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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.
J. Globevnik 《Monatshefte für Mathematik》1980,90(3):195-205
LetK be a compact Hausdorff space and letFK be a peak interpolation set for a function algebraAC(K). Let be a map fromK to the family of all convex subsets of such that the set {(z, x)zK, x(z)} is open inK×C and such thatg(z)(z) (zK) for somegA. We prove that everyfC(F) satisfyingf(s)(s) (sF) (f(s)closure (s) (sF)) admits an extensionfAA} satisfyingf(z)(z) (zK) (f(z))}closure (z) (zK), respectively). We prove a more general theorem of this kind and present various applications which generalize known dominated interpolation theorems for subspaces ofC(K). 相似文献
3.
We considered the following natural conjecture: For every sorting algorithm every key will be involved in(logn) comparisons for some input. We show that this is true for most of the keys and prove matching upper and lower bounds. Every sorting algorithm for some input will involven–n
/2+1 keys in at leastlog2
n comparisons,>0. Further, there exists a sorting algorithm that will for every input involve at mostn–n
/c
keys in greater thanlog2
n comparisons, wherec is a constant and>0. The conjecture is shown to hold for natural algorithms from the literature. 相似文献
4.
{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
5.
S. Sivaganesan 《Annals of the Institute of Statistical Mathematics》1993,45(1):187-199
Range of the posterior probability of an interval over the -contamination class ={=(1–)0+q:qQ} is derived. Here, 0 is the elicited prior which is assumed unimodal, is the amount of uncertainty in 0, andQ is the set of all probability densitiesq for which =(1–)0+q is unimodal with the same mode as that of 0. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1–)0 except in one interval (resp. two disjoint intervals) where it is constant. 相似文献
6.
We show how the free boundary of an ideal fluid, subject to a generalized Bernoulli condition, can (under appropriate circumstances) be approximated. Our method is based on a class of free-boundary perturbation operatorsT
, 0<<1, which are all contracting relative to a suitable norm and class of boundaries, and whose fixed points converge to the desired free boundary solution as 0+.
Zusammenfassung Wir zeigen, wie der freie Rand einer idealen Flüssigkeit, welcher einer verallgemeinerten Bernoulli-Bedingung genügt, unter geeigneten Umständen approximiert werden kann. Unsere Methode stützt sich auf eine Klasse freier RandperturbationsoperatorenT , 0<<1, welche relativ zu einer geeigneten Norm und Ränderklasse kontrahierend sind und deren Fixpunkte gegen die gewünschte Lösung der freien Randaufgabe mit 0+ konvergieren.相似文献
7.
Summary We examine the problem:u+a(x)u–b(x)u=f(x) for 0<x<1,a(x)>0,b(x)>,
2
= 4>0,a, b andf inC
2 [0, 1], in (0, 1],u(0) andu(1) given. Using finite elements and a discretized Green's function, we show that the El-Mistikawy and Werle difference scheme on an equidistant mesh of widthh is uniformly second order accurate for this problem (i.e., the nodal errors are bounded byCh
2, whereC is independent ofh and ). With a natural choice of trial functions, uniform first order accuracy is obtained in theL
(0, 1) norm. On choosing piecewise linear trial functions (hat functions), uniform first order accuracy is obtained in theL
1 (0, 1) norm. 相似文献
8.
B. F. Skubenko 《Journal of Mathematical Sciences》1984,25(2):1089-1092
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.
В. Н. Деменко 《Analysis Mathematica》1989,15(1):17-35
p- . E R
n -, f () p(R
n)., ER
n 2nq
0, E— - q
0(q
0-1). : q0>2 n1 E
R
n 2nq
0, p- p<0. , f-[-, ]n, f A
p(R
n) ,
p([-, ]n) (1 << ). 相似文献
10.
For a compact operator in a Hilbert space, let sn(A), n =1, 2,... be the singular numbers and let N(s; A) =card{n N:sn(A)>, s>0. For 0
a p and not on the individual elementAa, (H. Weyl's lemma); this allows us to write p (a), pp (a), ap. One obtains certain results regarding the functionals p, p (and about the analogous functionals for the positive and negative eigenvalues in the casea=a *=A *:A a. In particular: I. Ifa 1 a 2p, then. II.Let a 1,a 2 pP ,.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matetmaticheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 21–30, 1983. 相似文献
11.
We consider the family {X
, 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is
t
X
=
X
+b({X
})+({X
})
. Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X
}A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes. 相似文献
12.
U. A. Akramov 《Journal of Mathematical Sciences》1992,59(6):1137-1142
Let M be the complete module of a purely real algebraic field of degree n 3, let be a lattice in this module, and let F(X) be its form. We use to denote any lattice for which we have = , where is a nondiagonal matrix for which – I . With each lattice we can associate a factorizable formF
(X) in a natural manner. We denote the complete set of forms corresponding to the set {} by {F
(X)}. It is proved that for any > 0 there exists an > 0 such that for eachF
(X) {F
} we have |F
(X0)| for some integer vector X0 0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 5–12, 1990.In conclusion, the author would like to express his deep gratitude to B. F. Skubenko for stating the problem and for his constant attention. 相似文献
13.
T. I. Akhobadze 《Analysis Mathematica》1982,8(2):79-102
. , , –1<<0. .
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
14.
We prove that if (,D) is a positivity preserving form on L
2
(E;m), and if (u
n)n is a sequence in D() converging m-almost everywhere to u L
2
(E;m), then (u,u) lim infn (u
n
,u
n
). 相似文献
15.
Guy Bouchitte 《Applied Mathematics and Optimization》1990,21(1):289-314
Given that, are two Lipschitz continuous functions of to + and thatf(x, u, p) is a continuous function of
× ×
N
to [0, + [ such that, for everyx, f(x,·, 0) reaches its minimum value 0 at exactly two points(x) and(x), we prove the convergence ofF
(u) = (1/)
f (x, u, Du) dx when the perturbation parameter goes to zero. A formula is given for the limit functional and a general minimal interface criterium is deduced for a wide class of two-phase transition models. Earlier results of [19], [21], and [22] are extended with new proofs. 相似文献
16.
On the existence of multiple solutions of nonhomogeneous elliptic equations involving critical Sobolev exponents 总被引:3,自引:0,他引:3
Dao-Min Cao Huan-Song Zhou 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(1):89-96
Letp=2N/(N –2),N 3 be the limiting Sobolev exponent and
N
a bounded smooth domain. We show that for H
–1(),f satisfies some conditions then–u=c
1
u
p–1 +f(x,u) + admits at least two positive solutions. 相似文献
17.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
18.
The aim of this contribution is to examine the S-continued fraction method of obtaining bounds on the effective dielectric constant e of a two-phase composite for the case where the dielectric coefficients 1and 2 of both components are either complex or real. The starting point for our study is a power expansion of e
(z) at(z)=0 (z)=2/1-1. The obtained S-continued fraction bounds have an interesting mathematical structure convenient for theoretical and numerical investigations of e. They also agree with the earlier estimations reported by Bergman and Milton. Specific examples of calculation of bounds on e by theS-continued fraction method are also provided. 相似文献
19.
We obtain estimates for the -entropy and -capacity of sets of periodic functions with mean value zero that have a (, )-derivative belonging to the space L
2(0, 2). 相似文献
20.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献