Author Keywords: Chemometrics; Modelling; Fitting; Polynomial analytical function; Linear regression; Experimental design 相似文献
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91.
An algorithm for searching the best polynomial analytical function for describing different experimental systems is presented. It is based
1. (1)on the generation of all possible analytical functions of a given order, with a given number of terms and with a given number of independent variables, and
2. (2)on the calculation of the parameters of all selected functions using the linear regression method.
To show the ability of the program two different examples are given:
1. (1) searching the best univariate polynomial model, and
2. (2) modelling of the stability of a two-component mixture as a function of three factors.
92.
Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic
structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed
and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that
the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature.
Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy
may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type
functions.
Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002 相似文献
93.
Mohamed Habibullah S. K. Katti 《Annals of the Institute of Statistical Mathematics》1991,43(2):391-404
In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well. 相似文献
94.
TH型区间值模糊正规子群 总被引:8,自引:1,他引:8
本文在区间值模糊集空间上,引入了幂等区间范数TH,在此基础上,定义了TH型区间值模糊正规子群,并研究了它的一些性质和结构特征,从而拓广了区间值模糊集的理论。 相似文献
95.
《Optimization》2012,61(1):77-94
In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors. 相似文献
96.
Kang Qun Zhang 《数学学报(英文版)》2012,28(6):1135-1154
In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity. 相似文献
97.
This Letter investigates generalized function synchronization of continuous and discrete complex networks by impulsive control. By constructing the reasonable corresponding impulsively controlled response networks, some criteria and corollaries are derived for the generalized function synchronization between the impulsively controlled complex networks, continuous and discrete networks are both included. Furthermore, the generalized linear synchronization and nonlinear synchronization are respectively illustrated by several examples. All the numerical simulations demonstrate the correctness of the theoretical results. 相似文献
98.
99.
《Optimization》2012,61(1-2):35-110
We endeavour to answer the question of the title, or rather the question of how much one can extend convex analysis to a wider framework in which some convexity features remain. Subdifferential calculus and duality are the main directions we consider 相似文献
100.
《Optimization》2012,61(4):677-687
In this paper we give a necessary and sufficient condition for the pseudoconvexity of a function f which is the ratio of a quadratic function over an affine function. The obtained results allow to suggest a simple algorithm to test the pseudoconvexity of f and also to characterize the pseudoconvexity of the sum of a linear and a linear fractional function. 相似文献