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1.
We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient and or necessary conditions for existence of such sharp minima, some of which are new even in the single objective setting.This research was supported by a Central Research Grant of The Hong Kong Polytechnic University (Grant No. G-T 507). Research of the first author was also supported by the National Natural Science Foundation of PR China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M). 相似文献
2.
Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat’s rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke’s normal cones or the limiting normal cones) for Pareto efficient points.This research was supported by a postdoctoral fellowship scheme (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. Research of the first author was also supported by the National Natural Science Foundation of P. R. China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, P. R. China (Grant No. 2003A002M). 相似文献
3.
WANG YuShun WANG Bin & QIN MengZhao School of Mathematics Computer Science Nanjing Normal University Nanjing China LASG 《中国科学A辑(英文版)》2008,51(11):2115-2136
In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations,
which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions
are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between
different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the
applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs
for the nonlinear Klein-Gordon equation.
This work was supported by the National Basic Research Program (Grant No. 2005CB321703). The first author was supported by
the National Natural Science Foundation of China (Grant Nos. 40405019, 10471067) and the Major Research Projects of Jiangsu
Province (Grant No. BK2006725); the second author was supported by the National Natural Science Foundation of China (Innovation
Group) (Grant No. 40221503) and the third author was supported by the National Natural Science Foundation of China (Grant
No. 10471145) 相似文献
4.
The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science
Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002) 相似文献
5.
In this paper, we give an overview of representation theorems for various static risk measures: coherent or convex risk measures,
risk measures with comonotonic subadditivity or convexity, law-invariant coherent or convex risk measures, risk measures with
comonotonic subadditivity or convexity and respecting stochastic orders.
This work was supported by National Natural Science Foundation of China (Grant No. 10571167), National Basic Research Program
of China (973 Program) (Grant No. 2007CB814902), and Science Fund for Creative Research Groups (Grant No. 10721101) 相似文献
6.
Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ 总被引:7,自引:0,他引:7
XingHuaWANG ChongLI 《数学学报(英文版)》2003,19(2):405-412
Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average. 相似文献
7.
The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient
conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional
Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion.
This work was supported by the National Natural Science Foundation of China (Grant No. 10562002), Colleges and Universities
Doctoral Subject Research Funds (Grant No. 20070126002) and the Natural Science Foundation of Inner Mongolia (Grant No. 200508010103) 相似文献
8.
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite
matrices are investigated.
Supported by National Natural Science Foundation of China (No. 10531070), National Basic Research Program of China 973 Program
(No. 2006CB805900), National Research Program of China 863 Program (No. 2006AA11Z209) and the Natural Science Foundation of
Shanghai (Grant No. 06ZR14049). 相似文献
9.
Li Wei 《中国科学A辑(英文版)》2009,52(7):1539-1545
The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this
paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin
probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like
claims.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation
Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the
Research Grant of Renmin University of China (Grant No. 08XNA001) 相似文献
10.
Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence
estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence
estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper,
three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of
weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator.
We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives
of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance
of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed
using the proposed estimators.
This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National
Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by
National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation
of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research
Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10
th
five year plan of 211 Project for Shanghai University of Finance and Economics (the 3
rd
phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444) 相似文献
11.
In this paper, one level set method is applied to finding the interface of discontinuity of the conductivity in EIT(electrical
impedance tomography) problem. By choosing one suitable velocity function, a level set reconstruction algorithm is proposed.
The theoretical results for EIT problem and regularization are given. Finally the numerical examples demonstrate that the
reconstruction algorithm is efficient and stable.
The work was supported by the National Natural Science Foundation of China (Grant Nos. 10431030, 10771138), the Shanghai Natural
Science Foundation (Grant No. 07JC14001), the National Basic Research Program (Grant No. 2005CB321701) and Ministry of Education
of China and State Administration of Foreign Experts Affairs of China under an 111 project (Grant No. B08018). 相似文献
12.
In this paper, we investigate the expectation of the size of the largest table in an (α, θ)-Chinese restaurant process by
using and developing an idea originated in the work by Shepp, which discusses random permutation.
This work was supported by National Natural Science Foundation of China (Grant No. 10671036) and the National Basic Research
Program of China (Grant No. 2007CB814904) 相似文献
13.
JinYun Guo 《中国科学A辑(英文版)》2009,52(3):511-516
In this paper, we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram
can be generalized to the m-Cartan matrix of a McKay quiver. We also describe the McKay quiver for a finite abelian subgroup of a special linear group.
This work was supported by National Natural Science Foundation of China (Grant No. 10671061) and the Research Foundation for
Doctor Programme (Grant No. 200505042004) 相似文献
14.
In this paper we obtain local L
p
estimates for the parabolic polyharmonic equations by a straightforward approach.
Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic
Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported
by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant
No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017) 相似文献
15.
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality. 相似文献
16.
MingSheng Liu 《中国科学A辑(英文版)》2009,52(1):87-93
The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates
are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.
This work was supported by the Research Foundation for Doctor Programme (Grant No. 20050574002) and the National Natural Science
Foundation of China (Grant No. 10471048) 相似文献
17.
In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations
on the torus perturbed by a Lévy process. The existence of invariant measure of the solutions are proved also.
This work was supported by National Basic Research Program of China (Grant No. 2006CB8059000), Science Fund for Creative Research
Groups (Grant No. 10721101), National Natural Science Foundation of China (Grant Nos. 10671197, 10671168), Science Foundation
of Jiangsu Province (Grant Nos. BK2006032, 06-A-038, 07-333) and Key Lab of Random Complex Structures and Data Science, Chinese
Academy of Sciences 相似文献
18.
Using a construction theorem of cryptogroups and congruence methods, we determine an 18-element lattice, generated by {NOBG, ROBG, OBG, NBA, RBA, BA}, of subvarieties of completely regular semigroups.
This work was supported by the National Natural Science Foundation of China (Grant No. 10871161) and the Research Foundations
for Doctor Programme of Southwest University (Grant Nos. SWNUB2005020, SWNUB2008001) 相似文献
19.
We classify all the Weierstrass semigroups of a pair of points on a curve of genus 3, by using its canonical model in the plane. Moreover, we count the dimension of the moduli of curves which have a pair of points with a specified Weierstrass semigroup.This work has been supported by the Japan Society for the Promotion of Science and the Korea Science and Engineering Foundation (Project No. 976-0100-001-2). Also the first author is partially supported by Korea Research Foundation Grant (KRF-99-005-D00003). 相似文献
20.
Xing-zhong YOU~ Guo-hua QIAN~ Wu-jie SHI~ 《中国科学A辑(英文版)》2007,50(10):1493-1500
We prove that if G is a finite group in which the elements of the same order outside the center are conjugate,then either G is abelian or G(?)S_3. 相似文献