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171.
Ramiro Pino Olivier Bokanowski Eduardo V. Ludeña Roberto López Boada 《Theoretical chemistry accounts》2007,118(3):557-561
Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum
Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension
of this theorem to finite subspaces.
Contribution to the Serafin Fraga Memorial Issue. 相似文献
172.
《Journal of Pure and Applied Algebra》2022,226(12):107134
The notion of a group action can be extended to the case of gyrogroups. In this article, we examine a digraph and graph associated with a gyrogroup action on a finite nonempty set, called a Schreier digraph and graph. We show that algebraic properties of gyrogroups and gyrogroup actions such as being gyrocommutative, being transitive, and being fixed-point-free are reflected in their Schreier digraphs and graphs. We also prove graph-theoretic versions of the three fundamental theorems involving actions: the Cauchy–Frobenius lemma (also known as the Burnside lemma), the orbit-stabilizer theorem, and the orbit decomposition theorem. Finally, we make a connection between gyrogroup actions and actions of symmetric groups by evaluation via Schreier digraphs and graphs. 相似文献
173.
Ram Manohar & Rajen Kumar Sinha 《计算数学(英文版)》2022,40(2):147-176
This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators. 相似文献
174.
《Discrete Mathematics》2022,345(9):112954
One of the remarkable contributions in the study of symmetric Cayley graphs on nonabelian simple groups is the complete classification of such graphs that are cubic and nonnormal. This naturally motivates the study of cubic (normal and nonnormal) symmetric bi-Cayley graphs on nonabelian simple groups. In this paper, the full automorphism groups of these graphs are determined, and necessary and sufficient conditions are given for a graph being a cubic normal symmetric Cayley or bi-Cayley graph on a nonabelian simple group (one may then find many examples). As an application, we also prove that cubic symmetric Cayley graphs on nonabelian simple groups are stable. 相似文献
175.
The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF
1, ...,F
m ordered by their relative importance. The objective is to minimize the least important criterionF
m subject to the schedule being optimal with respect to the more important criterionF
m–1 which is minimized on the set of schedules minimizing criterionF
m–2 and so on. The most important criterion isF
1, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF
1, ...,F
m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF
1, ...,F
m–1 and the maximum cost is an example of functionF
m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne. 相似文献
176.
Jianxing Bi 《数学学报(英文版)》1995,11(3):300-306
LetG be a finite group. If
for every primer, whereR
1 Syl
r
G andR
2 Syl
r
(L
n
(q)), thenG L
n
(q). 相似文献
177.
We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2
4 – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2
4 –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R
g
2
>/<R
e
2
>=0.14026±0.00007, <R
m
2
>/<R
e
2
>=0.43961±0.00034, and *=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent
1=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for
1. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R
g
2
>/<R
e
2
>=0.1599±0.0002 and *=0.2471±0.0003; since *>0, hyperscaling holds. The approach to * is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2
4 – for two-dimensional SAWs. 相似文献
178.
Mark D. Haiman 《Journal of Algebraic Combinatorics》1994,3(1):17-76
We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring
in two sets of variables by the ideal generated by all S
n invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = {x
1, ..., x
n} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory. 相似文献
179.
A. Salam 《Numerical Algorithms》1996,11(1):327-337
The vector -algorithm is obtained from the scalar -algorithm by taking the pseudo-inverse of a vector instead of the inverse of a scalar. Thus the vector -algorithm is known only through its rules contrarily to the scalar -algorithm and some other extrapolation algorithms.The aim of this paper is to provide an algebraic approach to the vector -algorithm. 相似文献
180.
Peter J. Cameron 《Designs, Codes and Cryptography》1996,8(3):109-133
The main theme of this article is that counting orbits of an infinite permutation group on finite subsets or tuples is very closely related to combinatorial enumeration; this point of view ties together various disparate stories. Among these are reconstruction problems, the relation between connected and arbitrary graphs, the enumeration of N-free posets, and some of the combinatorics of Stirling numbers.Dedicated to Hanfried Lenz on the occasion of his 80th birthday. 相似文献