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991.
It is known that the Banach completion Y = bX of a normed lattice X need not preserve the properties to be Dedekind complete or σ-Dedekind complete. In this paper it is proved that the countable
interpolation property and the property to be sequentially order complete are preserved under the Banach completion. To prove
this results we found some sufficient conditions (which are close to necessary ones) on X which secure for Y to have the countable interpolation property and (respectively) to be sequentially order complete. These conditions are obtained
with the help of the newly developed techniques based on representations of normed lattices. It is well known that order continuity,
and σ-order continuity of a norm are preserved under the Banach completion. Here necessary and sufficient conditions on X to secure these properties in Y are discussed.
Mathematics Subject Classification 2000: 46B42, 46E15 相似文献
992.
In this paper we introduce a concept of variational convergence for mappings taking values in order topological vector spaces. This variational convergence notion is shown to be well adapted to the (epi)-convergence of composed convex functions, in the sense that it is preserved after composition with nondecreasing functions. It is proved how this stability result can be applied to the continuity of multipliers under perturbations associated with a family of constrained optimization problems. Other applications are also given. 相似文献
993.
Anita T.?LaytonEmail author Michael L.?MinionEmail author 《BIT Numerical Mathematics》2005,45(2):341-373
This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations;
such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn,tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical
quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature
nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau,
and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that
include or exclude function values computed at the left-hand endpoint tn. Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are
shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest
that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect
the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff
equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and
extent of order-reduction changes considerably. Specifically, a reduction of order to
is observed for uniform nodes as opposed to
for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff.
AMS subject classification (2000) 65B05 相似文献
994.
A finite algebra is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order ≤ on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; ≤). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras.* Research supported by the Hungarian research grant No. TO34137 and by the János Bolyai grant.** Research supported by the Thailand Research Fund. 相似文献
995.
David J. Grynkiewicz 《Acta Mathematica Hungarica》2005,107(1-2):161-174
Summary Let G be a finite abelian group, and let n be a positive integer. From the Cauchy-Davenport Theorem it follows that if G is a cyclic group of prime order, then any collection of n subsets A_1,A_2,\ldots,A_n of G satisfies \bigg|\sum_{i=1}^n A_i\bigg| \ge \min \bigg\{|G|,\,\sum_{i=1}^n |A_i|-n+1\bigg\}. M.~Kneser generalized the Cauchy--Davenport Theorem for any abelian group. In this paper, we prove a sequence-partition analog of the Cauchy--Davenport Theorem along the lines of Kneser's Theorem. A particular case of our theorem was proved by J.~E. Olson in the context of the Erdős--Ginzburg--Ziv Theorem. 相似文献
996.
Using the fixed point method we prove an existence result for positive solutions of nonlinear second order ordinary differential equations. An application to semilinear Schrödinger equations in exterior domains is also presented. Mathematics Subject Classification (2000) 34C10 相似文献
997.
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test functions higher order derivatives. The class includes the size and zero bias transformations, and when specializing to weighting by polynomial functions, relates distributional families closed under independent addition, and in particular the infinitely divisible distributions, to the family of transformations induced by their associated orthogonal polynomial systems. For these families, generalizing a well known property of size biasing, sums of independent variables are transformed by replacing summands chosen according to a multivariate distribution on its index set by independent variables whose distributions are transformed by members of that same family. A variety of the transformations associated with the classical orthogonal polynomial systems have as fixed points the original distribution, or a member of the same family with different parameter. 相似文献
998.
In this note new Rosenbrock methods for ODEs, DAEs, PDEs and PDAEs of index 1 are presented. These solvers are of order 3,
have 3 or 4 internal stages, and fulfil certain order conditions to obtain a better convergence if inexact Jacobians and approximations
of
are used. A comparison with other Rosenbrock solvers shows the advantages of the new methods.
AMS subject classification (2000) 34A09, 65L80 相似文献
999.
1000.
Let X(ω) be a random element taking values in a linear space endowed with the partial order ≤; let 0 be the class of nonnegative order-preserving functions on such that, for each g∈0, E[g(X)] is defined; and let 1?0 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf1E[g(X)]/g(x) ≤ inf1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability. 相似文献