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1.
Let n > 1 and let C n denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire mappings F:C nC n and for holomorphic automorphisms of C n on discrete subsets of C n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into C n.For each closed complex submanifold (or subvariety) M ⊂ C n of complex dimension m < n we construct a domain ΩC n containing M and a biholomorphic map F: Ω → C n onto C n with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C n−mC n at infinitely many points. If m = n − 1, we construct F as above such that C nF(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C mC m−1 such that the complement C m+1F(C m )is hyperbolic.  相似文献   

2.
Summary This note is concerned with the following problem: Given a systemA·x=b of linear equations and knowing that certains of its subsystemsA 1·x 1=b 1, ...,A m ·x m =b m can be solved uniquely what can be said about the regularity ofA and how to find the solutionx fromx 1, ...,x m ? This question is of particular interest for establishing methods computing certain linear or quasilinear sequence transformations recursively [7, 13, 15].Work performed under NATO Research Grant 027-81  相似文献   

3.
This is the second in a series of two papers in which we construct a convolution product for the set ?′ (R) of associated homogeneous distributions (AHDs) with support in R. In Part I we showed that if f a and g b are AHDs with degrees of homogeneity a ? 1 and b ? 1, the convolution f a * g b exists as an AHD, if the resulting degree of homogeneity a + b?1 ? N. In this article, we develop a functional extension process, based on the Hahn–Banach theorem, to give a meaning to the convolution product of two AHDs of degrees a ? 1 and b ? 1, in the critical case that a + b ? 1 ∈ N. With respect to this construction, the structure (?′(R), *) is shown to be closed.  相似文献   

4.
Monteiro  Luiz F.  Abad  Manuel  Savini  Sonia  Sewald  Julio 《Order》1999,16(3):277-289
If F B(2 n – 1) denotes the Boolean algebra with 2 n – 1 free generators and P(2 n ) is the Cartesian product of 2 n Boolean algebras all equal to F B(2 n – 1), we define on P(2 n ) an existential quantifier by means of a relatively complete Boolean subalgebra of P(2 n ) and we prove that (P(2n),) is the monadic Boolean algebra with n free generators. Every element of P(2 n ) is a 2 n -tuple whose coordinates are in F B(2 n – 1); in particular, so are the n generators of P(2 n ). We indicate in this work the coordinates of the n generators of P(2 n ).  相似文献   

5.
In this paper, the author discusses the multilinear singular integrals with certain θ-type Calderdn- Zygmund operators and obtain the boundedness from weak H^1 (R^n) to weak L^1 (R^n).  相似文献   

6.
The paper considers a boundary value problem with the help of the smallest closed extensionL :H kH k 0×B h 1×...×B h N of a linear operatorL :C (0) (R + n ) →L(R + n L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) (R + n )) denotes the linear space of smooth functionsR n C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 , resp.),L(R n−1) is the Schwartz class of functionsR n−1C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ) and for the uniqueness of solutionsL U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established.  相似文献   

7.
    
Abstract. Let G be a group of affine transformations of the plane R 2 and let the family F consist of all topological discs in R 2 whose boundary is subject to some smoothness condition (general, rectifiable, piecewise C 1 , piecewise C 2 ). Are any two members D,E ∈ F congruent by dissection with respect to G such that all the pieces in the corresponding dissections of D and E belong to F as well? We give an affirmative answer if G contains all affine transformations and F consists of the discs whose boundary is piecewise C 1 . An example shows that C 1 cannot be replaced by C 2 . Moreover, if G is either the group of equiaffine transformations or the group of similarities, then congruence by dissection of two convex discs D and E turns out to be essentially equivalent to congruence by dissection of the boundaries bd(D ) and bd(E ).  相似文献   

8.
LetI be a σ-ideal on a Polish space such that each set fromI is contained in a Borel set fromI. We say thatI fails to fulfil theΣ 1 1 countable chain condition if there is aΣ 1 1 equivalence relation with uncountably many equivalence classes none of which is inI. Assuming definable determinacy, we show that if the family of Borel sets fromI is definable in the codes of Borel sets, then eachΣ 1 1 set is equal to a Borel set modulo a set fromI iffI fulfils theΣ 1 1 countable chain condition. Further we characterize the σ-idealsI generated by closed sets that satisfy the countable chain condition or, equivalently in this case, the approximation property forΣ 1 1 sets mentioned above. It turns out that they are exactly of the formMGR(F)={A : ∀FF AF is meager inF} for a countable family F of closed sets. In particular, we verify partially a conjecture of Kunen by showing that the σ-ideal of meager sets is the unique σ-ideal onR, or any Polish group, generated by closed sets which is invariant under translations and satisfies the countable chain condition. Research partially supported by NSF grant DMS-9317509.  相似文献   

9.
The genus g of an q-maximal curve satisfies g=g 1q(q−1)/2 or . Previously, q-maximal curves with g=g 1 or g=g 2, q odd, have been characterized up to q-isomorphism. Here it is shown that an q-maximal curve with genus g 2, q even, is q-isomorphic to the non-singular model of the plane curve ∑ i =1} t y q /2 i =x q +1, q=2 t , provided that q/2 is a Weierstrass non-gap at some point of the curve. Received: 3 December 1998  相似文献   

10.
For a submanifoldM n of a Riemannian manifoldM q, the concept of a torsion bivector at the point x M n for given one- and two-dimensional directions fromT x M n is introduced using only the first and second fundamental forms ofM n. Its relation to the concept of Gaussian torsion is then established. It is proved that: 1) equality to zero of the torsion bivector is necessary and, whenM n is a nondevelopable surface of a space of constant curvature with nonzero second fundamental form, is also sufficient for the "flattening" ofM n into some totally geodesicM n+1 inM q; 2) when n = 2, the independence of the nonzero torsion bivector of direction characterizes a minimalM 2 inM q.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 39–42, 1991.  相似文献   

11.
We discuss the problem of boundedness fromLp(Rn) toLp(Rn) (1/p+1/p′=1, 1?p?2) of operators of the typeM=F−1ei?(ξ)a(ξ) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property ofΣ=?−1(1), and its dependence has been exactly determined in the casesn=2, 1?p?2 andn?3,p=1, 2 (M. Sugimoto,Math. Z.215(1994), 519–531;222(1996), 521–531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest casen=3.  相似文献   

12.
A generator of the complex algebra within the framework of general formulation obeys the quadratic equation of the type e2 = a1ea0. In this paper we construct the general complex algebras of the n-th order where the generators obey n-order polynomial equation of the type en = an - 1en - 1an - 2en - 2 + ... + (−)n + 1a0, with real coefficients ak, k = 0, 1, ... n − 1. This algebra induces a generalized trigonometry ((n + 1)-gonometry), subyacent to the n-th order oscillator model and to the n-th order Hamilton equations.  相似文献   

13.
§ 1  IntroductionWe are interested in the existence ofthree-solutions ofthe following second-order dif-ferential equations with nonlinear boundary value conditionsx″=f( t,x,x′) ,   t∈ [a,b] ,( 1 .1 )g1 ( x( a) ,x′( a) ) =0 ,   g2 ( x( b) ,x′( b) ) =0 ,( 1 .2 )where f:[a,b]×R1 ×R1 →R1 ,gi:R1 ×R1 →R1 ( i=1 ,2 ) are continuous functions.The study ofthe existence of three-solutions ofboundary value prolems forsecond or-der differential equations was initiated by Amann[1 ] .In[1 …  相似文献   

14.
Klaus Metsch 《Combinatorica》1995,15(1):105-110
SupposeS is a planar space withv>4 points and letq be the positive real number such thatv=q 3+q2+q+1. Assuming a weak non-degeneracy condition, we shall show thatS has at least (q2+1)(q2+q+1) lines with equality iffq is a prime power andS=PG(3,q).  相似文献   

15.
Let W → 𝔸 2 be the universal Weierstrass family of cubic curves over ?. For each N ≥ 2, we construct surfaces parameterizing the three standard kinds of level N structures on the smooth fibers of W. We then complete these surfaces to finite covers of 𝔸 2. Since W → 𝔸 2 is the versal deformation space of a cusp singularity, these surfaces convey information about the level structure on any family of curves of genus g degenerating to a cuspidal curve. Our goal in this note is to determine for which values of N these surfaces are smooth over (0, 0). From a topological perspective, the results determine the homeomorphism type of certain branched covers of S 3 with monodromy in SL2 (?/N).  相似文献   

16.
ABSTRACT

Let (A, ?) be a structurable algebra. Then the opposite algebra (A op , ?) is structurable, and we show that the triple system B op A(x, y, z):=Vopx,y(z)=x(y¯z)+z(y¯x)?y(x¯z), x, y, z ∈ A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A=𝔸1?𝔸2 denotes tensor products of composition algebras, (?) is the standard conjugation, and () denotes a certain pseudoconjugation on A, we show that the triple systems B op 𝔸1?𝔸2 ( x , y¯, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dim𝔸1, dim𝔸2) ≠ (2, 2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras.  相似文献   

17.
Let V be a finite dimensional affine subspace of l1=l1 N and suppose thath∈l1/V. For 1<p<∞, leth p be the best lp-approximation toh from V andh be the strict best l-approximation toh from V. We show thath p converges toh at rate no worse than 1/p. A condition is given which is sufficient to guarantee that exists. This research was partially supported by a grant from the Office of the Vice Chancellor for Academic Affairs, Indiana University-Purdue University at Fort Wayne.  相似文献   

18.
Let X represent either the space C[-1,1] L p (α,β) (w), 1 ≦ p < ∞ on [-1, 1]. Then Xare Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X 1 αβ of Xsuch that every f ∈ X 1 αβ can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Our method to prove such an approximation problem is Fourier–Jacobi analysis based on the convergence of Fourier–Jacobi expansions. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

19.
Let H be a proof system for quantified propositional calculus (QPC). We define the Σqj-witnessing problem for H to be: given a prenex Σqj-formula A, an H-proof of A, and a truth assignment to the free variables in A, find a witness for the outermost existential quantifiers in A. We point out that the Σq1-witnessing problems for the systems G*1and G1 are complete for polynomial time and PLS (polynomial local search), respectively. We introduce and study the systems G*0 and G0, in which cuts are restricted to quantifier-free formulas, and prove that the Σqj-witnessing problem for each is complete for NC1. Our proof involves proving a polynomial time version of Gentzen’s midsequent theorem for G*0 and proving that G0-proofs are TC0-recognizable. We also introduce QPC systems for TC0 and prove witnessing theorems for them. We introduce a finitely axiomatizable second-order system VNC1 of bounded arithmetic which we prove isomorphic to Arai’s first order theory AID + Σb 0-CA for uniform NC1. We describe simple translations of VNC1 proofs of all bounded theorems to polynomial size families of G*0 proofs. From this and the above theorem we get alternative proofs of the NC1 witnessing theorems for VNC1 and AID.This research was carried while this author was a student at the University of Toronto.  相似文献   

20.
Simultaneous reduction of a lattice basis and its reciprocal basis   总被引:3,自引:0,他引:3  
M. Seysen 《Combinatorica》1993,13(3):363-376
Given a latticeL we are looking for a basisB=[b 1, ...b n ] ofL with the property that bothB and the associated basisB *=[b 1 * , ...,b n * ] of the reciprocal latticeL * consist of short vectors. For any such basisB with reciprocal basisB * let . Håstad and Lagarias [7] show that each latticeL of full rank has a basisB withS(B)exp(c 1·n 1/3) for a constantc 1 independent ofn. We improve this upper bound toS(B)exp(c 2·(lnn)2) withc 2 independent ofn.We will also introduce some new kinds of lattice basis reduction and an algorithm to compute one of them. The new algorithm proceeds by reducing the quantity . In combination with an exhaustive search procedure, one obtains an algorithm to compute the shortest vector and a Korkine-Zolotarev reduced basis of a lattice that is efficient in practice for dimension up to 30.  相似文献   

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