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1.
Ursula Felgenhauer 《Annals of Operations Research》2001,101(1-4):23-42
The theory of discretization methods to control problems and their convergence under strong stable optimality conditions in recent years has been thoroughly investigated by several authors. A particularly interesting question is to ask for a natural smoothness category for the optimal controls as functions of time.In several papers, Hager and Dontchev considered Riemann integrable controls. This smoothness class is characterized by global, averaged criteria. In contrast, we consider strictly local properties of the solution function. As a first step, we introduce tools for the analysis of L
elements at a point. Using afterwards Robinson's strong regularity theory, under appropriate first and second order optimality conditions we obtain structural as well as certain pseudo-Lipschitz properties with respect to the time variable for the control.Consequences for the behavior of discrete solution approximations are discussed in the concluding section with respect to L
as well as L
2 topologies. 相似文献
2.
S. G. Samko 《Analysis Mathematica》1995,21(3):213-236
I
(x)
D
(x)
. , L
p
(x)
, , (I
(x)
)–1, (I
(x)
)–1, , I
(x)
(L
p
).
Partly supported by the Fulbright grant during author's Visiting Professorship at the University of New Haven, Mathematics Department, West Haven, Connecticut 06516, USA, and by the Russian Foundation for Basic Research (Project 94-01-00577-a). 相似文献
Partly supported by the Fulbright grant during author's Visiting Professorship at the University of New Haven, Mathematics Department, West Haven, Connecticut 06516, USA, and by the Russian Foundation for Basic Research (Project 94-01-00577-a). 相似文献
3.
Arjen E. Ronner 《Probability Theory and Related Fields》1984,66(4):613-620
Summary The consistency and asymptotic normality of p-norm estimators (1<p<2) is established by applying some of the ideas of Huber (1973), where asymptotic normality of the so-called M-estimators for regression parameters is shown. A central role is played by a weight function . Huber assumed that , and are bounded. This is, however, not the case for p-norm estimators with 1<p<2, but some of his ideas can still be applied. 相似文献
4.
A. V. Lipin 《Journal of Mathematical Sciences》1989,44(6):856-861
In the note one considers operators T, acting in a Hilbert space and satisfying an equation of the form (T)=A, where is a polynomial, while A is a given normal operator, assumed to be either reductive or unitary. Under these conditions one computes some spectral characteristics of the operator T (spectral multiplicity, disc, lattice of invariant subspaces, etc.). Fundamental examples are the weighted substitution operators (TL2(X,)L2(X,), Tf=·(f·), where is a periodic automorphism of (X,), L (X, ).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 157–164, 1987.The author expresses his sincere gratitude to N. K. Nikol'skii for the formulation of the problem and for the useful discussion of the results. 相似文献
5.
Dieter Jungnickel 《Journal of Geometry》1979,12(2):168-174
In his Finite Geometries, Dembowski asserted that the class of uniform projective Hjelmslev planes of order q and a certain class of symmetric divisible partial designs coincide. We give a counterexample for q=2 and prove the validitiy of Dembowski's assertion for all q3. 相似文献
6.
D. V. Leladze 《Analysis Mathematica》1991,17(4):281-295
n- (n1) fL
p
([–, ]
n
),=1 = (L
C) . , , f([–, ]
n
). 相似文献
7.
Horst J. Klepp 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1992,43(2):335-356
Summary The periodic response of a single-freedom multi-body system with friction-affected constraints acted upon by a harmonic excitation is determined by numerical simulation. The contribution of the constraints to the generalized friction force, the influence of gravity and zero-gravity environment, and the consequences, when several constraints are considered without friction, are investigated. The effects of a small artificial damping on the response, and the possibilities of an equivalent damping for the friction-affected constraints are also examined.
Zusammenfassung Die periodische Bewegung eines Mehrkörpersystems mit einem Freiheitsgrad und reibungsbehafteten Bindungen bei harmonischer Erregung wird durch numerische Simulation bestimmt. Untersucht werden der Beitrag der Bindungen zur verallgemeinerten Reibungskraft, der Einfluß des Schwerefeldes und der Schwerelosigkeit und die Folgen, wenn einige Bindungen als reibungsfrei angenommen werden. Die Auswirkungen einer kleinen künstlichen Dämpfung auf die Bewegung, und die Möglichkeiten einer äquivalenten Dämpfung an Stelle der reibungsbehafteten Bindungen wird auch untersucht.相似文献
8.
9.
Hans -J. Runckel 《Analysis Mathematica》1984,10(4):295-299
A, ()=0, c(z)- T - TY=AY. A y(t)=y(, t) Ty=y Y(t). - c(T)y=0. 相似文献
10.
11.
12.
13.
E. Porteus 《Journal of Optimization Theory and Applications》1982,36(3):419-432
The study of infinite-horizon nonstationary dynamic programs using the operator approach is continued. The point of view here differs slightly from that taken by others, in that Denardo's local income function is not used as a starting point. Infinite-horizon values are defined as limits of finite-horizon values, as the horizons get long. Two important conditions of an earlier paper are weakened, yet the optimality equations, the optimality criterion, and the existence of optimal structured strategies are still obtained. 相似文献
14.
In this paper, we show that a necessary and sufficient condition for the fulfillment of the relation s
m
(k) (f) – f(k)
p
0 as m , 1 < p < , k 0,1,2,..., is that f B
,p
, where B
,p
= B
L
p
(R), and B
denotes the subset of all entire functions of exponential type which are bounded on R, B
,p
is usually called Paley-Wiener class, and s
m
(f) is the unique cardinal spline of degree m – 1 interpolating f at the integers. Moreover, we obtain three equivalent forms for the characterization of the class B
,p
. 相似文献
15.
— [0,1] ,E — - e=1 [0,1]. I —
E
=1, E=L
2 x
e
=xL
2 x E.
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
16.
Summary The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in a -finite measure space (X, , ). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the -algebra . This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces. 相似文献
17.
Liu Yongping 《Analysis Mathematica》1995,21(2):107-124
18.
S. Zlobec 《Journal of Global Optimization》1995,7(3):229-259
Mathematical programs, that become convex programs after freezing some variables, are termed partly convex. For such programs we give saddle-point conditions that are both necessary and sufficient that a feasible point be globally optimal. The conditions require cooperation of the feasible point tested for optimality, an assumption implied by lower semicontinuity of the feasible set mapping. The characterizations are simplified if certain point-to-set mappings satisfy a sandwich condition.The tools of parametric optimization and basic point-to-set topology are used in formulating both optimality conditions and numerical methods. In particular, we solve a large class of Zermelo's navigation problems and establish global optimality of the numerical solutions.Research partly supported by NSERC of Canada. 相似文献
19.
. . 相似文献
20.
This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy). 相似文献