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1.
《中学生数学》2006,(22)
Sketches and diagrams are sometimes useful in problem solving.For example,four runners are in a one-mile race:A,B,C,and D.Points are awarded only to the person finishing first or sec- ond.The first-place winner gets more points than the second-place winner.How many different arrangements of first-and second-place winner are possible? 相似文献
2.
On a Problem Proposed by Kartsatos 总被引:1,自引:0,他引:1
Zhou Haiyun 《东北数学》1999,(1)
§1.IntroductionandPreliminariesLetXbearealreflexiveBanachspacewithnormandnormalizeddualitymappingJ.Asusual,wesupposethatthesp... 相似文献
3.
W.M. Priestly 《Semigroup Forum》1998,56(3):301-322
t , for t ≥ 0, be a strongly continuous Markovian semigroup acting on C(X), where X is a compact Hausdorf space, and let D
denote the domain of its infinitesimal generator Z. Suppose D contains a (perhaps finite) family of functions f separating
the points of X and satisfying Zf2 = 2fZf. If either
(1) there exists δ > 0 such that (Tt f)2∈ D if 0 ≤ t ≤δ for each f in this family; or
(1′) for some core D′ of Z, g ∈ D′ implies g2∈ D, then the underlying Markoff process on X is deterministic. That is, there exists a semiflow — a semigroup (under composition)
of continuous functions φt from X into X — such that Ttf(x) = f(φt (x)). If the domain D should be an algebra then conditions (1) and (1′) hold trivially. Conversely, if we have a separating
family satisfying Zf2 = 2fZf then each of these conditions implies that D is an algebra. It is an open question as to whether these conditions
are redundant. If the functions φt are homeomorphisms from X onto X, then of course we have a Markovian group induced by a flow. This result is obtained by
first providing general results about the null-space N of the (function-valued) positive semidefinite quadratic form defined
by < f, g > = Z(fg) - fZg - gZf. The set N can be defined for any generator Z of a strongly continuous Markovian semigroup
and is equivalently given by
N = {f ∈ D| f2∈ D and Zf2 = 2fZf}
= {f ∈ D| Tt(f2)-(Ttf)2 is o(t2) in C(X)}.
In the general case N is an algebra closed under composition with any C1-function φ from the reals to the reals, and Z(φ[f]) = (Zf)φ′[f] if f ∈ N. This "chain rule" on N (on which Z must act as
a derivation) is a special case of a theorem for C2-functions φ which holds more generally for all f in d, viz.,
Z(φ[f] = (Zf) φ′[f] + ? <f, f> φ″[f],
Provided Z is a local operator and D is an algebra. In this case the form < f, g > itself enjoys the relation
< φ[f], ψ[g] > = φ′ [f] ψ′[g] < f, g >,
for C2functions φ and ψ. Some of the results and their proofs continue to hold when the setting is switched from the commutative
C*-algebra C(X) to a general (noncommutative) C*-algebra A. In the norm continuous case we obtain a sharp characterization
of Markovian semigroups that are groups: Let Tt = etz , defined for t ≥ 0, be a Markovian semigroup acting on a C*-algebra A that is norm continuous, i.e., ||Tt - I|| ⇒ 0 as t ⇒ 0 +. Assume Z(a2) = a(Za) + (Za) a for some (perhaps finite) set of self-adjoint elements a that generate a Jordan algebra dense among the
self-adjoint elements of A. The etz , -∞ < t < ∞, is a group of Markovian operators. 相似文献
4.
Y. G. Stoyan T. Romanova G. Scheithauer A. Krivulya 《Computational Optimization and Applications》2011,48(3):675-695
The problem of covering a compact polygonal region, called target region, with a finite family of rectangles is considered.
Tools for mathematical modeling of the problem are provided. Especially, a function, called Γ-function, is introduced which
indicates whether the rectangles with respect to their configuration form a cover of the target region or not. The construction
of the Γ-function is similar to that of Φ-functions which have been proved to be an efficient tool for packing problems. A
mathematical model of the covering problem based on the Γ-function is proposed as well as a solution strategy. The approach
is illustrated by an example and some computational results are presented. 相似文献
5.
In this article, we discuss necessary and sufficient conditions for the crossed product S = Rα G by a twisted partial action α of a finite group G on a ring R to be separable over its center. 相似文献
6.
is valid, where ω(f,δ) is the modulus of continuity of f. Furthermore they asked that: (1.3) If Theorem A can be extended to matrix summability? Later, P. D. Kathal, A. S. B. Holland and B. N. Sahney partially answered this problem. They proved the following Theorem B If {Λ_(n,k)} is monotonic non-increasing for all 0≤k≤n and Λ_(n,k)≥0 (0≤k≤n),Λ_(n,k)=0 (k>n), then we have 相似文献
7.
Liang Zhian 《东北数学》1997,(1)
TheSpecialClasGeneratedbyaPrimePI┐Ring*LiangZhian(梁治安)(DepartmentofMathematics,InnerMongoliaUniversity,Hohhot,010021)Abstract... 相似文献
8.
IP Waicheung 《中国科学A辑(英文版)》2006,49(9):1211-1222
In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test. 相似文献
9.
Mohamed El Otmani 《Journal of Theoretical Probability》2009,22(3):601-619
In this paper, we study the reflected solution of one-dimensional backward stochastic differential equation driven by Teugels
martingales and an independent Brownian motion. We prove the existence and uniqueness of the solution using a penalization
method combined with Snell envelope theory.
相似文献
10.
Jing-min He Rong Wu Hua-yue Zhang 《应用数学学报(英文版)》2008,24(1):117-128
In this paper we mainly study the ruin probability of a surplus process described by a piecewise deterministic Markov process (PDMP). An integro-differential equation for the ruin probability is derived. Under a certain assumption, it can be transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Using the same argument as that in Asmussen and Nielsen, the ruin probability and its upper bounds are obtained. Finally, we give an analytic expression for ruin probability and its upper bounds when the claim-size is exponentially distributed. 相似文献
11.
1 IntroductionIn many practical problems we often cannot observe the behavior of all states for a Markov chain (see [3-5]). A natural question is that from the observable data of a part of states, can one still obtain all statistical characteristics of the Markov chains. In this paper we give the positive answer for this question and prove the surprising result that the transition rate matrix of the birth-death chains with reflecting barriers and Markov chains on a star graph can be uniquely … 相似文献
12.
The optimal harvesting problem for a stochastic logistic jump-diffusion process is studied in this paper. Two kinds of environmental noises are considered in the model. One is called white noise which is described by a standard Brownian motion, and the other is called jumping noise which is described by a Lévy process. For three types of yield functions (time averaging yield, expected yield and sustainable yield), the optimal harvesting efforts, the corresponding maximum yields and the steady states of population mean under optimal harvesting strategy are respectively given. A new equivalent relationship among these three different objective functions is showed by the ergodic method. This method provides a new approach to the optimal harvesting problem. Results in this paper show that environmental noises have important effect on the optimal harvesting problem. 相似文献
13.
This paper investigates a damped stochastic wave equation driven by a non-Gaussian Lévy noise. The weak solution is proved
to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition semigroup
under mild conditions. 相似文献
14.
Mediterranean Journal of Mathematics - In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments.... 相似文献
15.
For the Jacobi-type Bernstein–Durrmeyer operator M
n,κ
on the simplex T
d
of ℝ
d
, we proved that for f∈L
p
(W
κ
;T
d
) with 1<p<∞,
K2,\varPhi(f,n-1)k,p £ c||f-Mn,kf||k,p £ c¢K2,\varPhi(f,n-1)k,p+c¢n-1||f||k,p,K_{2,\varPhi}\bigl(f,n^{-1}\bigr)_{\kappa,p}\leq c\|f-M_{n,\kappa}f\|_{\kappa,p}\leq c'K_{2,\varPhi}\bigl(f,n^{-1}\bigr)_{\kappa ,p}+c'n^{-1}\|f\|_{\kappa,p}, 相似文献
16.
Let μ
Σ be the natural measure on R
N
(N≥3) supported by a compact oriented analytic hypersurface Σ, ψ a smooth function on R
N
and P(D) a differential operator in N variables of order m. We determine a sufficient condition on the number λ such that the Fourier integral of the distribution P(D)ψ
μ
Σ be summable by Cesàro means of order λ to zero in a point outside the hypersurface. This condition depends on m and on the position of the point with respect to the caustic of the hypersurface. 相似文献
17.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
18.
LetL
n be the set of lines (no two parallel) determining ann-sided bounded faceF in the Euclidean plane. We show that the number,f(L
n), of triples fromL
n that determine a triangle containingF satisfies
and these bounds are best. This result is generalized tod-dimensional Euclidean space (without the claim that the upper bound is attainable). 相似文献
19.
We consider an infinite-server queue, where the arrival and service rates are both governed by a semi-Markov process that
is independent of all other aspects of the queue. In particular, we derive a system of equations that are satisfied by various
“parts” of the generating function of the steady-state queue-length, while assuming that all arrivals bring an amount of work
to the system that is either Erlang or hyperexponentially distributed. These equations are then used to show how to derive
all moments of the steady-state queue-length. We then conclude by showing how these results can be slightly extended, and
used, along with a transient version of Little’s law, to generate rigorous approximations of the steady-state queue-length
in the case that the amount of work brought by a given arrival is of an arbitrary distribution.
相似文献
20.
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion. We derive a maximum principle and the associated stochastic variational inequality, which both are generalizations of the classical case. 相似文献
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