摘要：
Let X1,...,X(N) (where N > m) be independent N(m)(mu, SIGMA) random vectors, and put [GRAPHICS] where T is upper-triangular with positive diagonal elements. The author considers the problem of estimating SIGMA, and restricts his attention to the class of estimates D = {T' DELTA*T + Nb* XBAR XBAR':DELTA* is any diagonal matrix and b* is any nonnegative constant} because it has the following attractive features: (a) Its elements are all quadratic forms of the sufficient and complete statistics (XBAR, T). (b) It contains all estimates of the form aA + NbXBARXBAR' (a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0), which construct a complete subclass of the class of nonnegative quadratic estimates D* = {X'BX : B greater-than-or-equal-to 0} (where X = (X1,...,X(N)') for any strict convex loss function. (c) It contains all invariant estimates under the transformation group of upper-triangular matrices. The author obtains the characteristics for an estimate of the form T' DELTAT + NbXBARXBAR' (DELTA = diag{delta1,...,delta(m)} greater-than-or-equal-to 0 and b greater-than-or-equal-to 0) of SIGMA to be admissible in D when the loss function is chosen as tr(SIGMA-1 SIGMA - I)2, and shows, by an example, that aA + NbXBARXBAR' (a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0) is admissible in D* can not imply its admissibility in D.
摘要：
A fundamental comparison theorem is established for general semilinear parabolic systems via the notions of sectorial operators, analytic semigroups and the application of the Tychonoff Fixed Point Theorem. Based on this result, we establish a maximum principle for systems of general parabolic operators and general comparison theorems for parabolic systems with quasimonotone or mixed quasimonotone nonlinearities. These results cover and extend most currently used forms of maximum principles and comparison theorems. A global existence theorem for parabolic systems is derived as an application which, in particular, gives rise to some global existence results for Fujita type systems and certain generalisations.
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,1992年122(1-2):161-175 ISSN：0308-2105
通讯作者：
DENG, YB
作者机构：
[DENG, YB] Department of Mathematics, Huazhong Normal University, Wuhan 430070, P.R. China
通讯机构：
[DENG, YB] H;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
摘要：
In this paper we discuss the problem -DELTAu + c2u = u(p) + muf(x), u > 0, u is-an-element-of H-1(R(N)), n > 2. ((*)mu) We show that for c > 0 there exists a positive constant mu* such that (*)mu possesses at least one solution if mu is-an-element-of (0, mu*) and no solutions if mu > mu*. Furthermore,there exists a positive constant mu** less-than-or-equal-to mu* such that (*)mu possesses at least two solutions if mu is-an-element-of (0, mu**), 2 < N < 6. For N greater-than-or-equal-to 6, mu is-an-element-of (0, mu**), we show that problem (*)mu possesses a unique solution if f(x) is radial with f'(r) < 0 (r = Absolute value of x).
期刊：
Journal of Graph Theory,1992年16(3):247-255 ISSN：0364-9024
通讯作者：
MAO, JZ
作者机构：
Department of Mathematics Huazhong Normal University Wuhan Hubei Peoples's Republic of China
通讯机构：
[MAO, JZ] H;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN,PEOPLES R CHINA.
摘要：
In this paper we prove that all geodetic blocks of diameter two can be divided in four types, i.e., Moore graphs with diameter two, regular pyramids with altitude 2, type AP and type PP. We also give the answers to the questions posed by J. G. Stemple in 1974.
摘要：
§ 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space W<sub>t</sub><sup>2</sup><sup>1,2</sup>（O, +∞） into L<sub>t</sub><sup>2</sup><sup>q</sup>（O, ∞）, v】2. When v=N-1 we can get the radial solutions of problem where 2<sup>*</sup>=2N/N-2 is the critical exponent of the Sobolev embedding H<sup>1</sup>（R<sup>n</sup>）→L<sup>Q</sup>（R<sup>N</sup>）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|<sup>l-1</sup>u+f（u） is lower then |u|<sup>v+3/v-1</sup> i.e.
期刊：
Journal of Mathematical Analysis and Applications,1991年154(1):116-133 ISSN：0022-247X
通讯作者：
DENG, YB
作者机构：
ACAD SINICA,INST MATH SCI,WUHAN 430071,PEOPLES R CHINA.;ZHONGSHAN UNIV,DEPT MATH,GUANGZHOU,PEOPLES R CHINA.;[DENG, YB] HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
通讯机构：
[DENG, YB] H;HUAZHONG NORMAL UNIV,DEPT MATH,WUHAN 430070,PEOPLES R CHINA.
摘要：
Definition 1. If （?）A∈A<sub>I</sub>, the zero solution of（1.2 ）is absolutely stable, then we say the interval system （1.1）is Robust absolutely stable, which is denoted by （1.1）∈RAS. Definition 2. If （?）A∈A<sub>I</sub>, the zero solution of （1.2） is absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, then we call the interval system （1.1）Robust absolutely stable for partial variables x<sub>j0</sub>, …, x<sub>n+1</sub>, which is denoted by （1.1）∈RAS （j0→n+1）.
作者机构：
ACAD SINICA,WUHAN INST MATH SCI,WUHAN,PEOPLES R CHINA.;HUA ZHONG NORMAL UNIV,DEPT MATH,WUHAN,PEOPLES R CHINA.;[CAO, DM] 中科院武汉物理与数学所;[DENG, YB] 华中师范大学
摘要：
This paper is concerned with the existence and the nodal character of the nontrivial solutions in the entire space for some semilinear elliptic equation involving critical Sobolev exponent.
