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201.
V. I. Inozemtsev 《Journal of statistical physics》1990,59(5-6):1143-1155
Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2)
j, k=1,j k
N
P(j – k)
j
k
, where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version. 相似文献
202.
A simple and quite general approach is proposed to derive criteria for transience and ergodicity of a certain class of irreducibleN-dimensional Markov chains in
+
N
assuming a boundedness condition on the second moment of the jumps. The method consists in constructing convenient smooth supermartingales outside some compact set. The Lyapounov functions introduced belong to the set of quadratic forms in
+
N
and do not always have a definite sign. Existence and construction of these forms is shown to be basically equivalent to finding vectors satisfying a system of linear inequalities.Part I is restricted toN=2, in which case a complete characterization is obtained for the type of random walks analyzed by Malyshev and Mensikov, thus relaxing their condition of boundedness of the jumps. The motivation for this work is partly from a large class of queueing systems that give rise to random walks in
+
N
相似文献
203.
Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG()
D
. The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably. 相似文献
204.
P. S. Szczepaniak 《Journal of Optimization Theory and Applications》1989,63(3):459-468
This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included. 相似文献
205.
Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type
(whereB
j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution. 相似文献
206.
207.
Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms. 相似文献
208.
M Riedel 《Journal of multivariate analysis》1985,16(2):241-252
Let X1, X2,…, be independent, identically distributed random variables. Suppose that the linear forms L1 = Σj=1∞ajXj and L2 = Σj=1∞bjXj exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X1 is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L1 and L2 have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions. 相似文献
209.
The addition of the macrocyclic polyether 18-Crown-6 (18C6) increases the selectivity of oxidation of ethylbenzene to -phenylethylhydroperoxide (PEH) in the presence of Ni(acac)2. The initial oxidation rate, selectivity and degree of conversion of ethylbenzene to PEH are greater than those catalyzed by Ni(acac)2 only. The efficiency of the macrocyclic ligand as an activator of Ni(acac)2 exceeds that of monodentate donor ligands. The high selectivity of the process is due to both the primary Ni(acac)2 · 18C6 complexes and the products of their transformation in the course of oxidation. The mechanism of ethylbenzene oxidation catalyzed by Ni(acac)2 · 18C6 complexes is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1406–1411, August, 1994. 相似文献
210.
Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N
2
and N
2
+
partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species Th
, electrons Te
, and vibrational T
v
temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =Te/Th
was varied between 1 and 2 as well as the ratio
v
=T
v
/T
h
for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N
2
are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N
+
. The effects of v
and e
on thermodynamic and transport properties of N
2
are then discussed. 相似文献