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991.
Possible generalization of Boltzmann-Gibbs statistics 总被引:31,自引:0,他引:31
Constantino Tsallis 《Journal of statistical physics》1988,52(1-2):479-487
With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
k [1 –
i=1
W
p
i
q
]/(q-1), whereq characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit. 相似文献
992.
Herbert Fischer 《Computational Optimization and Applications》1992,1(3):327-344
This paper is concerned with automatic differentiation methods for computing the reduced gradient M
t
G and the reduced Hessian matrix M
t
HM. Hereby G is the gradient and H is the Hessian matrix of a real function F of n variables, and M is a matrix with n rows and k columns where kn. The reduced quantities are of particular interest in constrained optimization with objective function F. Two automatic differentiation methods are described, a standard method that produces G and H as intermediate results, and an economical method that takes a shortcut directly to the reduced quantites. The two methods are compared on the basis of the reqired computing time and storage. It is shown that the costs for the economical method are less than (k
2+3k+2)/(n
2+3n+2) times the expenses for the standard method. 相似文献
993.
In the Fermat-Weber problem, the location of a source point in
N
is sought which minimizes the sum of weighted Euclidean distances to a set of destinations. A classical iterative algorithm known as the Weiszfeld procedure is used to find the optimal location. Kuhn proves global convergence except for a denumerable set of starting points, while Katz provides local convergence results for this algorithm. In this paper, we consider a generalized version of the Fermat-Weber problem, where distances are measured by anl
p norm and the parameterp takes on a value in the closed interval [1, 2]. This permits the choice of a continuum of distance measures from rectangular (p=1) to Euclidean (p=2). An extended version of the Weiszfeld procedure is presented and local convergence results obtained for the generalized problem. Linear asymptotic convergence rates are typically observed. However, in special cases where the optimal solution occurs at a singular point of the iteration functions, this rate can vary from sublinear to quadratic. It is also shown that for sufficiently large values ofp exceeding 2, convergence of the Weiszfeld algorithm will not occur in general. 相似文献
994.
If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of finding maximum sets of GN constraints and finding maximum embedded GN submatrices are shown to be NP-complete, indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty-three real-world problems. The best of four algorithms for identifying GN constraint sets finds a set which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN constraints identified comprise more than 62.3% of the total constraints in these problems. The algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was identified as a GN submatrix in these problems, on average.The act of being wise is the act of knowing what to overlook.William James (ca. 1890) 相似文献
995.
Xuguang Zhang Xiaopo Zhang Yong Wang Feng Chen Youbin Li Yonghui Li 《Natural product research》2018,32(5):529-535
A new diarylheptanoid, namely trans-(4R,5S)-epoxy-1,7-diphenyl-3-heptanone (1), and a new natural product, 7-(4″-hydroxy-3″-methoxyphenyl)-1-phenyl-hepta-4E,6E-dien-3-one (2), were obtained from the aqueous extract of Alpinia officinarum Hance, together with three other diarylheptanoids, 5-hydroxy-1,7-diphenyl-3-heptanone (3), 1,7-diphenyl-4E-en-3-heptanone (4) and 5-methoxy-1,7-diphenyl-3-heptanone (5). The structures were characterised mainly by analysing their physical data including IR, NMR and HRMS. This study highlights that the 4,5-epoxy moiety in 1 is rarely seen in diarylheptanoids. In addition, the five isolates were tested for their differentiation activity of 3T3-L1 preadipocytes. The results showed that these compounds could dose-dependently promote adipocyte differentiation without cytotoxicity (IC50 > 100 μM). 相似文献
996.
Dynamical Behavior and Exact Traveling Wave Solutions for Three
Special Variants of the Generalized Tzitzeica Equation 下载免费PDF全文
The dynamics and bifurcations of traveling wave solutions are
studied for three nonlinear wave equations. A new phenomenon, such
as a composed orbit, which consists of two or three heteroclinic
orbits, may correspond to a solitary wave solution, a periodic wave
solution or a peakon solution, is found for the equations. Some
previous results are extended. 相似文献
997.
Xiaofang Duan Junliang Lu Yaping Ren Rui Ma 《Journal of Nonlinear Modeling and Analysis》2022,4(4):628-649
The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional
propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and
physical equation than the KdV equation. Therefore, the research
on the BBM equation is very important. In this article, we put
forward an effective algorithm, the modified hyperbolic function
expanding method, to build the solutions of the BBM equation. We, by
utilizing the modified hyperbolic function expanding method,
obtain the traveling wave solutions of the BBM equation.
When the parameters are taken as special values, the solitary
waves are also derived from the traveling waves. The traveling
wave solutions are expressed by the hyperbolic functions, the
trigonometric functions and the rational functions. The modified
hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial
differential equations. 相似文献
998.
基于广义判断形式的模糊排序方法 总被引:7,自引:1,他引:7
广义判断下的AHP(GJAHP)是一种广义AHP。它是在研究不完全信息下的决策排序问题时,通过构造广义判断矩阵的数学模型而建立的一种广义AHP。本文应用集值统计的方法,在区间判断标度基础上确定模糊判断矩阵元素的正模糊数表示。给出了基于模糊区间数排序权值向量的特征根算法。讨论了Fuzzy环境下求解各种判断形式的模糊排序权值向量的方法。 相似文献
999.
Dirk Hachenberger 《Designs, Codes and Cryptography》1996,8(1-2):135-143
We study the structure of a finite groupG admitting a Kantor family (F, F
*) of type (s, t) and a nontrivial normal subgroupX which isfactorized byF F
*. The most interesting cases, giving necessary conditions on the structure ofG and the parameterss andt, are those where a further Kantor family is induced inX, or where a partial congruence partition is induced in the factor groupG/X. Most of the known finite generalized quadrangles can be constructed as coset geometries with respect to a Kantor family. We show that the parameters of a skew translation generalized quadrangle necessarily are powers of the same prime. Furthermore, the structure of nonabelian groups admitting a Kantor family consisting only of abelian members is considered.Dedicated to Hanfried Lenz on the occasion of his 80th birthday 相似文献
1000.
Zhang Zhenqiu 《数学学报(英文版)》1996,12(2):133-140
In this paper, we investigate the generalized Sublaplacian. We give the expression of the restriction operators explicitly. By introducing the generalized -twisted convolutions, we obtain the estimates of the restriction operators in the mixedL
p
spaces. Finally, we get a restriction theorem associated with the generalized Sublaplacian. 相似文献