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1.
We give an example of a bounded pseudoconvex domain in , the Wu metric of which (associated to the Kobayashi-Royden or the Azukawa metric) is not upper semicontinuous. 相似文献
2.
Abstract The strong laws of large numbers with the convergence in the sense of the uniform Hausdorff metric for stationary sequences of random upper semicontinuous functions is established. This approach allows us to deduce many results on the convergence in uniform Hausdorff metric of random upper semicontinuous functions from the relevant results on real-valued random variables that appear as their support functions. 相似文献
3.
It is shown that if k( x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k( x) B
X* is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its local Lipschitz-constant function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed. 相似文献
4.
We study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of lower semicontinuous bounded-from-below objective functions
. We establish the existence of a G
δ
everywhere dense subset ℱ of
such that, for any objective function belonging to ℱ, the corresponding minimization problem possesses a solution. 相似文献
5.
The idea of defining the expectation of a random variable as its integral with respect to a probability measure is extended to certain lattice-valued random objects and basic results of integration theory are generalized. Conditional expectation is defined and its properties are developed. Lattice valued martingales are also studied and convergence of sub- and supermartingales and the Optional Sampling Theorem are proved. A martingale proof of the Strong Law of Large Numbers is given. An extension of the lattice is also studied. Studies of some applications, such as on random compact convex sets in R
n and on random positive upper semicontinuous functions, are carried out, where the generalized integral is compared with the classical definition. The results are also extended to the case where the probability measure is replaced by a -finite measure. 相似文献
6.
Let be analytic on the unit disk with . In 1989, D. Marshall conjectured the existence of the universal constant such that whenever the area, counting multiplicity, of a portion of over is . Recently, P. Poggi-Corradini (2007) proved this conjecture with an unspecified constant by the method of extremal metrics. In this note we show that such a universal constant exists for a much larger class consisting of analytic functions omitting two values of a certain doubly-sheeted Riemann surface. We also find a numerical value, , which is sharp for the problem in this larger class but is not sharp for Marshall's problem. 相似文献
8.
We obtain an upper bound for the upper subderivative of the marginal function of an abstract parametric optimization problem when the objective function is lower semicontinuous. Moreover, we apply the result to a nonlinear program with right-hand side perturbations. As a result, we obtain an upper bound for the upper subderivative of the marginal function of a nonlinear program with right-hand side perturbations, which is expressed in dual form in terms of appropriate Lagrange multipliers. Finally, we present conditions which imply that the marginal function is locally Lipschitzian. 相似文献
9.
Given a lower semicontinuous function , we prove that the points of , where the lower Dini subdifferential contains more than one element, lie in a countable union of sets which are isomorphic to graphs of some Lipschitzian functions defined on . Consequently, the set of all these points has a null Lebesgue measure. 相似文献
10.
Given a family of real-valued functions defined in a normed vector space X, we study a class of -convex functions having a simpler representation for the --subdifferential. The case = X* with X being a Banach space (the Fenchel case) is particularly analysed, and we find that the sublinear lower semicontinuous functions satisfy the simpler representation with respect to X*. As a side result, we provide various new subdifferential-type charaterizations of positively homogeneous functions among those which are lower semicontinuous and convex. In addition, we also discuss that family related to the the so-called prox-bounded functions. In this more general framework our simpler representation may give rise to a new notion of enlargement of the subdifferential.Mathematics Subject Classifications (2000) 47H05, 46B99, 47H17.This work is based on research material supported in part by CONICYT-Chile through FONDECYT 101-0116 and FONDAP-Matemáticas Aplicadas II. 相似文献
11.
While there are several interesting examples of partitions of R
3 into elements which individually are geometrically nice — circles or segments — the partitions themselves fail to be nice, in the sense of forming continuous or upper semicontinuous decompositions. We show that this is no accident: R
3 has no continuous decomposition into circles, and no open subset of R
n
has an upper semicontinuous decomposition into convex compact nonsingleton sets. 相似文献
12.
The existence of solutions is established for implicit differential inclusions in involving the sum of a maximal monotone mapping and an upper semicontinuous mapping with compact, closed values. A question of Wenzel is answered in the affirmative. 相似文献
13.
We establish qualitative results of Phragmèn–Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of . 相似文献
14.
Let denote the class of functions which are univalent and holomorphic on the unit disc. We derive a simple differential equation for the Loewner flow of the Schwarzian derivative of a given . This is used to prove bounds on higher order Schwarzian derivatives which are sharp for the Koebe function. As well we prove some two-point distortion theorems for the higher order Schwarzians in terms of the hyperbolic metric. 相似文献
15.
A very important property of a deterministic self-similar set is that its Hausdorff dimension and upper box-counting dimension coincide. This paper considers the random case. We show that for a random self-similar set, its Hausdorff dimension and upper box-counting dimension are equal 相似文献
16.
Let f be analytic in a hyperbolic region . The Bloch constant
f
of f is defined by
, where ( z)| dz| is the Poincaré metric in . Suppose is hyperbolic and
where
. Then for all f with f() , we have
f
1/(). In this paper we study the extremal functions defined by
f
=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China. 相似文献
17.
We construct biharmonic nonharmonic maps between Riemannian manifolds M and N by first making the ansatz that M N be aharmonic map and then deforming the metric conformally on M to render biharmonic. The deformation will, in general, destroy theharmonicity of . We call a metric which renders the identity mapbiharmonic, a biharmonic metric. On an Einstein manifold, theonly conformally equivalent biharmonic metrics are defined byisoparametric functions. 相似文献
18.
We derive an upper bound for the concentration of the sum of i.i.d. random variables with values in
by appealing to functions of positive type and the structure theory of set addition. 相似文献
19.
Given a closed set , the set of all points at which the metric projection onto is multi-valued is nonempty if and only if is nonconvex. The authors analyze such a set, characterizing the unbounded connected components of . For compact, the existence of an asymptote for any unbounded component of is obtained. 相似文献
20.
In this paper we present a topology on the space of real-valued functions defined on a functionally Hausdorff space $X$ that is finer than the topology of pointwise convergence and for which (1) the closure of the set of continuous functions $\mathcal{C }(X)$ is the set of upper semicontinuous functions on $X$ , and (2) the pointwise convergence of a net in $\mathcal{C }(X)$ to an upper semicontinuous limit automatically ensures convergence in this finer topology. 相似文献
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