首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
LetH be a separable infinite-dimensional complex Hilbert space. We prove that if : (H)(H) is a*-preserving ring homomorphism whose range contains a rank-one operator and an operator with dense range, then is an isometric linear or conjugate-linear algebra automorphism of (H). In particular, if the unilateral shift is contained in the range of a*-endomorphism of (H), then is bijective.Research partially supported by the Hungarian National Research Science Foundation, Operating Grant Number OTKA 1652 and K&H Bank Ltd., Universitas Foundation.  相似文献   

2.
For a bounded regular Jordan domain in R 2, we introduce and study a new class of functions K() related on its Green function G. We exploit the properties of this class to prove the existence and the uniqueness of a positive solution for the singular nonlinear elliptic equation u+(x,u)=0, in D(), with u=0 on and uC(), where is a nonnegative Borel measurable function in ×(0,) that belongs to a convex cone which contains, in particular, all functions (x,t)=q(x)t ,>0 with nonnegative functions qK(). Some estimates on the solution are also given.  相似文献   

3.
The (,d, d, – 1)-problem is that of finding large graphs with maximum degree and diameterd such that the subgraphs obtained by deleting any set of up to – 1 vertices have diameterd. In this paper, we deduce upper bounds on the order of such graphs and present some of the largest known ones. We argue that these graphs can be used to construct extremely "robust" networks, and explain why we require this robustness property when designing transputer networks for certain applications. In particular, we investigate the suitability of the odd graphO 4 as a topology for such networks.  相似文献   

4.
Summary This paper is concerned with the rate of convergence to zero of theL pmetrics np1p, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that the np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1p, p, np/np is universally bounded away from zero and infinity asn.  相似文献   

5.
We develop an iterated homology theory for simplicial complexes. Thistheory is a variation on one due to Kalai. For a simplicial complex of dimension d – 1, and each r = 0, ...,d, we define rth iterated homology groups of . When r = 0, this corresponds to ordinary homology. If is a cone over , then when r = 1, we get the homology of . If a simplicial complex is (nonpure) shellable, then its iterated Betti numbers give the restriction numbers, h k,j , of the shelling. Iterated Betti numbers are preserved by algebraic shifting, and may be interpreted combinatorially in terms of the algebraically shifted complex in several ways. In addition, the depth of a simplicial complex can be characterized in terms of its iterated Betti numbers.  相似文献   

6.
For a complete manifold M with constant negative curvature, weprove that the rough Laplacian R defines topological isomorphisms in the scale of Sobolev spaces H p s (M) ofp-forms for all p, 0 < p< n. For the de Rham Laplacian and M= n , the Poincaréhyperbolic space, this is shown too for 0 pn,pn/2, p (n± 1)/2.  相似文献   

7.
LetA andA+A be Hermitian positive definite matrices. Suppose thatA=LDL H and (A+A)=(L+L)(D+D)(L+L)H are theLDL H decompositons ofA andA+A, respectively. In this paper upper bounds on |D| F and |L| F are presented. Moreover, perturbation bounds are given for theLU decomposition of a complexn ×n matrix.  相似文献   

8.
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   

9.
The discriminant function is a certain rigid analytic modularform defined on Drinfelds upper half-plane . Its absolutevalue may be considered as a function on theassociated Bruhat–Tits tree T. We compare log with the conditionally convergent complex-valued Eisenstein series Edefined on T and thereby obtain results about the growth of and of some related modular forms. We further determine to what extent roots may be extracted of (z)/(nz),regarded as a holomorphic function on . In some cases, this enables us to calculate cuspidal divisor class groups of modular curves.  相似文献   

10.
Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector 0 H( 0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0) 0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them.  相似文献   

11.
(, ) — R m ×R n . f R m ×R n fp,q, f L p (R m) x y, Lq(Rn). ׃ q,r cƒ p,r , ׃ R m ×R n , , , q r . , ( ¦¦) K 0 (y); p, g r , K 0.  相似文献   

12.
The notion pasting sum (P i , i ) of two R 2-planes (or Salzmann planes) (P i , i ) is developed. Necessary and sufficient conditions for it to be an R 2-plane again are given. The notion is applied to classify all flat projective planes whose collineation group contains a sub-group with (isomorphism type of , fixed element configuration)=(2, x).  相似文献   

13.
On the distribution of square-full and cube-full integers   总被引:1,自引:0,他引:1  
LetN r (x) be the number ofr-full integers x and let r (x) be the error term in the asymptotic formula forN r (x). Under Riemann's hypothesis, we prove the estimates 2(x)x1/7+, 3(x)x97/804+(>0), which improve those of Cao and Nowak. We also investigate the distribution ofr-full andl-free numbers in short intervals (r=2,3). Our results sharpen Krätzel's estimates.  相似文献   

14.
Let m , 0 m+ in Kato's class. We investigate the spectral function s( + m) where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists a unique 1 > 0 such that s( + 1m) = 0. Under suitable conditions on m+ it follows that 0 is an eigenvalue of + 1m with positive eigenfunction.  相似文献   

15.
Let s 0 and let + s be the set of functions x defined on a finite interval I and such that, for all collections of s + 1 pairwise different points t 0,..., t s I, the corresponding divided differences [x; t 0,...,t s ] of order s are nonnegative. Let + s B p + s B p, 1 p where B p is a unit ball in the space L p, and let + s L q + s L q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]>, where M n is the collection of all affine linear manifolds M n in L q such that dim M n n and M n + s L q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004.  相似文献   

16.
The paper considers a real polynomial p(x)=0+1x+...+nxn(0 > 0) for which there hold inequalities 1>0, 3>0, ... or 2>0, 4>0, ..., where 1, 2, ..., jn are the Hurwitz determinants for polynomial p(x). It is proven that polynomial p(x) can have, in the right half-plane, only real roots, where the quantity of positive roots of polynomial p(x) equals the quantity of changes of sign in the system of coefficients a0, a2, ..., an–2, an, when n is even, and 0, a2,..., an–1, an, when n is odd. From the proven theorem, in particular, there follows the Liénard and Shepherd criterion of stability.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 13–21, July, 1977.  相似文献   

17.
Let denote a bipartite distance-regular graph with diameter D 3 and valency k 3. Let 0 > 1 ··· > D denote the eigenvalues of and let q h ij (0 h, i, j D) denote the Krein parameters of . Pick an integer h (1 h D – 1). The representation diagram = h is an undirected graph with vertices 0,1,...,D. For 0 i, j D, vertices i, j are adjacent in whenever i j and q h ij 0. It turns out that in , the vertex 0 is adjacent to h and no other vertices. Similarly, the vertex D is adjacent to D – h and no other vertices. We call 0, D the trivial vertices of . Let l denote a vertex of . It turns out that l is adjacent to at least one vertex of . We say l is a leaf whenever l is adjacent to exactly one vertex of . We show has a nontrivial leaf if and only if is the disjoint union of two paths.  相似文献   

18.
The essence of this article lies in a demonstration of the fact that for some random search methods (r.s.m.) of global optimization, the number of the objective function evaluations required to reach a given accuracy may have very slow (logarithmic) growth to infinity as the accuracy tends to zero. Several inequalities of this kind are derived for some typical Markovian monotone r.s.m. in metric spaces including thed-dimensional Euclidean space d and its compact subsets. In the compact case, one of the main results may be briefly outlined as a constructive theorem of existence: if is a first moment of approaching a good subset of-neighbourhood ofx 0=arg maxf by some random search sequence (r.s.s.), then we may choose parameters of this r.s.s. in such a way that E c(f) In2 . Certainly, some restrictions on metric space and functionf are required.  相似文献   

19.
Ruth Haas 《Acta Appl Math》1998,51(2):113-122
Let Sr() be the module of all splines of smoothness r on the rectilinear partition which subdivides some domain D. Further, let Sr() be the module of all splines of smoothness r on which also subdivides D, where is a finer subdivision of . We study the relationship between a generating set of Sr() and a generating set for Sr(). This paper gives an algorithm for extending a generating set for Sr() to one for for Sr(). This method is built on algebraic properties of splines and the Gröbner Basis Algorithm.  相似文献   

20.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号