lapidus [6] who proved numerically
the existence of one stable limit cycle.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
We examine a few computational geometric problems concerning the structures of polymers. We use a standard model of a polymer, a polygonal chain (path of line segments) in three dimensions. The chain can be reconfigured in any manner as long as the edge lengths and the angles between consecutive edges remain fixed, and no two edges cross during the motion. We discuss preliminary results on the following problems.Given a chain, select some interior edge
, defining two subchains which are adjacent to
. We keep the two subchains individually rigid and rotate one around
while leaving the other fixed in space, while maintaining the vertex-angles at
. We call this motion an edge spin at
. An O(n
2) algorithm for this problem is given as well as an (nlogn) lower bound on the time complexity.In determining whether a chain can be reconfigured from one conformation to another, it is useful to consider reconfiguring through some canonical conformation. In our three-dimensional case, the most obvious choice is to flatten a chain into the plane. However, we demonstrate that determining if a given chain can be reconfigured into the plane without self-intersecting is NP-hard, even if the restriction that it must lie monotonically is added. We then provide an O(n) algorithm to decide if a chain has a non-crossing convex coil conformation (where all angles turn in the same direction), although we cannot yet decide if a sequence of motions to reconfigure a chain into a convex coil conformation exists. 相似文献
11.
H. Taşeli 《Journal of mathematical chemistry》2004,36(1):1-12
A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrödinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the
-polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the
-polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined. 相似文献
12.
The local structure of Co2+ at the
-,
, and
-cation sites of zeolite ZSM-5 was calculated in terms of density functional theory using the cluster approach. The local geometry of the oxygen environment of Co2+ is characterized; it is found that the ion stabilization energy increases in the series
. 相似文献
13.
HF and CAS calculations for linear geometry of Fe(CH)2 with
symmetry have been performed. The basis sets used were DZ and DZ + P with ECP on the iron atom. Two closedshell and one quintet RHF wave functions have been found,
and
. All of them are singlet and triplet unstable in the wide range of Fe–CH distances. Singlet instability leads to the Charge Density Wave (CDW) brokensymmetry wave function with two electrons on carbon
or
orbital in the dissociation limit. Triplet instabilities lead to two brokensymmetry HF wave functions of Axial Spin Density Wave (ASDW) type, ASDW1 and ASDW2. In the dissociation limit they give carbon atoms with two electrons on
and
orbitals coupled to singlet and triplet, respectively. The stability conditions for CDW, ASDW1 and ASDW2 instabilities have been derived. Other HF wave functions with spin symmetry unrestricted have been also found. CAS(8,8), CAS(10,10) and CAS(12,12) calculations for singlet, triplet and quintet states of Fe(CH)2 have been carried out. In all CAS calculations the singlet state has the lowest energy. The Fe–CH equilibrium distances obtained from closedshell RHF wave functions are much shorter and from brokensymmetry wave functions are much longer than those obtained from CAS calculations. 相似文献
14.
The enthalpies and entropies of evaporation of Al(CH3)3–Sn(CH3)4and Ga(CH3)3–Sn(CH3)4solutions were determined. It was established that solvates are formed in these systems and that the dissociation energies of specific interactions in them change in the following order:
(10.3) >
>
>
(4.08 kJ mol–1),
(6.52) >
(5.14) >
>
(4.08 kJ mol–1). 相似文献
15.
Summary A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs
and
, related by a chemical transformation
, the reaction graph
is determined using a maximal common subgraph defined for vertex mapping
. A binary operation defined for graphs constructed over the same vertex set enables us to decompose the reaction graph
into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at
and ending at
corresponds to a breakdown of the transformation
into a sequence of intermediates. 相似文献
16.
Mario Piris 《Journal of mathematical chemistry》1999,25(1):47-54
The basic ideas of the Improved Bardeen–Cooper–Schrieffer (IBCS) approach to the first and secondorder Reduced Density Matrices (1 and 2RDM) are briefly reviewed. The molecular orbital occupations
are expressed by means of new quantities
, which, satisfying a trigonometric relation, guarantee the nonidempontent condition. Thus, a variational method is introduced to determine
, involving only an unconstrained minimization which may be performed using a conjugate gradient technique. A new effective Hamiltonian
which is composed of the Coulomb, exchange and exchangetime inversion operators is also presented. It leads exactly to equations of Hartree–Fock type, however, the electronic field includes now an arbitrary number of orbitals and fractional occupation numbers. Accordingly, a generalized selfconsistentfield method is proposed: the iterative procedure is repeated until convergence is reached for the actual density matrix. 相似文献
17.
Luminescence Behavior of Polynuclear Alkynylcopper(I) Phosphines 总被引:1,自引:0,他引:1
A series of soluble trinuclear and tetranuclear copper(I) complexes containing 3-l acetylides
, and
have been synthesized and shown to exhibit rich photoluminescent behavior at room temperature. The electrochemistry of the trinuclear Cu(I) acetylide complexes and the excited-state redox properties of
have been investigated. The X-ray crystal structures of
and
have been determined. 相似文献
18.
Anna Rita Campanelli Fabio Ramondo Aldo Domenicano István Hargittai 《Structural chemistry》1999,10(1):29-40
The molecular structure and conformation of p-bis(trimethylsilyl)benzene have been investigated by gas-phase electron diffraction, ab initio MO calculations at the HF/6-31G*, MP2(f.c.)/6-31G*, and B3LYP/6-31G* levels, and MM3 molecular mechanics calculations. The calculations indicate the syn- and anti-coplanar conformations, with two
bonds in the plane of the benzene ring, to be energy minima. The perpendicular conformations, with two
bonds in a plane orthogonal to the ring plane, are transition states. The two coplanar conformers have nearly the same energy with a low interconversion barrier, 0.3–0.5 kJ mol–1. The calculated lengths of the
and
bonds differ by only a few thousandths of an angstrom, in agreement with electron diffraction results from molecules containing either
or
bonds. The geometrical distortion of the benzene ring in p-bis(trimethylsilyl)-benzene may be described by superimposing independent distortions from each of the two SiMe3 groups. The electron diffraction intensities from a previous study (Rozsondai, B.; Zelei, B.; Hargittai, I. J. Mol. Struct.
1982, 95, 187) have been reanalyzed, imposing constraints from the theoretical calculations, and using a model based on a 1:1 mixture of the two coplanar conformers. The effective torsion angles of the SiMe3 groups may indicate nearly free rotation. Important geometrical parameters from the present electron diffraction analysis are
, and
. While the mean bond lengths are virtually the same from the previous and present analyses, the new ipso angle is in better agreement with the MO calculations [HF, 116.9° MP2(f.c.), 117.1° B3LYP, 116.9°]. 相似文献
19.
We derive two expansions of the Randles–Sevcik function
: an asymptotic expansion of
for x and its Taylor expansion at any x
0
. These expansions are accompanied by error bounds for the remainder at any order of the approximation. 相似文献
20.
Dieter Erle 《Journal of mathematical chemistry》1998,24(4):365-378
For a class of dynamical systems of the form
, we prove boundedness of all solutions in the positive time direction. We discuss the existence of stable limit cycles for the simplest autocatalytic reaction involving two internal and two external reactants, as well as for a number of other models arising in applications. 相似文献