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1.
u1,…,ur are in kx1,…,xs with k and deg(u1,…,ur) finite. Intending applications to Hilbert–Kunz theory, we code the numbers into a function φu, which empirically satisfies many functional equations related to “magnification by p,” where p=chark. p-fractals, introduced here, formalize these ideas.In the first interesting case (r=3, s=2), the φu are p-fractals. Our proof uses functions φI attached to ideals I and square-free elements h of A=kx,y. The finiteness of the set of ideal classes in and the existence of “magnification maps” on this set show the φI to be p-fractals.We describe further functional equations coming from a theory of reflection maps on ideal classes, and the paper concludes with examples and open questions.  相似文献   

2.
Given a Newtonian coalgebra we associate to it a chain complex. The homology groups of this Newtonian chain complex are computed for two important Newtonian coalgebras arising in the study of flag vectors of polytopes:R a, b and Rc, d. The homology of Ra, b corresponds to the homology of the boundary of then -crosspolytope. In contrast, the homology of Rc, d depends on the characteristic of the underlying ring R. In the case the ring has characteristic 2, the homology is computed via cubical complexes arising from distributive lattices. This paper ends with a characterization of the integer homology ofZ c, d.  相似文献   

3.
4.
We consider linearly ordered, Archimedean dimension groups (G,G+,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G+,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C*-algebra is the Fibonacci C*-algebra.  相似文献   

5.
It is first observed that a uniformly bounded cosine operator function C() and the associated sine function S() are totally non-stable. Then, using a zero-one law for the Abel limit of a closed linear operator, we prove some results concerning strong mean stability and uniform mean stability of C(). Among them are: (1) C() is strongly (C,1)-mean stable (or (C,2)-mean stable, or Abel-mean stable) if and only if 0ρ(A)σc(A); (2) C() is uniformly (C,2)-mean stable if and only if S() is uniformly (C,1)-mean stable, if and only if , if and only if , if and only if C() is uniformly Abel-mean stable, if and only if S() is uniformly Abel-mean stable, if and only if 0ρ(A).  相似文献   

6.
Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian □h and complex vertical Laplacian □v on the holomorphic tangent bundle T1,0M of M, and then we obtain a precise relationship among □h,□v and the Hodge–Laplace operator on (T1,0M,,), where , is the induced Hermitian metric on T1,0M by F. As an application, we prove a vanishing theorem of holomorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.  相似文献   

7.
8.
LetXbe a Banach space. GivenMa subspace ofXwe denote withPMthe metric projection ontoM. We defineπ(X) sup{PMMa proximinal subspace ofX}. In this paper we give a bound forπ(X). In particular, whenX=Lp, we obtain the inequality PM2|2/p−1|, for every subspaceMofLp. We also show thatπ(X)=π(X*).  相似文献   

9.
The famous Gelfand formula ρ(A)=limsupnAn1/n for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is substantially restricted by a lack of estimates for the rate of convergence of the quantities An1/n to ρ(A). In the paper this deficiency is made up to some extent. By using the Bochi inequalities we establish explicit computable estimates for the rate of convergence of the quantities An1/n to ρ(A). The obtained estimates are then extended for evaluation of the joint spectral radius of matrix sets.  相似文献   

10.
Let S be a set of n4 points in general position in the plane, and let h<n be the number of extreme points of S. We show how to construct a 3-connected plane graph with vertex set S, having max{3n/2,n+h−1} edges, and we prove that there is no 3-connected plane graph on top of S with a smaller number of edges. In particular, this implies that S admits a 3-connected cubic plane graph if and only if n4 is even and hn/2+1. The same bounds also hold when 3-edge-connectivity is considered. We also give a partial characterization of the point sets in the plane that can be the vertex set of a cubic plane graph.  相似文献   

11.
Sharp tridiagonal pairs   总被引:1,自引:0,他引:1  
Let denote a field and let V denote a vector space over with finite positive dimension. We consider a pair of -linear transformations A:VV and A*:VV that satisfies the following conditions: (i) each of A,A* is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A*ViVi-1+Vi+Vi+1 for 0id, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A* such that for 0iδ, where and ; (iv) there is no subspace W of V such that AWW, A*WW, W≠0, WV. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0id the dimensions of coincide. We say the pair A,A* is sharp whenever dimV0=1. A conjecture of Tatsuro Ito and the second author states that if is algebraically closed then A,A* is sharp. In order to better understand and eventually prove the conjecture, in this paper we begin a systematic study of the sharp tridiagonal pairs. Our results are summarized as follows. Assuming A,A* is sharp and using the data we define a finite sequence of scalars called the parameter array. We display some equations that show the geometric significance of the parameter array. We show how the parameter array is affected if Φ is replaced by or or . We prove that if the isomorphism class of Φ is determined by the parameter array then there exists a nondegenerate symmetric bilinear form , on V such that Au,v=u,Av and A*u,v=u,A*v for all u,vV.  相似文献   

12.
13.
The continuity conditions at the endpoints of interpolation theorems, TaBjMj aAj for j=0, 1, can be written with the help of the approximation functional: E(tTaB1B0)LM0 aA0 and E(tTaB0B1)LM1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the L norms can be replaced by BMO( +) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition fL0, i.e., f*L, where f*(γ)=μ{|f|>γ} is the distribution function of f, can be replaced in interpolation with L(pq) spaces by the weaker f*BMO( +).  相似文献   

14.
Let σ be an orthogonal representation of a group G on a real Hilbert space. We show that σ is irreducible if and only if its commutant σ(G)' is isomorphic to , or . This result is an analogue of the classical Schur lemma for unitary representations. In both cases (orthogonal and unitary), a representation is irreducible if and only if its commutant is a field. If σ is irreducible, we show that there exists a unitary irreducible representation π of G such that the complexification σ is unitarily equivalent to π if σ(G)' , to π π̄ if σ(G)' , and to π π if σ(G)' (here π̄ denotes the contragredient representation of π). These results are classical for a finite-dimensional σ, but seem to be new in the general case.  相似文献   

15.
This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g(x,t)=g(x,t,t/) possessing the average g0(x,t) as →0+, where 0<0<1. Firstly, with assumptions (A1)–(A5) on the functions g(x,t,ξ) and g0(x,t), we prove that the Hausdorff distance between the uniform attractors and in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O() as →0+. Then we establish that the Hausdorff distance between the uniform attractors and in space V is also less than O() as →0+. Finally, we show for each [0,0].  相似文献   

16.
Let be an ideal of subsets of a metric space X,d. This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of which reduces to ordinary continuity when consists of the finite subsets of X and agrees with uniform continuity on members of when is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions.  相似文献   

17.
P.M. Cohn has proved the remarkable theorem, that every invertible n × n matrix over a free algebra is the product of elementary n × n matrices, see [C1], [C2]. In this note we prove the analogue for symplectic 2 × 2 matrices over free algebras relative to a homogeneous involution: every symplectic 2 × 2 matrix is the product of elementary symplectic 2 × 2 matrices.In Section 1 we define the group Sp2(R) of symplectic 2 × 2 matrices over an involutive ring R. The group ESp2(R) generated by elementary symplectic matrices is introduced in Section 3.In Section 2 we prove a reducibility criterion for homogeneous polynomials in a free algebra KX over a commutative field K. It leads to a special form in the factorization of symmetric homogeneous polynomials, see Corollary to Proposition 2.2.We prove in Section 4 that ESp2(KX) = Sp2(KX), if the involution on KX is homogeneous.In a subsequent article we will show that the main result is also true for 2g × 2g symplectic matrices over free algebras relative to homogeneous involutions, g ≥ 1. It seems that a proof of this result will be much more complicated than the case g = 1.  相似文献   

18.
A left cancellative and left amenable semigroup S satisfies the Strong Følner Condition. That is, given any finite subset H of S and any >0, there is a finite nonempty subset F of S such that for each sH, |sFF|<|F|. This condition is useful in defining a very well behaved notion of density, which we call Følner density, via the notion of a left Følner net, that is a net FααD of finite nonempty subsets of S such that for each sS, (|sFαFα|)/|Fα| converges to 0. Motivated by a desire to show that this density behaves as it should on cartesian products, we were led to consider the set LIM0(S) which is the set of left invariant means which are weak* limits in l(S)* of left Følner nets. We show that the set of all left invariant means is the weak* closure of the convex hull of LIM0(S). (If S is a left amenable group, this is a relatively old result of C. Chou.) We obtain our desired density result as a corollary. We also show that the set of left invariant means on is actually equal to . We also derive some properties of the extreme points of the set of left invariant means on S, regarded as measures on βS, and investigate the algebraic implications of the assumption that there is a left invariant mean on S which is non-zero on some singleton subset of βS.  相似文献   

19.
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2nu1 (HSOLSSOM(2nu1)). For u2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n3u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n9 and n3u/2+1 or (2) n263 and n2(u-2). In this paper we show that in (1) the condition n9 can be extended to n30 and that in (2), the condition n263 can be improved to n4, except possibly for 19 pairs (n,u), the largest of which is (53,28).  相似文献   

20.
Uzy Hadad   《Journal of Algebra》2007,318(2):607-618
Let R be a ring generated by l elements with stable range r. Assume that the group ELd(R) has Kazhdan constant 0>0 for some dr+1. We prove that there exist (0,l)>0 and , s.t. for every nd, ELn(R) has a generating set of order k and a Kazhdan constant larger than . As a consequence, we obtain for where n3, a Kazhdan constant which is independent of n w.r.t. generating set of a fixed size.  相似文献   

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