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1.
For the general fixed effects linear model:Y=X+, N(0,V),V0, we obtain the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS in the class of all estimators under the loss function (d -S)D(d -S), whereD0 is known. For the general random effects linear model: =XV 11 X+XV 12+V 21 X+V 220, we also get the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS+Q in the class of all estimators under the loss function (d -S -Q)D(d -S -Q), whereD0 is known.  相似文献   

2.
We discuss the evaluation of the Hilbert transformf –1 1 (t-)–1 w(, )(t)dt,–1<<1, of the Jacobi weight functionw(, )(t)=(1–t))(1+t) by analytic and numerical means and also comment on the recursive computation of the quantitiesf –1 1 )(t–)–1 n (t;w (, )) w (, )(t)dt,n=0, 1, 2, ..., where n (·;w (, )) is the Jacobi polynomial of degreen.The work of the first author was supported in part by the National Science Foundation under grant DCR-8320561. The work of the second author was supported by the National Science Foundation under grant DMS-8419086.  相似文献   

3.
Summary A totally umbilical pseudo-Riemannian submanifold with the parallel mean curvature vector field is said to be an extrinsic sphere. A regular curve in a pseudo-Riemannian manifold is called a circle if it is an extrinsic sphere. LetM be ann-dimensional pseudo-Riemannian submanifold of index (0n) in a pseudo-Riemannian manifold with the metricg and the second fundamental formB. The following theorems are proved. For 0 = +1 or –1, 1 = +1, –1 or 0 (2–2 0+ 12n–2–2) and a positive constantk, every circlec inM withg(c, c) = 0 andg( c c, c c) = 1 k 2 is a circle in iffM is an extrinsic sphere. For 0 = +1 or –1 (–0n–), every geodesicc inM withg(c, c) = 0 is a circle in iffM is constant isotropic and B(x,x,x) = 0 for anyx T(M). In this theorem, assume, moreover, that 1n–1 and the first normal space is definite or zero at every point. Then we can prove thatM is an extrinsic sphere. When = 0 orn, this fact does not hold in general.  相似文献   

4.
. , A 0,A 1,— - lim supA j - H, . , - - . , , ; , , . - . - .  相似文献   

5.
Summary Let A be the set of all points of the plane , visited by 2-dimensional Brownian motion before time 1. With probability 1, all points of A are twist points except a set of harmonic measure zero. Twist points may be continuously approached in \A only along a special spiral. Although negligible in the sense of harmonic measure, various classes of cone points are dense in A, with probability 1. Cone points may be approached in \A within suitable wedges.Research supported in part by NSF Grant DMS 8419377  相似文献   

6.
, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1].  相似文献   

7.
{p mn } - 00>0, (1, 1) (1.1) (1.2). {s mn } J p - ( bJ p -lims mn =), (1.3) 0<x,y<1 p s (, )/p(x, y) x, y 1-. {r mn } - , (1.5) 0<, <1. N rp - , (1.6). , bJ p -lims mn = bJ q -lim(N rps) mn =. J p - . , .  相似文献   

8.
Let M be a complete module of a purely algebraic field of degree n3, let be the lattice of this module and let F(X) be its form. By we denote any lattice for which we have = , where is a nondiagonal matrix satisfying the condition ¦-I¦ , I being the identity matrix. The complete collection of such lattices will be denoted by {}. To each lattice we associate in a natural manner the decomposable form F(X). The complete collection of forms, corresponding to the set {}, will be denoted by {F} It is shown that for any given arbitrarily small interval (N–, N+), one can select an such that for each F(X) from {F} there exists an integral vector X0 such that N– < F(X0) < N+.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 167–171, 1981.  相似文献   

9.
10.
The following statement is proved. Letu be a subharmonic function in the region and u the associated measure. Then there exists a functionf holomorphic in and such that if f is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for= u and for= f . In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.

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