共查询到20条相似文献,搜索用时 140 毫秒
1.
Salvatore A. Marano 《Set-Valued Analysis》1996,4(3):287-300
Let be a bounded domain in n (n3) having a smooth boundary, let be an essentially bounded real-valued function defined on × h, and let be a continuous real-valued function defined on a given subset Y of Y h. In this paper, the existence of strong solutions u W
2,p (, h) W
o
1,p
(n/2<p<+) to the implicit elliptic equation (–u)=(x,u), with u=(u1, u2, ..., uh) and u=(u
1, u
2, ..., u
h), is established. The abstract framework where the problem is placed is that of set-valued analysis. 相似文献
2.
Singular integral equations with Cauchy kernel and piecewise-continuous matrix coefficients on open and closed smooth curves are replaced by integral equations with smooth kernels of the form(t–)[(t–)
2–n
2
(t)
2]–1,0, wheren(t), t , is a continuous field of unit vectors non-tangential to . we give necessary and sufficient conditions under which the approximating equations have unique solutions and these solutions converge to the solution of the original equation. For the scalar case and the spaceL
2() these conditions coincide with the strong ellipticity of the given equation.This work was fulfilled during the first author's visit to the Weierstrass Institute for Applied Analysis and Stochastics, Berlin in October 1993. 相似文献
3.
A. M. Kagan 《Journal of Mathematical Sciences》1986,34(2):1482-1487
Summary Denote by
k
a class of familiesP={P} of distributions on the line R1 depending on a general scalar parameter , being an interval of R1, and such that the moments µ1()=xdP
,...,µ2k
()=x
2k
dP
are finite, 1 (), ..., k (), k+1 () ...,
k
() exist and are continuous, with 1 () 0, and
j
+1 ()= 1 ()
j
() +[2() -1()2]
j
()/ 1 (), J=2, ..., k. Let 1=¯x=x
1 + ... +x
n/n, 2=x
1
2 + ... +x
n
2/n, ...,
k
=(x
1
k
+ ... +x
n
k/n denote the sample moments constructed for a sample x1, ..., xn from a population with distribution Pg. We prove that the estimator of the parameter by the method of moments determined from the equation 1= 1() and depending on the observations x1, ..., xn only via the sample mean ¯x is asymptotically admissible (and optimal) in the class
k
of the estimators determined by the estimator equations of the form 0 () + 1 () 1 + ... +
k
()
k
=0 if and only ifP
k
.The asymptotic admissibility (respectively, optimality) means that the variance of the limit, as n (normal) distribution of an estimator normalized in a standard way is less than the same characteristic for any estimator in the class under consideration for at least one 9 (respectively, for every ).The scales arise of classes
1
2... of parametric families and of classes 1 2 ... of estimators related so that the asymptotic admissibility of an estimator by the method of moments in the class
k
is equivalent to the membership of the familyP in the class
k
.The intersection consists only of the families of distributions with densities of the form h(x) exp {C0() + C1() x } when for the latter the problem of moments is definite, that is, there is no other family with the same moments 1 (), 2 (), ...Such scales in the problem of estimating the location parameter were predicted by Linnik about 20 years ago and were constructed by the author in [1] (see also [2, 3]) in exact, not asymptotic, formulation.Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 41–47, 1981. 相似文献
4.
For a systemY of partial differential equations, the notion of a covering
Y
is introduced whereY
is infinite prolongation ofY. Then nonlocal symmetries ofY are defined as transformations of
which conserve the underlying contact structure. It turns out that generating functions of nonlocal symmetries are integro-differential-type operators. 相似文献
5.
Let: E M be a fiber bundle and let be an infinitesimal Lie transformation group acting onE. We announce various new results concerning the cohomology of the invariant variational bicomplex (
*,*
(J(E)), dH, dV) and the associated invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transformation groups. 相似文献
6.
We denote byK
k
,k, 2, the set of allk-uniform hypergraphsK which have the property that every element subset of the base ofK is a subset of one of the hyperedges ofK. So, the only element inK
2
2
are the complete graphs. If is a subset ofK
k
then there is exactly one homogeneous hypergraphH
whose age is the set of all finite hypergraphs which do not embed any element of . We callH
-free homogeneous graphsH
n
have been shown to be indivisible, that is, for any partition ofH
n
into two classes, oue of the classes embeds an isomorphic copy ofH
n
. [5]. Here we will investigate this question of indivisibility in the more general context of-free homogeneous hypergraphs. We will derive a general necessary condition for a homogeneous structure to be indivisible and prove that all-free hypergraphs for K
k
with 3 are indivisible. The-free hypergraphs with K
k
2
satisfy a weaker form of indivisibility which was first shown by Henson [2] to hold forH
n
. The general necessary condition for homogeneous structures to be indivisible will then be used to show that not all-free homogeneous hypergraphs are indivisible.This research has been supported by NSERC grant 69–1325. 相似文献
7.
Let G=A
ut(T) be the group of automorphisms of a homogeneous tree and let d(v,gv) denote the natural tree distance. Fix a base vertex e in T. The function (g)=exp(–d(e,ge)), being positive definte on G, gives rise to a semigroup of states on G whose infinitesimal generator d/d|=0=log() is conditionally positive definite but not positive definite. Hence, log() corresponds to a nontrivial cocycle (g): GH
in some representation space H
. In contrast with the case of PGL(2,), the representation is not irreducible.Let
o
(g) be the derivative of the spherical function corresponding to the complementary series of A
ut(T). We show that –d(e,ge) and
o
(g) come from cohomologous cocycles. Moreover,
o
is associated to one of the two (irreducible) special representations of A
ut(T). 相似文献
8.
We show that there are no entire, positive, stable solutions in
n
of the Euler equation corresponding to the singular variational integral
,>0, if+n<5.236.... Furthermore we prove a related result for smooth boundaries of least-energy |x
n+1||D
U
| in
n+1. 相似文献
9.
Let be a graph with diameter d 2. Recall is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of the distance partition{{z V() | (z, y) = i, (x, z) = j} | 0 i, j d}is equitable and its parameters do not depend on the edge xy. Let be 1-homogeneous. Then is distance-regular and also locally strongly regular with parameters (v,k,,), where v = k, k = a
1, (v – k – 1) = k(k – 1 – ) and c
2 + 1, since a -graph is a regular graph with valency . If c
2 = + 1 and c
2 1, then is a Terwilliger graph, i.e., all the -graphs of are complete. In [11] we classified the Terwilliger 1-homogeneous graphs with c
2 2 and obtained that there are only three such examples. In this article we consider the case c
2 = + 2 3, i.e., the case when the -graphs of are the Cocktail Party graphs, and obtain that either = 0, = 2 or is one of the following graphs: (i) a Johnson graph J(2m, m) with m 2, (ii) a folded Johnson graph J¯(4m, 2m) with m 3, (iii) a halved m-cube with m 4, (iv) a folded halved (2m)-cube with m 5, (v) a Cocktail Party graph K
m × 2 with m 3, (vi) the Schläfli graph, (vii) the Gosset graph. 相似文献
10.
On a variational problem with lack of compactness: the topological effect of the critical points at infinity 总被引:5,自引:0,他引:5
Abbas Bahri Yanyan Li Olivier Rey 《Calculus of Variations and Partial Differential Equations》1995,3(1):67-93
We study the subcritical problemsP
:–u=u
p–,u>0 on;u=0 on , being a smooth and bounded domain in N,N–3,p+1=2N/N–2 the critical Sobolev exponent and >0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P0).
Résumé Nous étudions les problèmes sous-critiquesP :–u=u p–,u > 0 sur;u=0 sur –où est un domaine borné et régulier de N,N–3,p + 1=2N/N –2 est l'exposant critique de Sobolev, et >0 tend vers zéro, afin de calculer la différence de toplogie induite par les points critiques à l'infini entre les ensembles de niveau de la fonctionnelle correspondant au cas limite (P0).相似文献
11.
Donald I. Cartwright Anna Maria Mantero Tim Steger Anna Zappa 《Geometriae Dedicata》1993,47(2):167-223
If (P, L) is a projective plane and is a triangle presentation compatible with a point-line correspondence :P L, then gives rise to a group and a thick building of typeÃ
2 on the vertices of which acts simply transitively. We find all triangle presentations (up to natural equivalence) compatible with some point-line correspondence :P L, when (P, L) is the projective plane of orderq=2 orq=3. For some, but not all, of these , is isomorphic to the building associated withG=PGL(3,K) whereK is a local field with discrete valuation and residual field of orderq. We identify the for which this is the case, and in these cases, find embeddings of intoG. We also describe the arithmetic nature of these groups. 相似文献
12.
One investigates the scattering theory for the positive self-adjoint operatorH=–· acting in
with = × and a bounded open set in
n–1,n2. The real-valued function belongs toL
(), is bounded from below byc>0 and there exist real-valued functions
1 and
2 inL
() such that –
j
,j=1,2 is a short range perturbation of
j
when (–1)
j
x
n
+. One assumes
j
=
(j)
1R,j=1,2, with
(j)
L
bounded from below byc>0. One proves the existence and completeness of the generalized wave operators
j
±
=s –
j
e
–itHj
,j=1,2, withH
j
=–·
j
and
j
: equal to 1 if (–1)
j
x
n
>0 and to 0 if (–1)
j
x
n
<0. The ranges ofW
j
±
:=(
j
±
)* are characterized so that
W
1
±
=Ran and
. The scattering operator can then be defined. 相似文献
13.
Tomasz Rolski 《Probability Theory and Related Fields》1990,84(1):27-37
Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A
* and the Palm version A
0 corresponding to A
*. Let (T
i
,i) be the inter-point distance sequence in A and (T
i
0
,i) in A
0. We prove that forj, the sequence (T
i+j,i) converges in distribution to (T
i
0
,i). If the intensity function is periodic then the convergence is in variation. 相似文献
14.
P
(f) — , f L
p
- , k . f 02k–2 P
(f) 0. 相似文献
15.
B. Schultz-Heinecke 《Periodica Mathematica Hungarica》1989,20(2):115-145
For any algebraA let(A) be the set of partial automorphisms (isomorphisms between subalgebras). With the natural multiplication it is an inductive groupoid in the sense of Ehresmann.(A) is complete iff every subset of(A) which is compatible with the semi-ordering has an upper bound. The fact, whether(A) is complete or not, depends on the defining operations ofA. For every direct familyF = (, (A
)
,(), , of algebras such that all
,, with are one-to-one functions, the direct limit is complete iff all(A) are complete. We give some theorems on the decomposition of inductive groupoids, and employ them in proving the completeness of(A) to variousA.In particular, we obtain that, in case whenG is a finite group,(G) is complete iffG is either cyclic or direct product of a noncyclic group of order 4 and a cyclic group of odd order. For finite acyclic ringsR and finite fieldsK the inductive groupoids(R) and(K) are complete.Further we deal with the question, to what extent algebras are determined by their inductive groupoids. (An algebraA of a classS is defined by(A) iff, for any algebraB of the classS, isomorphism between(A) and(B) implies isomorphism betweenA andB.) Particular attention is paid to finite groups. In general, algebras of classesS are not defined within the classS by their inductive groupoids. 相似文献
16.
The non-commutative torus C
*(n,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C
*n/S, 1) for a totally skew multiplier 1 on n/S. D. Poguntke [9] proved that A
is stably isomorphic to C(S) C(*( Zn/S, 1) C(S) A Mkl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule. 相似文献
17.
M. F. Timan 《Analysis Mathematica》1978,4(1):75-82
N- (p, q) (1 p
N-, L p - L q -. , , , L L q - , , . 相似文献
18.
В. Ф. Гапошкин 《Analysis Mathematica》1985,11(3):193-199
(C, ). , . 0<<1. 1) - (
k
),
k
=a
k
, (C, ),
. 2)
, , (C, ) ;
k
= =¦a
k
¦. 相似文献
19.
Amos Nevo 《Geometriae Dedicata》2003,100(1):187-218
Let G denote a semisimple group, a discrete subgroup, B=G/P the Poisson boundary. Regarding invariants of discrete subgroups we prove, in particular, the following:(1) For any -quasi-invariant measure on B, and any probablity measure on , the norm of the operator () on L
2(B,) is equal to (), where is the unitary representation in L
2(X,), and is the regular representation of .(2) In particular this estimate holds when is Lebesgue measure on B, a Patterson–Sullivan measure, or a -stationary measure, and implies explicit lower bounds for the displacement and Margulis number of (w.r.t. a finite generating set), the dimension of the conformal density, the -entropy of the measure, and Lyapunov exponents of .(3) In particular, when G=PSL2() and is free, the new lower bound of the displacement is somewhat smaller than the Culler–Shalen bound (which requires an additional assumption) and is greater than the standard ball-packing bound.We also prove that ()=G() for any amenable action of G and L
1(G), and conversely, give a spectral criterion for amenability of an action of G under certain natural dynamical conditions. In addition, we establish a uniform lower bound for the -entropy of any measure quasi-invariant under the action of a group with property T, and use this fact to construct an interesting class of actions of such groups, related to 'virtual' maximal parabolic subgroups. Most of the results hold in fact in greater generality, and apply for instance when G is any semi-simple algebraic group, or when is any word-hyperbolic group, acting on their Poisson boundary, for example. 相似文献
20.
Since the genus of the modular curve X_1 (8) = _1 (8)
* is zero, we find a field generator j
1,8(z) = 3(2z)/3(4z) (3(z) :=
n
ein
2z
) such that the function field over X
1(8) is (j
1,8). We apply this modular function j
1,8 to the construction of some class fields over an imaginary quadratic field K, and compute the minimal polynomial of the singular value of the Hauptmodul N(j
1,8) of (j
1,8). 相似文献