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1.
In the present note a theorem about strong suitability of the space of algebraic polynomials of degree n in C[a,b] (Theorem A in [1]) is generalized to the space of spline polynomials [a, b ]n, k (n2, 0) in C[a, b]. Namely, it is shown that the following theorem is valid: for arbitrary numbers 0, 1, ..., n+k, satisfying the conditions (ii–1) (i+1{ i< 0(i=1, ..., n +k–1), there is a unique polynomials n,k (t) [a, b ]/n,k and pointsa=0,<1<...< n+k– 1< n+k = b (11 <n, ..., kk<n+k–1), such that sn,k(i) = i(i=0, ..., n + k), sn,k(i)=0 (i=1, ..., n + k–1).Translated from Matematicheskii Zametki, Vol. 11, No. 3, pp. 251–258, March, 1972.  相似文献   

2.
Let {X k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X k , 1 k n} and satisfying a k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max1 m n k=1 m k X k > x) P (sum k=1 n k X k > x) sum k=1 n P ( k X k > x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence { k , 1 k n}. An application to ruin theory is proposed.  相似文献   

3.
In this paper, we study the Hodge decompositions ofK-theory and cyclic homology induced by the operations k and k , and in particular the decomposition of the Loday symbols x,y, ...z. Except in special cases, these Loday symbols do not have pure Hodge index. InK n (A) they can project into every componentK n (i) for 2in, and the projection of the Loday symbol x,y, ...,z intoK n (n) is a multiple of the generalized Dennis-Stein symbol x,y, ...,z. Our calculations disprove conjectures of Beilinson and Soulé inK-theory, and of Gerstenhaber and Schack in Hochschild homology.Partially supported by National Security Agency grant MDA904-90-H-4019.Partially supported by National Science Foundation grant DMS-8803497.  相似文献   

4.
Let T n be an n×n unreduced symmetric tridiagonal matrix with eigenvalues 1<2<< n and W k is an (n–1)×(n–1) submatrix by deleting the kth row and the kth column from T n , k=1,2,...,n. Let 12 n–1 be the eigenvalues of W k . It is proved that if W k has no multiple eigenvalue, then 1<1<2<2<< n–1< n–1< n ; otherwise if i = i+1 is a multiple eigenvalue of W k , then the above relationship still holds except that the inequality i < i+1< i+1 is replaced by i = i+1= i+1.  相似文献   

5.
A survey of known results and additional new ones on Knaster's problem: on the standard sphere Sn–1Rn find configurations of points A1, , Ak, such that for any continuous map fSn–1Rm one can find a rotation a of the sphere Sn–1 such that f(a(A1)==f(a(Ak)) and some problems closely connected with it. We study the connection of Knaster's problem with equivariant mappings, with Dvoretsky's theorem on the existence of an almost spherical section of a multidimensional convex body, and we also study the set {a S0(n)f(a(A1))==f(a(Ak))} of solutions of Knaster's problem for a fixed configuration of points A1, , AkSn–1 and a map fSn–1Rm in general position. Unsolved problems are posed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 169–178, 1987.  相似文献   

6.
Let A n, i be a triangular array of sign-symmetric exchangeable random variables satisfying nE(A 2 n, i )1, nE(A 4 n, i )0, n 2 E(A 2 n, 1 A 2 n, 2)1. We show that [nt] i=1 A ni, 0t1, converges to Brownian motion. This is applied to show that if A is chosen from the uniform distribution on the orthogonal group O n and X n(t)=[nt] i=1 A ii, then X n converges to Brownian motion. Similar results hold for the unitary group.  相似文献   

7.
Anthony Bak 《K-Theory》1991,4(4):363-397
A functorial filtration GL n =S–1L n S0L n S i L n E n of the general linear group GL n, n 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S–1 L n (A)/S0L n (A) is abelian, that S0L n (A) S1L n (A) is a descending central series, and that S i L n (A) = E n(A) whenever i the Bass-Serre dimension of A. In particular, the K-functors k 1 S i L n =S i L n /E n are nilpotent for all i 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S i L n (A)/S i+1 L n (A)S i L n+ 1(A)/S i+1 L n + 1 (A) is injective whenever n i + 3, so that one has stability results without stability conditions, and if A is commutative then S0L n (A) agrees with the special linear group SL n (A), so that the functor S0L n generalizes the functor SL n to noncommutative rings. Applying the above to subgroups H of GL n (A), which are normalized by E n(A), one obtains that each is contained in a sandwich GL n (A, ) H E n(A, ) for a unique two-sided ideal of A and there is a descending S0L n (A)-central series GL n (A, ) S0L n (A, ) S1L n (A, ) S i L n (A, ) E n(A, ) such that S i L n (A, )=E n(A, ) whenever i Bass-Serre dimension of A.Dedicated to Alexander Grothendieck on his sixtieth birthday  相似文献   

8.
Let 1, 2, ... be a sequence of independent identically distributed random variables with zero means. We consider the functional n = k=o n (S k ) where S1=0, Sk= i=1 k i (k1) and(x)=1 for x0,(x) = 0 for x<0. It is readily seen that n is the time spent by the random walk Sn, n0, on the positive semi-axis after n steps. For the simplest walk the asymptotics of the distribution P (n = k) for n and k, as well as for k = O(n) and k/n<1, was studied in [1]. In this paper we obtain the asymptotic expansions in powers of n–1 of the probabilities P(hn = nx) and P(nx1 n nx2) for 0<1, x = k/n 2<1, 0<1x122<1.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 613–620, April, 1974.The author wishes to thank B. A. Rogozin for valuable discussions in the course of his work.  相似文献   

9.
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT L/F ()=1 andTr L/F (i)=i fori=2,...n.  相似文献   

10.
For the nth order nonlinear differential equation y (n)(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y (j)(ai) = 0,1 i k, 0 j n i - 1, 0 =a 1 < a 2 < < a k = 1, and i=1 k n i =n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone.  相似文献   

11.
Let {X i, 1in} be a negatively associated sequence, and let {X* i , 1in} be a sequence of independent random variables such that X* i and X i have the same distribution for each i=1, 2,..., n. It is shown in this paper that Ef( n i=1 X i)Ef( n i=1 X* i ) for any convex function f on R 1 and that Ef(max1kn n i=k X i)Ef(max1kn k i=1 X* i ) for any increasing convex function. Hence, most of the well-known inequalities, such as the Rosenthal maximal inequality and the Kolmogorov exponential inequality, remain true for negatively associated random variables. In particular, the comparison theorem on moment inequalities between negatively associated and independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population.  相似文献   

12.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K 1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K 1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism.  相似文献   

13.
Summary In this paper we search, from the orthogonal polynomial theory, for conditions which allow to obtain cubature formulae on compacts of n , with weight function, and which are exact on the spaceR( k 1, k2, ..., kn) of all polynomials of degree k i respectively to each variablex i , 1in.  相似文献   

14.
The imaginary powersA it of a closed linear operatorA, with inverse, in a Banach spaceX are considered as aC 0-group {exp(itlogA);t R} of bounded linear operators onX, with generatori logA. Here logA is defined as the closure of log(1+A) – log(1+A –1). LetA be a linearm-sectorial operator of typeS(tan ), 0(/2), in a Hilbert spaceX. That is, |Im(Au, u)| (tan )Re(Au, u) foru D(A). Then ±ilog(1+A) ism-accretive inX andilog(1+A) is the generator of aC 0-group {(1+A) it ;t R} of bounded imaginary powers, satisfying the estimate (1+A) it exp(|t|),t R. In particular, ifA is invertible, then ±ilogA ism-accretive inX, where logA is exactly given by logA=log(1+A)–log(1+A –1), and {A it;t R} forms aC 0-group onX, with the estimate A it exp(|t|),t R. This yields a slight improvement of the Heinz-Kato inequality.  相似文献   

15.
In this paper we introduce and study a cohomology theory {H n (–,A)} for simplicial sets with coefficients in symmetric categorical groups A. We associate to a symmetric categorical group A a sequence of simplicial sets {K(A,n)} n0, which allows us to give a representation theorem for our cohomology. Moreover, we prove that for any n3, the functor K(–,n) is right adjoint to the functor n , where n (X ) is defined as the fundamental groupoid of the n-loop complex n (X ). Using this adjunction, we give another proof of how symmetric categorical groups model all homotopy types of spaces Y with i (Y)=0 for all in,n+1 and n3; and also we obtain a classification theorem for those spaces: [–,Y]H n (–, n (Y)).  相似文献   

16.
Letk be a field and an abstract simplicial complex with vertex set . In this article we study the structure of the Ext modules Ext a i (A/m (l ,k[]) of the Stanley-Reisner ringk[] whereA=k[x 1,...,x n ] andm l =(x l 1 ,...,x l n ). Using this structure theorem we give a characterization of Buchsbaumness ofk[] by means of the length of the modules Ext A i (A/m l ,k[]). That isk[] is Buchsbaum if and only if for allik[], the length of the modules Ext A i (A/m l ,k[]) is independent ofl.  相似文献   

17.
Summary In this paper, we study the convergence of formal power series solutions of functional equations of the formP k(x)([k](x))=(x), where [k] (x) denotes thek-th iterate of the function.We obtain results similar to the results of Malgrange and Ramis for formal solutions of differential equations: if(0) = 0, and(0) =q is a nonzero complex number with absolute value less than one then, if(x)=a(n)x n is a divergent solution, there exists a positive real numbers such that the power seriesa(n)q sn(n+1)2 x n has a finite and nonzero radius of convergence.
  相似文献   

18.
Yair Caro 《Order》1996,13(1):33-39
Bialostocki proposed the following problem: Let nk2 be integers such that k|n. Let p(n, k) denote the least positive integer having the property that for every poset P, |P|p(n, k) and every Z k -coloring f: P Z k there exists either a chain or an antichain A, |A|=n and aA f(a) 0 (modk). Estimate p(n, k). We prove that there exists a constant c(k), depends only on k, such that (n+k–2)2c(k) p(n, k) (n+k–2)2+1. Another problem considered here is a 2-dimensional form of the monotone sequence theorem of Erdös and Szekeres. We prove that there exists a least positive integer f(n) such that every integral square matrix A of order f(n) contains a square submatrix B of order n, with all rows monotone sequences in the same direction and all columns monotone sequences in the same direction (direction means increasing or decreasing).  相似文献   

19.
Denoting by dimA the dimension of the affine hull of the setA, we prove that if {K i:i T} and {K i j :i T} are two finite families of convex sets inR n and if dim {K i :i S} = dim {K i j :i S}for eachS T such that|S| n + 1 then dim {K i :i T} = dim {K i : {i T}}.  相似文献   

20.
For integrals –1 1 w(x)f(x)dx with and with analytic integrands, we consider the determination of optimal abscissasx i o and weightsA i o , for a fixedn, which minimize the errorE n (f)= –1 1 w(x)f(x)dx i =1n A i f(x i ) over an appropriate Hilbert spaceH 2(E ; w(z)) of analytic functions. Simultaneously, we consider the simpler problem of determining intermediate-optimal weightsA i *, corresponding to (preassigned) Gaussian abscissasx i G , which minimize the quadrature error. For eachw(x), the intermediate-optimal weightsA i * are obtained explicitly, and these come out proportional to the corresponding Gaussian weightsA i G . In each case,A i G =A i *+O( –4n ), . For , a complete explicit solution for optimal abscissas and weights is given; in fact, the set {x i G ,A i *;i=1,...,n} to provides the optimal abscissas and weights. For otherw(x), we study the closeness of the set {x i G ,A i *;i=1,...,n} to the optimal solution {x i o ,A i o ;i=1,...,n} in terms of n (), the maximum absolute remainder in the second set ofn normal equations. In each case, n () is, at least, of the order of –4n for large.  相似文献   

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