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1.
Let Γ be a distance-regular graph of diameter d ≥ 3 with c 2 > 1. Let m be an integer with 1 ≤ m ≤ d − 1. We consider the following conditions:
  (SC) m : For any pair of vertices at distance m there exists a strongly closed subgraph of diameter m containing them.
  (BB) m : Let (x, y, z) be a triple of vertices with ∂Γ(x, y) = 1 and ∂Γ(x, z) = ∂Γ(y, z) = m. Then B(x, z) = B(y, z).
  (CA) m : Let (x, y, z) be a triple of vertices with and |C(z, x) ∩ C(z, y)| ≥ 2. Then C(x, z) ∪ A(x, z) = C(y, z) ∪ A(y, z).
In [12] we have shown that the condition (SC) m holds if and only if both of the conditions (BB) i and (CA) i hold for i = 1,...,m. In this paper we show that if a 1 = 0 < a 2 and the condition (BB) i holds for i = 1,...,m, then the condition (CA) i holds for i = 1,...,m. In particular, the condition (SC) m holds. Applying this result we prove that a distance-regular graph with classical parameters (d, b, α, β) such that c 2 > 1 and a 1 = 0 < a 2 satisfies the condition (SC) i for i = 1,...,d − 1. In particular, either (b, α, β) = (− 2, −3, −1 − (−2) d ) or holds.  相似文献   

2.
We give the definition of the full potential with descendants, which is a genus expansion of the Barannikov-Kontsevich solution of the WDVV equation. This potential satisfies the Getzler relation, which comes from the geometry of the moduli space of curves Open image in new window .  相似文献   

3.
In this paper, we show that, for each p 〉 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable.  相似文献   

4.
Suppose π1(E, F) is the space of all absolutely 1-summing operators between two Banach spacesE andF. We show that ifF has a copy of c0, then π1 (E, F) will have a copy of c0, and under some conditions ifE has a copy of ℓ1 then π1 (E, F) would have a complemented copy of ℓ1.  相似文献   

5.
Three new summation formulas for 6 ψ 6 bilateral basic hypergeometric series attached to root systems are presented. Remarkably, two of these formulae, labelled by the A2n−1 and A2n root systems, can be reduced to multiple 6 φ 5 sums generalising the well-known van Diejen sum. This latter sum serves as the weight-function normalisation for the BC n q-Racah polynomials of van Diejen and Stokman. Two 8 φ 7-level extensions of the multiple 6 φ 5 sums, as well as their elliptic analogues, are conjectured. This opens up the prospect of constructing novel A-type extensions of the Koornwinder–Macdonald theory.  相似文献   

6.
This paper is concerned with the study of the set P -1(0), when P varies over all orthogonally additive polynomials on p and L p spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this class of polynomials.  相似文献   

7.
In this note, the exact value of the James constant for the l3-l1 space is obtained, J(l3-l1)=1.5573…. This result improves the known inequality, J(l3-l1)≤4/3√10, which was given by Dhompongsa, Piraisangjun and Saejung.  相似文献   

8.
The cell structure of the spaces ℳ2,1 and ℳ3,1 is considered. These are the spaces of complex curves of genus 2 and 3 with one marked point. For the space ℳ2,1, nine cells of the highest dimension 8 are described and their adjacency is studied. For the space ℳ3,1, a list of all 1726 cells of the highest dimension 14 (with orientation) is obtained. The list of adjacent couples of cells is also obtained. These lists can be found on the web.  相似文献   

9.
Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(KmPn), the crossing number of the Cartesian product KmPn. We prove that for m ≥ 3,n ≥ 1 and cr(KmPn)≥ (n − 1)cr(Km+2e) + 2cr(Km+1). For m≤ 5, according to Klešč, Jendrol and Ščerbová, the equality holds. In this paper, we also prove that the equality holds for m = 6, i.e., cr(K6Pn) = 15n + 3. Research supported by NFSC (60373096, 60573022).  相似文献   

10.
11.
Given an operator T : XY between Banach spaces, and a Banach lattice E consisting of measurable functions, we consider the point-wise extension of the operator to the vector-valued Banach lattices T E : E(X) → E(Y) given by T E (f)(ω) = T(f(ω)). It is proved that for any Banach lattice E which does not contain c 0, the operator T is an isomorphism on a subspace isomorphic to c 0 if and only if so is T E . An analogous result for invertible operators on subspaces isomorphic to 1 is also given.  相似文献   

12.
13.
We use the Algorithm Z on partitions due to Zeilberger, in a variant form, to give a combinatorial proof of Ramanujan’s 1 ψ 1 summation formula.  相似文献   

14.
The minimum number of total independent partition sets of VE of graph G(V,E) is called the total chromatic number of G denoted by χ t (G). If the difference of the numbers of any two total independent partition sets of VE is no more than one, then the minimum number of total independent partition sets of VE is called the equitable total chromatic number of G, denoted by χ et (G). In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order. Supported by the National Natural Science Foundation of China (No. 10771091).  相似文献   

15.
Let an algebraic curve f have a singular point of type Aμ or Dμ. Let be the curve obtained by smoothing the singular point of f. In this paper, local maximal meanders appearing under an M-smoothing in a neighborhood of the singular point are studied. A local maximal meander means that the number of real points of the intersection of with a coordinate axis in the neighborhood is maximal and the points belong to one of the components of . An M-smoothing means that the number of components of which appear in the neighborhood under the smoothing is also maximal. Bibliography: 9 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 193–217.  相似文献   

16.
We construct a class of modules for the twisted multi-loop algebra of type A 1×A 1 by applying Wakimoto free bosonic realization. We also discuss the structures and the irreducibility of the Fock space.  相似文献   

17.
Transformations for a bilateral 2 ψ 2-series are investigated by means of Abel’s lemma on summation by parts. Two q-extensions of Dougall’s classical identity for bilateral 2H2-sum are established. As by-products, the Rogers–Fine identity is recovered and a new proof is presented for Bailey’s identity of bilateral well-poised 6 ψ 6-series.  相似文献   

18.
We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the classes of continuous 2π-periodic functions whose (ψ, β)-derivatives belong to the set H ω in the case where the sequences ψ that generate the classes tend to zero not faster than a power function.  相似文献   

19.
The general summation theorem for well-poised 5 F 4-series discovered by Dougall (Proc. Edinb. Math. Soc. 25:114–132, 1907) is shown to imply several infinite series of Ramanujan-type for 1/π and 1/π 2, including those due to Bauer (J. Reine Angew. Math. 56:101–121, 1859) and Glaisher (Q. J. Math. 37:173–198, 1905) as well as some recent ones by Levrie (Ramanujan J. 22:221–230, 2010).  相似文献   

20.
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