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41.
Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
42.
N. B. Brusnikina A. V. Lotov 《Computational Mathematics and Mathematical Physics》2007,47(11):1779-1787
A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs. 相似文献
43.
Renato Bruni 《Annals of Operations Research》2007,150(1):79-92
The paper is concerned with the problem of binary classification of data records, given an already classified training set
of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered.
Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD
procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of
the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy
of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging
results are obtained and discussed. 相似文献
44.
Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry. 相似文献
45.
P. A. V. Ferreira M. E. S. Machado 《Journal of Optimization Theory and Applications》1996,89(3):659-680
Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNPq and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments. 相似文献
46.
In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order
where eachw
i
is strictly positive and eachy
i
is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n
2). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship. 相似文献
47.
For one-dimensional expanding mapsT with an invariant measure we consider, in a parameter space, the envelope
n
of the real lines associated to any couple of points of the orbit, connected byn iterations ofT. If the map hass inverses and is piecewise linear, then the sets
n
are just the union ofs
n
points and converge to the invariant Cantor set ofT. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on 1 to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and hass inverses, the sets
n
are homeomorphic to the Cantor set; they converge to the Cantor set ofT and their measures converge to the measure of the Cantor set whenn. The correspondence between the sets
n
allows one to define converging approximation schemes for the map an its measure: one replaces each of thes
n
disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set 1. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined. 相似文献
48.
We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985. 相似文献
49.
Björn O. Roos Valera Veryazov Per-Olof Widmark 《Theoretical chemistry accounts》2004,111(2-6):345-351
New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be2).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue 相似文献
50.