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201.
A. K. Ramazanov 《Mathematical Notes》1999,66(5):613-627
Suppose thatD={z:|z|<1}, L
2
(D) is the space of functions square-integrable over area inD,A
k
(D) is the set of allk-analytic functions inD, (A
1
(D)=A(D) is the set of all analytic functions inD),A
k
L
2
(D)=L
2
(D)∩A
k
(D),A
1
L
2
(D)=AL
2
(D),
. It is proved that the subspacesA
k
L
2
0
(D),k=1, 2,..., are orthogonal to one another and the spaceA
m
L
2
(D) is the direct sum of such subspaces fork=1, 2,...,m. The kernel of the orthogonal projection operator from the spaceA
m
L
2
(D) onto its subspacesA
k
L
2
0
(D) is obtained. These results are applied to the study of the properties of polyrational functions of best approximation in
the metricL
2
(D).
Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 741–759, November, 1999. 相似文献
202.
Almost-Sure Results for a Class of Dependent Random Variables 总被引:17,自引:0,他引:17
The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by
d
+
—the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes. 相似文献
203.
一类带干扰风险模型的推广 总被引:6,自引:0,他引:6
In this paper, the cLassicaL risk process perturbed by diffusion is genera]ized by alLowing for “size fluctuation“ and the rtl[n probabiLity for this new model is dlscussed. 相似文献
204.
This paper generalizes an inequality of Moser from the case that is in the Lebesgue space to certain subspaces, namely the Lorentz spaces , where . The conclusion is that is integrable, where . This is a higher degree of integrability than in the Moser inequality when . A formula for is given and it is also shown that no larger value of works.
205.
Marc Bourdon Hervé Pajot 《Proceedings of the American Mathematical Society》1999,127(8):2315-2324
In this paper we shall show that the boundary of the hyperbolic building considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of and the fact that every quasiconformal homeomorphism is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.
206.
The Furuta inequality with negative powers 总被引:2,自引:0,他引:2
Let be bounded linear operators on a Hilbert space satisfying . Furuta showed the operator inequality
as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.
as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.
207.
We prove the existence of a solution of the nonlinear equation in IRN and in exterior domains, respectively. We concentrate to the case when p ≥ N and the nonlinearity f(x, · ) is “superlinear” and “subcritical”. 相似文献
208.
Milan Kučera 《Czechoslovak Mathematical Journal》1999,49(3):449-474
Variational inequalities
are studied, where K is a closed convex cone in
, 3, B
is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some 0 for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some I 0. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at 0 constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system. 相似文献
209.
Given a continuous P0-function F : Rn Rn, we describe a method of constructing trajectories associated with the P0-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P0-function lead to P0-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P0-equations when the underlying function is P0. To generate the trajectories, we perturb the given P0-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem. 相似文献
210.
We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html. 相似文献