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1.
Carbery Anthony; Gorges Dirk; Marletta Gianfranco; Thiele Christoph 《Bulletin London Mathematical Society》2003,35(2):225-228
Suppose that R goes to infinity through a second-order lacunaryset. Let SR denote the Rth spherical partial inverse Fourierintegral on Rd. Then SRf converges almost everywhere to f, providedthat f satisfies
. 2000 Mathematics SubjectClassification 42B15, 42B25, 42B08. 相似文献
2.
Auslander-Regular Algebras and Maximal Orders 总被引:1,自引:0,他引:1
Let R be an Auslander-regular, Cohen-Macaulay, Noetherian ringthat is stably free. Then, we prove that R is a domain and amaximal order in its division ring of fractions. In particular,this applies to the Sklyanin algebra S and shows that, whenS satisfies a polynomial identity, it is actually a finite moduleover its centre. 相似文献
3.
An additive functor from the category of flat right R-modulesto the category of abelian groups is continuous if it is isomorphicto a functor of the form–R M, where M is a left R-module.It is shown that for any simple subfunctor A of– M thereis a unique indecomposable flat cotorsion module UR for whichA(U)0. It is also proved that every subfunctor of a continuousfunctor contains a simple subfunctor. This implies that everyflat right R-module may be purely embedded into a product ofindecomposable flat cotorsion modules. If CE(R) is the cotorsion envelope of RR and S= End;R CE(R),then a local ring monomorphism is constructed from R/J(R) toS/J(S). This local morphism of rings is used to associate asemiperfect ring to any semilocal ring. It also proved thatif R is a semilocal ring and M a simple left R-module, thenthe functor–R M on the category of flat right R-modulesis uniform, and therefore contains a unique simple subfunctor. 相似文献
4.
A noncommutative version of the Hilbert basis theorem is usedto show that certain R-symmetric algebras SR(V) are Noetherian.This result applies in particular to the coordinate ring ofquantum matrices AR(V) associated with an R-matrix R operatingon the tensor square of a vector space V, to show that, undera natural set of hypotheses on R, the algebra AR(V) is Noetherianand its augmentation ideal has a polynormal set of generators.As a corollary we deduce that these properties hold for thegeneric quantized function algebras Rq[G] over any field ofcharacteristic zero, for G an arbitrary connected, simply connected,semisimple group over C. That Rq[G] is Noetherian recovers aresult due to Joseph [10], with a different proof.1991 MathematicsSubject Classification 17B37, 16P40. 相似文献
5.
It is shown for a closed connected nonconvex and locally compactsubset S of a real normed linear space that ker S = {conv Sz: z D reg S}, where reg S denotes the set of regular pointsof S, D is a relatively open subset of S containing the setlnc S of local nonconvexity points of S, and Sz = {s S : zis visible from s via S}. An analogous intersection formula,with the set sph S of spherical points of S in place of regS, is shown to hold for a closed connected nonconvex set S ina real Banach space which is uniformly convex and uniformlysmooth. A routine procedure then leads to a Krasnosel'skii-typecharacterization of the dimension of the kernel of a closedconnected nonconvex subset S of Rd with lnc S bounded. Thisimproves a recent result by removing the hypothesis of compactnessof S and settles an open problem. 相似文献
6.
The relationship between the accuracy and stability of semi-discretizedfinite-difference schemes for the advection equation ut = uxis analysed. Given the scheme of accuracy p we establish that,subject to stability, p min {r+s+R+S, 2(r+R+1), 2(s+S)}. This is done by using the theory of order stars. Furthermore,we find stable methods which attain this bound for various choicesof r, s, R and S. 相似文献
7.
Let MS be the universal maximal operator over unit vectors ofarbitrary directions. This operator is not bounded in L2(R2).We consider a sequence of operators over sets of finite equidistributeddirections converging to MS. We provide a new proof of N. Katz'sbound for such operators. As a corollary, we deduce that MSis bounded from some subsets of L2 to L2. These subsets arecomposed of positive functions whose Fourier transforms havea logarithmic decay or which are supported on a disc. 1991 MathematicsSubject Classification 42B25. 相似文献
8.
The existence of an asymptotic average of linking numbers ofperiodic orbits of a basic set of an Axiom A flow in S3 or R3is proved. 相似文献
9.
Consider the group scheme where R is an arbitrary commutative ring with 1 0 and a unitx R* acts on R by multiplication. We will study the finiteness properties of subgroups of G(OS)where OS is an S-arithmetic subring of a global function field.The subgroups we are interested in are of the form where Q is a subgroup of OS*. The finiteness propertiesof these metabelian groups can be expressed in terms of the-invariant due to R. Bieri and R. Strebel. Theorem A. Let S be a finite set of places of a global functionfield (regarded as normalized discrete valuations) and OS thecorresponding S-arithmetic ring. Let Q be a subgroup of OS*.Then Q is finitely generated and for all integers n 1 the followingare equivalent:
- (1) OS Q is of type FPn;
- (2) OS is n-tameas a ZQ-module;
- (3) each p S restricts to a non-trivial homomorphism and the set is n-tame.
- (2) OS is n-tameas a ZQ-module;
- (1) the group OS Q is not of type FPr+1};
- (2) if Qhas maximum rank r = |S| 1 then the group OS Q is oftype FPr.
10.
The purpose of this note is to establish a new version of thelocal Steiner formula and to give an application to convex bodiesof constant width. This variant of the Steiner formula generalizesresults of Hann [3] and Hug [6], who use much less elementarytechniques than the methods of this paper. In fact, Hann askedfor a simpler proof of these results [4, Problem 2, p. 900].We remark that our formula can be considered as a Euclideananalogue of a spherical result proved in [2, p. 46], and thatour method can also be applied in hyperbolic space. For some remarks on related formulas in certain two-dimensionalMinkowski spaces, see Hann [5, p. 363]. For further information about the notions used below, we referto Schneider's book [9]. Let Kn be the set of all convex bodiesin Euclidean space Rn, that is, the set of all compact, convex,non-empty subsets of Rn. Let Sn1 be the unit sphere.For KKn, let NorK be the set of all support elements of K, thatis, the pairs (x, u)RnxSn1 such that x is a boundarypoint of K and u is an outer unit normal vector of K at thepoint x. The support measures (or generalized curvature measures)of K, denoted by 0(K.), ..., n1(K.), are the unique Borelmeasures on RnxSn1 that are concentrated on NorK andsatisfy [formula] for all integrable functions f:RnR; here denotes the Lebesguemeasure on Rn. Equation (1), which is a consequence and a slightgeneralization of Theorem 4.2.1 in Schneider [9], is calledthe local Steiner formula. Our main result is the following.1991 Mathematics Subject Classification 52A20, 52A38, 52A55. 相似文献
11.
We exhibit closed manifolds M covered by S2n1 x Rk forall n 2 and for sufficiently large k, with fundamental groupsof infinite virtual cohomological dimension. These examplesare based on results of Raghunathan on lattices in covers ofspin and symplectic groups, and address a problem first raisedby Wall. 相似文献
12.
On the number of homotopy types of fibres of a definable map 总被引:1,自引:0,他引:1
In this paper we prove a single exponential upper bound on thenumber of possible homotopy types of the fibres of a Pfaffianmap in terms of the format of its graph. In particular, we showthat if a semi-algebraic set SRm+n, where R is a real closedfield, is defined by a Boolean formula with s polynomials ofdegree less than d, and : Rm+nRn is the projection on a subspace,then the number of different homotopy types of fibres of doesnot exceed s2(m+1)n(2m nd)O(nm). As applications of our mainresults we prove single exponential bounds on the number ofhomotopy types of semi-algebraic sets defined by fewnomials,and by polynomials with bounded additive complexity. We alsoprove single exponential upper bounds on the radii of ballsguaranteeing local contractibility for semi-algebraic sets definedby polynomials with integer coefficients. 相似文献
13.
Bihermitian Structures on Complex Surfaces 总被引:2,自引:0,他引:2
Apostolov V.; Gauduchon P.; Grantcharov G. 《Proceedings London Mathematical Society》1999,79(2):414-428
Bihermitian complex surfaces are oriented conformal four-manifoldsadmitting two independent compatible complex structures. Non-anti-self-dualbihermitian structures on R4 and the four-dimensional torusT4 have recently been discovered by P. Kobak. We show that anoriented compact 4-manifold, admitting a non-anti-self-dualbihermitian structure, is a torus or K3 surface in the stronglybihermitian case (when the two complex structures are independentat each point) or, otherwise, must be obtained from the complexprojective plane or a minimal ruled surface of genus less than2 by blowing up points along some anti-canonical divisor (butthe actual existence of bihermitian structures in the lattercase is still an open question). The paper includes a generalmethod for constructing non-anti-self-dual bihermitian structureson tori, K3 surfaces and S1 x S3. Further properties of compactbihermitian surfaces are also investigated. 1991 MathematicsSubject Classification: 53C12, 53C55, 32J15. 相似文献
14.
Shapiro's cyclic sum is defined by ,
If K is the cone in Rn of points withnon-negative coordinates, it is shown that the minimum of Ein K is a fixed point of T2, where T is the non-linear operatordefined by (Tx)i = xni+1/(xni+2 + xni+3)2for i = 1,2,...,n. It is conjectured that Tx = Skx, where Sis the shift operator in Rn, and a proof is given under someadditional hypotheses. One of the consequences is a simple proofthat at the minimum point, ai(x) = ani+1k(x) fori = 1,2,...,n. 相似文献
15.
Stable Jacobson Radicals and Semiprime Smash Products 总被引:1,自引:0,他引:1
We prove that if H is a finite-dimensional semisimple Hopf algebraacting on a PI-algebra R of characteristic 0, and R is eitheraffine or algebraic over k, then the Jacobson radical of R isH-stable. Under the same hypotheses, we show that the smashproduct algebra R#H is semiprimitive provided that R is H-semiprime.More generally we show that the finite Jacobsonradical is H-stable, and that R#H is semiprimitive providedthat R is H-semiprimitive and all irreducible representationsof R are finite-dimensional. We also consider R#H when R isan FCR-algebra. Finally, we prove a general relationship betweenstability of the radical and semiprimeness of R#H; in particularif for a given H, any action of H stabilizes the Jacobson radical,then also any action of H stabilizes the prime radical. 2000Mathematics Subject Classification 16W30, 16N20, 16R99, 16S40. 相似文献
16.
We sharpen a recent result of Paternain and Petean by showingthat a closed 4-manifold which admits a Riemannian metric withzero topological entropy and infinite fundamental group eitheris aspherical or has a finite covering space homeomorphic toS3 x S1 or S2 x S1 x S1. 相似文献
17.
Let f, g: (Rn, 0) (Rp, 0) be two C map-germs. Then f and gare C0-equivalent if there exist homeomorphism-germs h and lof (Rn, 0) and (Rp, 0) respectively such that g = l f h1.Let k be a positive integer. A germ f is k-C0-determined ifevery germ g with jk g(0) = jk f(0) is C0-equivalent to f. Moreover,we say that f is finitely topologically determined if f is k-C0-determinedfor some finite k. We prove a theorem giving a sufficient conditionfor a germ to be finitely topologically determined. We explainthis condition below. Let N and P be two C manifolds. Consider the jet bundle Jk(N,P) with fiber Jk(n, p). Let z in Jk(n, p) and let f be suchthat z = jkf(0). Define
Whether (f) < k depends only on z, not on f. We can thereforedefine the set
Let Wk(N, P) be the subbundle of Jk(N, P) with fiber Wk(n, p).Mather has constructed a finite Whitney (b)-regular stratificationSk(n, p) of Jk(n, p) Wk(n, p) such that all strata aresemialgebraic and K-invariant, having the property that if Sk(N,P) denotes the corresponding stratification of Jk(N, P) Wk(N, P) and f C(N, P) is a C map such that jkf is multitransverseto Sk(N, P), jkf(N) Wk(N, P) = and N is compact (or f is proper),then f is topologically stable. For a map-germ f: (Rn, 0) (Rp, 0), we define a certain ojasiewiczinequality. The inequality implies that there exists a representativef: U Rp such that jkf(U 0) Wk (Rn, Rp = and suchthat jkf is multitransverse to Sk (Rn, Rp) at any finite setof points S U 0. Moreover, the inequality controlsthe rate jkf becomes non-transverse as we approach 0. We showthat if f satisfies this inequality, then f is finitely topologicallydetermined. 1991 Mathematics Subject Classification: 58C27. 相似文献
18.
We prove a nearly optimal bound on the number of stable homotopytypes occurring in a k-parameter semi-algebraic family of setsin R, each defined in terms of m quadratic inequalities. Ourbound is exponential in k and m, but polynomial in . More precisely,we prove the following. Let R be a real closed field and let = {P1, ... , Pm} R[Y1, ... ,Y,X1, ... ,Xk], with degY(Pi) 2, degX(Pi) d, 1 i m. Let S R+k be a semi-algebraic set,defined by a Boolean formula without negations, with atoms ofthe form P 0, P 0, P . Let : R+k Rk be the projection onthe last k coordinates. Then the number of stable homotopy typesamongst the fibers Sx = –1(x) S is bounded by (2mkd)O(mk). 相似文献
19.
Dualizing Complex and the Canonical Element Conjecture II 总被引:1,自引:0,他引:1
In this paper we continue our study of the Canonical ElementConjecture (henceforth C.E.C.) via the dualizing complex. Throughoutthe work (A, m, k) will denote a noetherian complete local ringA of dimension n, m its maximal ideal and k=A/m. Since A iscomplete, we can find a complete local Gorenstein ring (R, mR,k) (complete intersection) such that dim R=dim A and A=R/I.Let denote the canonical module of A, that is, =HomR (A, R),which may be identified with the annihilator of I in R, an idealof R. When A is a domain, we change notation and denote I byP; in this case P is a height 0 prime ideal of R. 相似文献
20.
As G. M. Bergman has pointed out, in the proof of the lemmaon p. 187, we cannot conclude that $$\stackrel{\¯}{S}$$is universal in the sense stated. However, the proof can becompleted as follows: Any element of $$\stackrel{\¯}{S}$$can be obtained as the first component of the solution u ofa system (AI)u+a = 0, (1) where A Sn, a nS and AI has an inverse over L. SinceS is generated by R and k{s}, A can (by the last part of Lemma3.2 of [1]) be taken to be linear in these arguments, say A= A0 + sA1, where A0 Rn, A0 Rn, A1 Kn. Multiplying by (IsA1)1,we reduce this equation to the form (SvBvI)u+a=0, (2) with the same solution u as before, where Bv Rn, sv k{s}1and a nS. Now consider the retraction S k{s} (3) obtained by mapping R 0. If we denote its effect by x x*,then (2) goes over into an equation I.v + a* 0, (4) which clearly has a unique solution v in k{s}; therefore theretraction (3) can be extended to a homomorphism $$\stackrel{\¯}{S}$$ k{s}, again denoted by x x*, provided we can show that u1*does not depend on the equation (1) used to define it. Thisamounts to showing that if an equation (1), or equivalently(2), has the solution u1 = 0, then after retraction we get v1= 0 in (4), i.e. a1* = 0. We shall use induction on n; if u1= 0 in (2), then by leaving out the first row and column ofthe matrix on the left of (2), we have an equation for u2,...,un and by the induction hypothesis, their values after retractionare uniquely determined. Now from (2) we have
where B = (bijv). Applying * and observing that bijvR, we seethat a1 * = 0, as we wished to show. The proof still appliesfor n = 1, so we have a well-defined mapping $$\stackrel{\¯}{S}$$ k{s}, which is a homomorphism. Now the proof of the lemma canbe completed as before. 相似文献