共查询到20条相似文献,搜索用时 109 毫秒
1.
James G. Lefevre 《Graphs and Combinatorics》2005,21(4):475-488
A K4 − e trade consists of two disjoint decompositions of some simple graph H into copies of K4 − e. The number of vertices of H is referred to as the foundation of the trade, while the number of copies of K4 − e in each of the decompositions is called the volume of the trade. We determine the values of v and s for which there exists a K4 − e trade of volume s and foundation v. 相似文献
2.
Ved Prakash Gupta 《Proceedings Mathematical Sciences》2008,118(4):583-612
We give an identification between the planar algebra of the subgroupsubfactor R ⋊ H ⊂ R ⋊ G and the G-invariant planar subalgebra of the planar algebra of the bipartite graph ★
n
, where n = [G: H]. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of
the standard invariant of R ⋊ H ⊂ R ⋊ G in terms of operator matrices.
We also obtain an identification between the planar algebra of the fixed algebra subfactor R
G
⊂ R
H
and the G-invariant planar subalgebra of the planar algebra of the ‘flip’ of ★
n
. 相似文献
3.
We consider the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation u
t
−u
txx
+2u
x
+3uu
x
=2u
x
u
xx
+uu
xxx
on the half-line x≥0. In this article, we aim to provide a characterization of the solution of the IBV problem in terms of the solution of a
matrix Riemann–Hilbert (RH) factorization problem in the complex plane of the spectral parameter. The data of this RH problem
are determined in terms of spectral functions associated to initial and boundary values of the solution. The construction
requires more boundary data than those needed for a well-posed IBV problem. Their dependence is expressed in terms of an algebraic
relation to be satisfied by the spectral functions. This RH formulation gives us the long-time asymptotics of a solution of
the CH-equation.
Dedicated to Gennadi Henkin in great admiration. 相似文献
4.
In the linear model Xn × 1 = Cn × pθp × 1 + En × 1, Huber's theory of robust estimation of the regression vector θp × 1 is adapted for two models for the partially specified common distribution F of the i.i.d. components of the error vector En × 1. In the first model considered, the restriction of F to a set [−a0, b0] is a standard normal distribution contaminated, with probability , by an unknown distribution symmetric about 0. In the second model, the restriction of F to [−a0, b0] is completely specified (and perhaps asymmetrical). In both models, the distribution of F outside the set [−a0, b0] is completely unspecified. For both models, consistent and asymptotically normal M-estimators of θp × 1 are constructed, under mild regularity conditions on the sequence of design matrices {Cn × p}. Also, in both models, M-estimators are found which minimize the maximal mean-squared error. The optimal M-estimators have influence curves which vanish off compact sets. 相似文献
5.
C. Krattenthaler Thomas W. Müller 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2008,78(1):99-147
Let q be an odd prime, m a positive integer, and let Γ
m
(q) be the group generated by two elements x and y subject to the relations x
2m
=y
qm
=1 and x
2=y
q
; that is, Γ
m
(q) is the free product of two cyclic groups of orders 2m respectively qm, amalgamated along their subgroups of order m. Our main result determines the parity behaviour of the generalized subgroup numbers of Γ
m
(q) which were defined in Müller (Adv. Math. 153:118–154, 2000), and which count all the homomorphisms of index n subgroups of Γ
m
(q) into a given finite group H, in the case when gcd (m,|
H
|)=1. This computation depends upon the solution of three counting problems in the Hecke group ℋ(q)=C
2*C
q
: (i) determination of the parity of the subgroup numbers of ℋ(q); (ii) determination of the parity of the number of index n subgroups of ℋ(q) which are isomorphic to a free product of copies of C
2 and of C
∞; (iii) determination of the parity of the number of index n subgroups in ℋ(q) which are isomorphic to a free product of copies of C
q
. The first problem has already been solved in Müller (Groups: Topological, Combinatorial and Arithmetic Aspects, LMS Lecture
Notes Series, vol. 311, pp. 327–374, Cambridge University Press, Cambridge, 2004). The bulk of our paper deals with the solution of Problems (ii) and (iii).
Research of C. Krattenthaler partially supported by the Austrian Science Foundation FWF, grant S9607-N13, in the framework
of the National Research Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献
6.
7.
In this paper we examine the classes of graphs whose Kn-complements are trees or quasi-threshold graphs and derive formulas for their number of spanning trees; for a subgraph H of Kn, the Kn-complement of H is the graph Kn–H which is obtained from Kn by removing the edges of H. Our proofs are based on the complement spanning-tree matrix theorem, which expresses the number of spanning trees of a graph as a function of the determinant of a matrix that can be easily constructed from the adjacency relation of the graph. Our results generalize previous results and extend the family of graphs of the form Kn–H admitting formulas for the number of their spanning trees.Final version received: March 18, 2004 相似文献
8.
9.
Jun Feng LI 《数学学报(英文版)》2005,21(6):1495-1508
In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p(R^n) to L^p(R^n) when the m-th order derivatives of A belong to L^p(R^n) for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are (L^p, L^p)-type operators for 1 〈 p 〈 ∞. 相似文献
10.
Let Bn( f,q;x), n=1,2,… be q-Bernstein polynomials of a function f : [0,1]→C. The polynomials Bn( f,1;x) are classical Bernstein polynomials. For q≠1 the properties of q-Bernstein polynomials differ essentially from those in the classical case. This paper deals with approximating properties of q-Bernstein polynomials in the case q>1 with respect to both n and q. Some estimates on the rate of convergence are given. In particular, it is proved that for a function f analytic in {z: |z|<q+} the rate of convergence of {Bn( f,q;x)} to f(x) in the norm of C[0,1] has the order q−n (versus 1/n for the classical Bernstein polynomials). Also iterates of q-Bernstein polynomials {Bnjn( f,q;x)}, where both n→∞ and jn→∞, are studied. It is shown that for q(0,1) the asymptotic behavior of such iterates is quite different from the classical case. In particular, the limit does not depend on the rate of jn→∞. 相似文献
11.
Daniel Soll 《Discrete Mathematics》2009,309(9):2782-2797
For n≥3, let Ωn be the set of line segments between the vertices of a convex n-gon. For j≥2, a j-crossing is a set of j line segments pairwise intersecting in the relative interior of the n-gon. For k≥1, let Δn,k be the simplicial complex of (type-A) generalized triangulations, i.e. the simplicial complex of subsets of Ωn not containing any (k+1)-crossing.The complex Δn,k has been the central object of many papers. Here we continue this work by considering the complex of type-B generalized triangulations. For this we identify line segments in Ω2n which can be transformed into each other by a 180°-rotation of the 2n-gon. Let Fn be the set Ω2n after identification, then the complex Dn,k of type-B generalized triangulations is the simplicial complex of subsets of Fn not containing any (k+1)-crossing in the above sense. For k=1, we have that Dn,1 is the simplicial complex of type-B triangulations of the 2n-gon as defined in [R. Simion, A type-B associahedron, Adv. Appl. Math. 30 (2003) 2-25] and decomposes into a join of an (n−1)-simplex and the boundary of the n-dimensional cyclohedron. We demonstrate that Dn,k is a pure, k(n−k)−1+kn dimensional complex that decomposes into a kn−1-simplex and a k(n−k)−1 dimensional homology-sphere. For k=n−2 we show that this homology-sphere is in fact the boundary of a cyclic polytope. We provide a lower and an upper bound for the number of maximal faces of Dn,k.On the algebraical side we give a term order on the monomials in the variables Xij,1≤i,j≤n, such that the corresponding initial ideal of the determinantal ideal generated by the (k+1) times (k+1) minors of the generic n×n matrix contains the Stanley-Reisner ideal of Dn,k. We show that the minors form a Gröbner-Basis whenever k∈{1,n−2,n−1} thereby proving the equality of both ideals and the unimodality of the h-vector of the determinantal ideal in these cases. We conjecture this result to be true for all values of k<n. 相似文献
12.
Michael A. Hill 《Topology and its Applications》2008,155(15):1730-1736
We provide a somewhat simpler computation of the homology of the image of j spectrum using general techniques for comodules over a coalgebra. We also compute the homotopy of the spectrum HFpj∧HFp, the spectrum which plays the role of HFp∧HFp in the category of j-modules. 相似文献
13.
Semeon Bogatyi Daciberg L. Gonçalves Elena Kudryavtseva Heiner Zieschang 《Central European Journal of Mathematics》2003,1(2):184-197
Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A
1,...,A
m
] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and
f∶W→V
It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills the Hurwitz congruence v(D)э0 mod 2. In the case l>1, the corresponding branched covering exists if and only if v(D)э0 mod 2, the number d/l is an integer, and each partition A
i
∈D splits into the union of l partitions of the number d/l. Here we give a purely algebraic proof of this result following the approach of Hurwitz [11].
The realization problem for the projective plane and l=1 has been solved in [7,8]. The case of the sphere is treated in [1, 2, 12, 7]. 相似文献
14.
We determine the classes (X, YT) of matrix transformations from X into YT where X is one of the classical sequence spaces c0, c, ?∞ and ?1 of all null, convergent and bounded complex sequences and all absolutely convergent complex series, T is a triangle, YT is the matrix domain of T in Y and Y is any of the sets of all sequences that are summable, summable to zero or bounded by the strong Cesàro method of order 1, with index 1 ? p < ∞. Furthermore, we determine the representations of the general bounded linear operators from c into Y. We also establish estimates for the norms of the operators in each case. 相似文献
15.
16.
BingJunYU MangXU 《数学学报(英文版)》2005,21(2):289-302
In this paper, for an arbitrary regular biordered set E, by using biorder-isomorphisms between the w-ideals of E, we construct a fundamental regular semigroup WE called NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further that WE can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroup S with the idempotent biordered set isomorphic to E, there exists a homomorphism from S to WE whose kernel is the greatest idempotent-separating congruence on S and the image is a full symmetric subsemigroup of WE. Moreover, when E is a biordered set of a semilattice Eo, WE is isomorphic to the Munn-semigroup TEo; and when E is the biordered set of a band B, WE is isomorphic to the Hall-semigroup WB. 相似文献
17.
Hai Jinke 《中国科学A辑(英文版)》2006,49(5):620-625
Let π be a set of primes and G a π-separable group. Isaacs defines the B
π
characters, which can be viewed as the “π-modular” characters in G, such that the B
p′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs’ work, Slattery has developed some Brauer’s ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer’s three main theorems to the π-blocks. In this paper, depending on Isaacs’ and Slattery’s work, we will extend the first main theorem for π-blocks. 相似文献
18.
Ricardo Uribe-Vargas 《Bulletin of the Brazilian Mathematical Society》2005,36(3):285-307
The focal curve of an immersed smooth curve γ : θ ↦ γ (θ), in Euclidean space ℝm+1, consists of the centres of its osculating hyperspheres. This curve may be parametrised in terms of the Frenet frame of γ (t, n1, . . . , nm), as Cγ (θ) = (γ +c1n1+ c2n2 + • • • + cmnm)(θ), where the coefficients c1, . . . , cm-1 are smooth functions that we call the focal curvatures of γ . We discovered a remarkable formula relating the Euclidean curvatures κi , i = 1, . . . ,m, of γ with its focal curvatures. We show that the focal curvatures satisfy a system of Frenet equations (not vectorial, but scalar!).
We use the properties of the focal curvatures in order to give, for ℓ = 1, . . . ,m, necessary and sufficient conditions for the radius of the osculating ℓ-dimensional sphere to be critical. We also give necessary
and sufficient conditions for a point of γ to be a vertex. Finally, we show explicitly the relations of the Frenet frame and the Euclidean curvatures of γ with the Frenet frame and the Euclidean curvatures of its focal curve Cγ. 相似文献
19.
Rong Bao GU Tai Xiang SUN Ting Ting ZHENG 《数学学报(英文版)》2005,21(4):873-880
Let G be a graph (i.e., a finite one-dimensional polyhedron) and f : G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f. 相似文献
20.
Pekka J. Nieminen Eero Saksman 《Journal of Mathematical Analysis and Applications》2004,298(2):501-522
Let φ and ψ be analytic self-maps of the unit disc, and denote by Cφ and Cψ the induced composition operators. The compactness and weak compactness of the difference T=Cφ−Cψ are studied on Hp spaces of the unit disc and Lp spaces of the unit circle. It is shown that the compactness of T on Hp is independent of p∈[1,∞). The compactness of T on L1 and M (the space of complex measures) is characterized, and examples of φ and ψ are constructed such that T is compact on H1 but non-compact on L1. Other given results deal with L∞, weakly compact counterparts of the previous results, and a conjecture of J.E. Shapiro. 相似文献