共查询到20条相似文献,搜索用时 15 毫秒
1.
A minimal surface of general type with pg(S) = 0 satisfies 1 K2 9, and it is known that the image of the bicanonical map is a surface for , whilst for , the bicanonical map is always a morphism. In this paper it is shown that is birationalif , and that the degree of is at most 2 if or By presenting two examples of surfaces S with and 8 and bicanonical map of degree 2, it is alsoshown that this result is sharp. The example with is, to our knowledge, a new example of a surfaceof general type with pg = 0. The degree of is also calculated for two other known surfacesof general type with pg = 0 and . In both cases, the bicanonical map turns out to be birational. 相似文献
2.
This paper is concerned with the oscillatory behaviour of first-orderdelay differential equations of the form
(1) where is non-decreasing, (t)< t for t t0 and . Let the numbers k andL be defined by
It is proved here that when L < 1 and 0 < k 1/e all solutionsof equation (1) oscillate in several cases in which the condition
holds, where 1 is the smaller root of the equation = ek. 2000Mathematics Subject Classification 34K11 (primary); 34C10 (secondary). 相似文献
3.
We prove uniqueness for the nonharmonic trigonometric series under the weaker condition (*) where , for some 0 < < 1. In other words, if satisfies the above condition (*), and if , then ak = 0 for all k = 0, 1,.... Finally, we statean improvement of Zygmund's uniqueness result as a corollary. 相似文献
4.
In this paper, perturbations of the left and right essentialspectra of 2 x 2 upper triangular operator matrix MC are studied,where is an operator acting on the Hilbert space H K. For given operators A and B, thesets and are determined, where le(T) and re(T) denote, respectively,the left essential spectrum and the right essential spectrumof an operator T. 2000 Mathematics Subject Classification 47A10,47A55. 相似文献
5.
Let X be a compact space,µ a Borel probability measureon X, T: X X a measure preserving continuous transformationand g: X R a continuous function. Then for some yX,
This Lemma is used to give an alternative proof of a resultby Ruzsa [6], which implies the following extension of a resultof Bergelson [1]. If E N satisfies
then there exists a set N such that n1|[1,n]| (E) for all, n 1, and any finite subset{1, ... k} satisfies Ø.
7 Moria St., Ramat Hasharon, Israel 相似文献
6.
For 1 k < and 1 p q , the problem of finding the bestconstant Cpq in the weighted inequality
involving the Riemann-Liouville integrals of theform
is considered. 相似文献
7.
Let Pn be the collection of all polynomials of degree at mostn with real coefficients. A subtle Bernstein-type extremal problemis solved by establishing the inequality
for all , and m= 1, 2, ..., where c is an absolute constant and
Some related inequalities and direct and inversetheorems about the approximation by elements of in Lq (R) are also discussed. 2000 Mathematics SubjectClassification 41A17 (primary). 相似文献
8.
Let K be a compact subset of Rn, 0 s n. Let , Ps denote s-dimensional packing premeasure andmeasure, respectively. We discuss in this paper the relationbetween and Ps. We prove:if , then ; and if , then for any > 0, there exists a compact subset F of K such that and Ps(F) Ps(K) .1991 Mathematics Subject Classification 28A80, 28A78. 相似文献
9.
A Radial Uniqueness Theorem for Sobolev Functions 总被引:1,自引:0,他引:1
We show that continuous functions u in the Sobolev space , 1 < p n, which have the limitzero in a certain weak sense in a set of positive p-capacityon B with
where B is the open unit ball of Rn and
for 0 > > , are identically zero. Conversely, we produce for each 1 > p n and each positive a non-constant function u in , continuous in , and a compact set EB of positive p-capacity such that u = 0 in E and the aboveinequality holds with exponent p l + . 相似文献
10.
Requirements for boundary conditions are found which imply sharpby order estimates in L-metrics of eigenfunctions of the ordinarydifferential operator
It is shown that the inequalities
for the eigenfunctions {y} yield certain restrictions on thespectrum. 1991 Mathematics Subject Classification 34L05. 相似文献
11.
Consider a scalar differential equation , where I is an open interval containing [0,T]. Assumethat f(t, x) is continuous with a continuous derivative , and weakly concave (or weakly convex)in x for all t I, though strictly concave (or strictly convex)for some t [0, T]. It is well known that in this case therecan be either no, one or two closed solutions; that is, solutions(t) for which (0) = (T) If there are two closed solutions, thenthe greater has a negative characteristic exponent and the smallerhas a positive one. It is easily seen that this is equivalentto a statement on localization of closed solutions. It is shownhow this statement can be generalized to systems of differentialequations . The requirements are that the coordinate functions ) be continuous with continuous derivatives with respect to x1,x2, ...,xn, that the fj are weakly concave (or weakly convex)in , and that a certain condition pertaining to strict concavity (or strict convexity) is fulfilled.2000 Mathematics Subject Classification 34C25, 34C12. 相似文献
12.
Grothendieck Spaces and Duals of Injective Tensor Products 总被引:1,自引:0,他引:1
Let E and F be Fréchet spaces. We prove that if E isreflexive, then the strong bidual is a topological subspace of . We also prove that if, moreover, E is Montel and F has the Grothendieckproperty, then has the Grothendieck property whenever either E or has the approximation property. A similar result is obtainedfor the property of containing no complemented copy of c0. 相似文献
13.
For an irreducible, crystallographic root system in a Euclideanspace V and a positive integer m, the arrangement of hyperplanesin V given by the affine equations (, x) = k, for and k =0, 1, ..., m, is denoted here by . The characteristic polynomial of is related in the paper to that of the Coxeter arrangement A(corresponding to m = 0), and the number of regions into whichthe fundamental chamber of A is dissected by the hyperplanesof is deduced to be equal to the product , where e1,e2, ..., el are the exponents of and h is the Coxeter number.A similar formula for the number of bounded regions follows.Applications to the enumeration of antichains in the root posetof are included. 2000 Mathematics Subject Classification 20F55(primary), 05A15, 52C35 (secondary). 相似文献
14.
A Relation between Hausdorff Dimension and a Condition on Time Sets for the Image by the Brownian Sheet to Possess Interior Points 总被引:2,自引:0,他引:2
We prove that if WN, d is a Brownian sheet mapping to Rd and E is a set in (0, )N of Hausdorff dimensiongreater than , then for almost every rotation about a point x and translation x such that x(E) (0, )N, the set x(E) is such that almost surely W(E) containsinterior points. The techniques are adapted from Kahane andRosen and generalize to higher dimensional time and range. 相似文献
15.
Soient F un corps commutatif localement compact non archimédienet un caractère additif non trivial de F. Soient unereprésentation du groupe de WeilDeligne de F,et sa contragrédiente. Nous calculons le facteur (, , ). De manière analogue, nous calculons le facteur (x, , ) pour toute représentationadmissible irréductible de GLn(F). En conséquence,si F est de caractéristique nulle et si et se correspondentpar la correspondance de Langlands construite par M. Harris,ou celle construite par les auteurs, alors les facteurs (, , s) et (x, , s) sont égaux pour tout nombre complexe s. Let F be a non-Archimedean local field and a non-trivial additivecharacter of F. Let be a representation of the WeilDelignegroup of F and its contragredient representation. We compute (, , ). Analogously, we compute (x, , ) for all irreducible admissible representations of GLn(F).Consequently, if F has characteristic zero, and , correspondvia the Langlands correspondence established by M. Harris orthe correspondence constructed by the authors, then we have(, , s) = (x, , s) for all sC. 1991 Mathematics Subject Classification22E50. 相似文献
16.
This paper treats the existence of multiple positive solutionsof the semi-positone SturmLiouville boundary value problem.
almost everywhere on [R0, R1],
where and f is allowed to take negative values (that is, f is semi-positone).When = 1, new results on the existence of one or two nonzeropositive solutions are obtained. These results generalize previousresults for positone cases (that is, f 0) to the semi-positonecases. We illustrate our results with an explicit example whichhas two nonzero positive solutions. These results are used todeduce results on intervals of eigenvalues for which there existone or two nonzero positive eigenfunctions. Applications ofthese eigenvalue results are provided. 2000 Mathematics SubjectClassification 34B18 (primary), 34B15, 34B16, 47H10, 47H30 (secondary). 相似文献
17.
In 1985, Sárközy proved a conjecture of Erdösby showing that ) is never square-free for sufficiently large n. By applying a new estimateon exponential sums, we prove that this also holds for if dis not too big. Let 0 < < 1, p0 N. For m m0 and 1 k m satisfying |m 2k| < m1 , there is a prime p > p0 suchthat . 相似文献
18.
Let Fn be the free group of rank n with basis x1, x2, ..., xn,and let d(G) denote the minimal number of generators of thefinitely generated group G. Suppose that n d(G). There existsan exact sequence
and wemay view the free abelian group as a right ZG-module by defining (rR')g = rg1R' for allg G, where g1 is any preimage of g under , and = (g1)1 r(g1),the conjugate of r by g1. We call the relation module of G associated with the presentation(1), and say that has ambient rank n. Furthermore, we call the group Fn/R' the free abelianizedextension of G associated with (1). 1991 Mathematics SubjectClassification 20F05, 20C07. 相似文献
19.
Let (an)n0 be a sequence of complex numbers, and, for n0, let
A number of results are proved relating the growth of the sequences(bn) and (cn) to that of (an). For example, given p0, if bn= O(np and for all > 0,then an=0 for all n > p. Also, given 0 < p < 1, then for all > 0 if and onlyif . It is further shown that, given rß > 1, if bn,cn=O(rßn), then an=O(n),where , thereby proving a conjecture of Chalendar, Kellay and Ransford. The principal ingredientsof the proogs are a Phragmén-Lindelöf theorem forentire functions of exponential type zero, and an estimate forthe expected value of e(X), where X is a Poisson random variable.2000 Mathematics Subject Classification 05A10 (primary), 30D15,46H05, 60E15 (secondary). 相似文献
20.
We prove that if an automorphism on the Cuntz algebra On satisfies(S1) = S1 for one isometry S1 of generators S1, ..., Sn suchthat , , l i n and a complex number with modulus one,then it is outer. In particular, any non trivial automorphismon On leaving one generator fixed is outer. 相似文献