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1.
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   

2.
Let B be a domain in the complex plane, let pn(z) and Pn(z) be polynomials of degree n where the zeros of Pn(z) lie in , let(z) be a finite function,(z) 0, z . We consider the problem of estimating from above the functions L[pn(z)]=(z)pn(z) – wpn(z), z , if ¦pn(z)¦ ¦Pn(z)¦ for zB. Under some very general conditions on B, z, (z), and w we prove the inequality ¦L[pn(z)]¦ ¦L[Pn(z)]¦.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 431–440, April, 1968.  相似文献   

3.
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   

4.
A new criterion of solvability of the interpolation problem f( n )=bn in the class of functions f, analytic in the right half-plane and such that there exists c 1(0;+) such that |f(z)|c 1exp((c1|z|)) for all z , where is a positive increasing continuous differentiable function on [0;+), for which (t)+ as t+ and there exists c 2(0;+) such that
for all t 1 is described.  相似文献   

5.
Let {S d (n)} n0 be the simple random walk inZ d , and (d)(a,b)={S d (n)Z d :anb}. Supposef(n) is an integer-valued function and increases to infinity asn tends to infinity, andE n (d) ={(d)(0,n)(d)(n+f(n),)}. In this paper, a necessary and sufficient condition to ensureP(E n d) ,i.o.)=0, or 1 is derived ford=3, 4. This problem was first studied by P. Erdös and S.J. Taylor.This work is partly supported by the National Natural Sciences Foundation of China.  相似文献   

6.
Summary We study integral functionals of the formF(u, )= f(u)dx, defined foru C1(;R k), R n . The functionf is assumed to be polyconvex and to satisfy the inequalityf(A) c0¦(A)¦ for a suitable constant c0 > 0, where (A) is then-vector whose components are the determinants of all minors of thek×n matrixA. We prove thatF is lower semicontinuous onC 1(;R k) with respect to the strong topology ofL 1(;R k). Then we consider the relaxed functional , defined as the greatest lower semicontinuous functional onL 1(;R k ) which is less than or equal toF on C1(;R k). For everyu BV(;R k) we prove that (u,) f(u)dx+c0¦Dsu¦(), whereDu=u dx+Dsu is the Lebesgue decomposition of the Radon measureDu. Moreover, under suitable growth conditions onf, we show that (u,)= f(u)dx for everyu W1,p(;R k), withp min{n,k}. We prove also that the functional (u, ) can not be represented by an inte- gral for an arbitrary functionu BVloc(R n;R k). In fact, two examples show that, in general, the set function (u, ) is not subadditive whenu BVloc(R n;R k), even ifu W loc 1,p (R n;R k) for everyp < min{n,k}. Finally, we examine in detail the properties of the functionsu BV(;R k) such that (u, )= f(u)dx, particularly in the model casef(A)=¦(A)¦.  相似文献   

7.
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 1x=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   

8.
We prove that, if f(x) L p [0,1], 1 < p < , f(x) 0, x [0,1], f 0, then there is a polynomial p(x) + n such that f - 1/p LP C(p)(f,n -1/2) LP where + n indicates the set of all polynomials of degree n with positive coeficients (see the definition (1) in the text).  相似文献   

9.
In his Inventiones papers in 1995 and 1998, Borcherds constructed holomorphic automorphic forms (f) with product expansions on bounded domains D associated to rational quadratic spaces V of signature (n2), starting from vector valued modular forms f of weight 1–n2 for SL2(Z) which are allowed to have poles at the cusp and whose nonpositive Fourier coefficients are integers c (–m), m0. In this paper, we use the Siegel–Weil formula to give an explicit formula for the integral ((f)) of –log||(f)||2 over X=\D, where || ||2 is the Petersson norm. This integral is given by a sum for m0 of quantities c (–m)(m), where (m) is the limit as Im() of the mth Fourier coefficient of the second term in the Laurent expansion at s=n2 of a certain Eisenstein series E(s) of weight (n2)+1 attached to V. The possible role played by the quantity ((f)) in the Arakelov theory of the divisors Z (m) on X is explained in the last section.  相似文献   

10.
Let(n) be the least integer such thatn may be represented in the formn=x 1 2 +x 2 3 +...+x (n) (n)+1 wherex 1,x 2, ...,x (n) are natural numbers. We computed(n) forn 250 000 and found that(n) 5 for all thesen exceptn=56, 160 for which(n)=6. Also(n) 4 for 41542<n<=250 000.  相似文献   

11.
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   

12.
On the space, , of Laurent polynomials (L-polynomials) we consider a linear functional which is positive definite on (0, ) and is defined in terms of a given bisequence, { k } . Two sequences of orthogonal L-polynomials, {Q n (z) 0 and , are constructed which span in the order {1,z –1,z,z –2,z 2,...} and {1,z,z –1,z 2,z –2,...} respectively. Associated sequences of L-polynomials {P n (z) 0 , and are introduced and we define rational functions , wherew is a fixed positive number. The partial fraction decomposition and integral representation of,M n (z, w) are given and correspondence of {M n (z, w)} is discussed. We get additional solutions to the strong Stieltjes moment problem from subsequences of {M n (z, w)}. In particular when { k } is a log-normal bisequence, {M 2n (z, w)} and {M 2n+1 (z, w)} yield such solutions.Research supported in part by the National Science Foundation under Grant DMS-9103141.  相似文献   

13.
LetG n ()be the semi-direct product of the symmetric groupS n by the Steinberg groupSt n ()of a ringWe first prove thatG n ()has a Coxeter-type presentation. The canonical morphism St n () GL n ()extends to a group homo Gn() GL n ()We next determine the kernel of for n = We also give an expression for the generator of the algebraic K group K 2(Z)of the integers in terms of permutation matrices.  相似文献   

14.
In the present work we study the existence and monotonicity properties of the imaginary zeros of the mixed Bessel functionM v(z)=(z2+)Jv(z)+zJv(z). Such a function includes as particular cases the functionsJ v(z)(==0), Jv(z)(=–v2,=1)x andH v(z)=Jv(z)+zJv(z), whereJ v(z) is the Bessel function of the first kind and of orderv>–1 andJ v(z), Jv(z) are the first two derivatives ofJ v(z). Upper and lower bounds found for the imaginary zeros of the functionsJ v(z), Jv(z) andH v(z) improve previously known bounds.
Zusammenfassung Dieser Artikel betrifft die Existenz und Monotonie von Eigenschaften imaginärer Nullen der gemischten BesselfunktionM v(z)=(z2+)Jv(z)+zJv(z). Eine solche Funktion enthält als Spezialfall die FunktionenJ v(z)(==0), Jv(z)(=–v2,=1) undH v(z)=Jv(z)+zJv(z), woJ v(z)die Besselfunktion von erster Art und Ordnungv>–1 andJ v(z), Jv(z) sind die erste und zweite Ableitung vonJ v(z). Untere und obere Schranken, die für die imaginären Nullen der FunktionenJ v(z), Jv(z) undH v(z) gefunden wurden, verbessern früher bekannte Resultate.
  相似文献   

15.
We obtain asymptotic estimates of meromorphic solutions to the differential equationP n (z, , )=P n–1 (z, , ,..., (m) ) in the angular domain P={z: arg z · }. Here Pn(z, w, w) is a polynomial in all variables, and of degree n with respect to w and w; Pn–1(z, w, w, ..., w(m)) is a polynomial in all variables, and of degree n –1 with respect to w, w, ..., w(m) In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 514–523, April, 1992.  相似文献   

16.
C. Hightower found two infinite sequences of gaps in the Markov spectrum, ( n , n ) and ( n , n ) with n and n both Markov elements, converging to . This paper exhibits Markov elements n * and n * such that, for alln 1, ( n * , n ) and ( n n * ) are gaps in the Markov spectrum. Other results include showing that, for alln 1, n is completely isolated, while the other endpoints of the gaps are limit points in the Markov spectrum.  相似文献   

17.
LetG(n) be the set of all nonoriented graphs with n enumerated points without loops or multiple lines, and let vk(G) be the number of mutually nonisomorphic k-point subgraphs of G G(n). It is proved that at least |G(n)| (1–1/n) graphs G G(n) possess the following properties: a) for any k [6log2n], where c=–c log2c–(1–c)×log2(1–c) and c>1/2, we havev k(G) > C n k (1–1/n2); b) for any k [cn + 5 log2n] we havev k(G) = C n k . Hence almost all graphs G G(n) containv(G) 2n pairwise nonisomorphic subgraphs.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 263–273, March, 1971.  相似文献   

18.
LetA be a subset of a balayage space (X,W) and a measure onX. It is shown that for every sequence n of measures such that limnn and limn n A = the limit measure is of the formf+[(1-f)]A for some (unique) Borel function 0f1Cb(A). Furthermore, conditions are given such that any such functionf occurs.  相似文献   

19.
Summary If 1, ... , are non-atomic probability measures on the same measurable space (S, ), then there is an -measurable partition {A i } i = 1 n of S so that i (A i )(n – 1 + m)–1 for all i=1, ..., n, where is the total mass of the largest measure dominated by each of the i S; moreover, this bound is attained for all n1 and all m in [0, 1]. This result is an analog of the bound (n+1-M) -1of Elton et al. [5] based on the mass M of the supremum of the measures; each gives a quantative generalization of a well-known cake-cutting inequality of Urbanik [10] and of Dubins and Spanier [2].Research partly supported by NSF Grants DMS-84-01604 and DMS-86-01608  相似文献   

20.
For any sequence of numbers n0, n=1 a n 2 =, a uniformly bounded orthonormal system of continuous functions n(x) which is complete in L2 (0, 1), and a sequence of numbers bn(0< bnan) are constructed such that n=1 Emphasis> bnn(x)= everywhere on (0, 1).Translated from Matematicheskie Zametki, Vol. 11, No. 5, pp. 499–508, May, 1972.  相似文献   

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