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1.
We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular, we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We use the theory of regularly varying functions to construct a sequence of smooth proper priors approaching an improper prior fast enough for establishing the admissibility. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior. 相似文献
2.
J. A. Siddiqi 《Aequationes Mathematicae》1990,40(1):235-247
Summary In this paper, we give necessary and sufficient conditions for a Carleman class in metricL
p
to be included in another or to be differentiable. 相似文献
3.
Christopher J. Catone 《Differential Geometry and its Applications》2008,26(4):404-418
In this paper we ask when a Finsler surface is projectively equivalent to a given Riemannian surface and when is a Finsler surface projectively equivalent to some Riemannian surface in general. We obtain a necessary and sufficient condition for projective equivalence in both cases. We then consider the latter condition in terms of the Christoffel symbols of the Riemannian metric and investigate when six functions of two variables are the Christoffel symbols of a Riemannian metric. We employ an exterior differential system to analyze when four functions of two variables are the four projective quantities of a Riemannian metric. We end the paper with a theorem which applies the necessary and sufficient condition to 2-dimensional Randers metrics. 相似文献
4.
R. Kasimbeyli 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2534-2547
In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. 相似文献
5.
Sheng Bau 《Graphs and Combinatorics》2002,18(2):201-208
A necessary and sufficient condition for the existence of a cycle containing a set of three vertices and an edge excluding
another edge is obtained for 3-connected cubic graphs by means of canonical contractions. A necessary and sufficient condition
is also obtained for a cyclically 4-connected cubic graph to have a cycle that contains a set of four vertices and that avoids
another vertex.
Received: October 4, 1999 Final version received: June 14, 2000 相似文献
6.
Piermarco Cannarsa 《Journal of Differential Equations》2008,245(3):616-636
In the classical time optimal control problem, it is well known that the so-called Petrov condition is necessary and sufficient for the minimum time function to be locally Lipschitz continuous. In this paper, the same regularity result is obtained in the presence of nonsmooth state constraints. Moreover, for a special class of control systems we obtain a local semiconcavity result for the constrained minimum time function. 相似文献
7.
Pham Huu Sach 《Numerical Functional Analysis & Optimization》2013,34(3-4):341-351
We give a new necessary and sufficient condition for convexity of a set-valued map F between Banach spaces. It is established for a closed map F having nonconvex values. The main tool in this paper is the coderivative of F which is constructed with the help of an abstract subdifferential notion of Penot . A detailed discussion is devoted to special cases when the contingent, the Fréchet and the Clarke-Rockafellar subdifFerentials Sixe used as this abstract subdifferential. 相似文献
8.
Francisco R. Villatoro 《Journal of Difference Equations and Applications》2013,19(7):681-691
The necessary and sufficient condition for an autonomous, ordinary differential equation to be exactly solved by a given Evans-Sanugi, nonlinear, one-step, finite difference method based on ‘classical means’ are derived. A necessary, but not sufficient, condition yields the most general nonlinearity for the differential equation which is independent of the step size. Examples of differential equations for which either nonlinear trapezoidal or nonlinear implicit midpoint methods based on arithmetic, harmonic, contraharmonic, quadratic, geometric, Heronian, centroidal and logarithmic means are exact, are presented. These new exact difference schemes may be useful in future developments of new Denk-Bulirsch, Le-Roux or Kojouhavov-Chen schemes for nonlinear evolution equations with or without blow-up. 相似文献
9.
Let (M, g) be a compact Kähler manifold and (E, F) be a holomorphic Finsler vector bundle of rank r ≥ 2 over M. In this paper, we prove that there exists a Kähler metric φ defined on the projective bundle P (E) of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for φ having positive scalar curvature is obtained, and a sufficient condition for φ having positive Ricci curvature is established. 相似文献
10.
In this paper we generalize and sharpen R.W. Chaney's results on unconstrained and constrained second-order necessary and sufficient optimality conditions [5–7] for general Lipschitz functions without the semismoothness assumptionCorresponding author. 相似文献
11.
??hen the distribution of random variable V_1,V_2 and V_3 composes an I\times J\times K contingency table, this paper research the collapsibility of entropy, and present necessary and sufficient conditions for simple collapsibility and strong collapsibility of mutual information by the research on collapsibility of entropy, which are considered under the condition of sub-independence. 相似文献
12.
hen the distribution of random variable V_1,V_2 and V_3 composes an I\times J\times K contingency table, this paper research the collapsibility of entropy, and present necessary and sufficient conditions for simple collapsibility and strong collapsibility of mutual information by the research on collapsibility of entropy, which are considered under the condition of sub-independence. 相似文献
13.
Withun Phuengrattana Suthep Suantai 《Journal of Computational and Applied Mathematics》2011,235(9):3006-3014
In this paper, we propose a new iteration, called the SP-iteration, for approximating a fixed point of continuous functions on an arbitrary interval. Then, a necessary and sufficient condition for the convergence of the SP-iteration of continuous functions on an arbitrary interval is given. We also compare the convergence speed of Mann, Ishikawa, Noor and SP-iterations. It is proved that the SP-iteration is equivalent to and converges faster than the others. Our results extend and improve the corresponding results of Borwein and Borwein [D. Borwein, J. Borwein, Fixed point iterations for real functions, J. Math. Anal. Appl. 157 (1991) 112-126], Qing and Qihou [Y. Qing, L. Qihou, The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval, J. Math. Anal. Appl. 323 (2006) 1383-1386], Rhoades [B.E. Rhoades, Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976) 741-750], and many others. Moreover, we also present numerical examples for the SP-iteration to compare with the Mann, Ishikawa and Noor iterations. 相似文献
14.
15.
We give a necessary and sufficient condition for the relation to hold as . Here α is an irrational number, denotes the fractional part of x and f is from a suitable class of functions with the property that or for a finite set of rational .
Received 11 January 2001; in revised form 10 August 2001 相似文献
16.
17.
On the orthogonal basis of the symmetry classes of tensors associated with the dicyclic group 总被引:1,自引:0,他引:1
A necessary and sufficient condition for the existence of orthogonal basis of decomposable symmetrized tensors for the symmetry classes of tensors associated with the dicyclic group is given. In particular we apply these conditions to the generalized quaternion group, for which the dimensions of the symmetry classes of tensors are computed. 相似文献
18.
19.
D. Blömker R. Tribe 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(2):175
The solutions to a large class of non-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of the stochastic representation, using a comparison scalar PDE.In cases where the representation fails to be integrable, a sequence of pruned trees is constructed, producing approximate stochastic representations that in some cases converge, globally in time, to the solution of the original PDE. 相似文献
20.
Ryan Berndt 《Journal of Mathematical Analysis and Applications》2011,379(1):439-443
We discuss conditions on weight functions, necessary or sufficient, so that the Fourier transform is bounded from one weighted Lebesgue space to another. The sufficient condition and the primary necessary condition presented are similar, one being phrased is terms of arbitrary measurable sets and the other in terms of cubes. We believe that the symmetry amongst the two conditions helps frame how a single condition, necessary and sufficient, might appear. 相似文献