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1.
A problem in extremal quasiconformal extensions 总被引:2,自引:0,他引:2
Yi Qi 《中国科学A辑(英文版)》1998,41(11):1135-1141
A constantK
0
(m)
(h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK
0(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and
sufficient condition is established forK
0
(m)
(h) =K
1(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK
0
(m)
(h)<K
1(h), wherek
1(h) is the maximal dilatation ofh. 相似文献
2.
A k-decomposition (G1,…,Gk) of a graph G is a partition of its edge set to form k spanning subgraphs G1,…,Gk. The classical theorem of Nordhaus and Gaddum bounds χ(G1) + χ(G2) and χ(G1)χ(G2) over all 2-decompositions of Kn. For a graph parameter p, let p(k;G) denote the maximum of over all k-decompositions of the graph G. The clique number ω, chromatic number χ, list chromatic number χℓ, and Szekeres–Wilf number σ satisfy ω(2;Kn) = χ(2;Kn) = χℓ(2;Kn) = σ(2;Kn) = n + 1. We obtain lower and upper bounds for ω(k;Kn), χ(k;Kn), χℓ(k;Kn), and σ(k;Kn). The last three behave differently for large k. We also obtain lower and upper bounds for the maximum of χ(k;G) over all graphs embedded on a given surface. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
3.
Tamar Burak 《Israel Journal of Mathematics》1973,16(4):404-417
Fort ∈ [a, b], letA(t) be the unbounded operator inH
0,p
(G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E
1(α)u (α)=u
α,E
2 (β)u (β)=u
β. Here [α, β) χ- [a, b],E
1 (α) andE
2 (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E
1 (α) and =A (β)E
2 (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ
i
,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ
1, | arg (b −t) |θ
2}.
Research partially supported by N. N. F. grant at Brandeis University. 相似文献
4.
In 1963, Vizing [Vichysl.Sistemy 9 (1963), 30–43] conjectured that γ(G × H) ≥ γ(G)γ(H), where G × H denotes the cartesian product of graphs, and γ(G) is the domination number. In this paper we define the extraction number x(G) and we prove that P2(G) ≤ x(G), and γ(G × H) ≥ x(G)γ(H), where P2(G) is the 2-packing number of G. Though the equality x(G) = γ(G) is proven to hold in several classes of graphs, we construct an infinite family of graphs which do not satisfy this condition. Also, we show the following lower bound: γ(G × H) ≥ γ(G)P2(H) + P2(G)(γ(H) − P2(H)). © 1996 John Wiley & Sons, Inc. 相似文献
5.
We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces SO(n)/SO(k1) ×⋯× SO(k
r
), for any choice of k
1,…,k
r
, k
1 + ⋯ + k
r
⩽ n. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented.
Also, the proof of integrability of the SO(n)-invariant Einstein metrics on SO(k
1 + k
2 + k
3)/SO(k
1) × SO(k
2) × SO(k
3) and on the Stiefel manifolds V (n, k) = SO(n)/SO(k) is given. 相似文献
6.
LetX be a closed subset of a topological spaceF; leta(·) be a continuous map fromX intoX; let {x
i} be a sequence generated iteratively bya(·) fromx
0 inX, i.e.,x
i+1 =a(x
i),i=0, 1, 2, ...; and letQ(x
0) be the cluster point set of {x
i}. In this paper, we prove that, if there exists a pointz inQ(x
0) such that (i)z is isolated with respect toQ(x
0), (ii)z is a periodic point ofa(·) of periodp, and (iii)z possesses a sequentially compact neighborhood, then (iv)Q(x
0) containsp points, (v) the sequence {x
i} is contained in a sequentially compact set, and (vi) every point inQ(x
0) possesses properties (i) and (ii). The application of the preceding results to the caseF=E
n leads to the following: (vii) ifQ(x
0) contains one and only one point, then {x
i} converges; (viii) ifQ(x
0) contains a finite number of points, then {x
i} is bounded; and (ix) ifQ(x
0) containsp points, then every point inQ(x
0) is a periodic point ofa(·) of periodp. 相似文献
7.
Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer proved that if Δ (G1) Δ (G2) < 0.5n, then G1 and G2 pack.
In this note, we study an Ore-type analogue of the Sauer–Spencer Theorem. Let θ(G) = max{d(u) + d(v): uv∈E(G)}. We show that if θ(G1)Δ(G2) < n, then G1 and G2 pack. We also characterize the pairs (G1,G2) of n-vertex graphs satisfying θ(G1)Δ(G2) = n that do not pack.
This work was supported in part by NSF grant DMS-0400498. The work of the first author was also partly supported by grant
05-01-00816 of the Russian Foundation for Basic Research. 相似文献
8.
Strongly Closed Subgraphs in a Distance-Regular Graph with <Emphasis Type="Italic">c</Emphasis><Subscript>2</Subscript> > 1 总被引:1,自引:1,他引:0
Akira Hiraki 《Graphs and Combinatorics》2008,24(6):537-550
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:
Suppose that the condition (SC)
m
holds. Then it has been known that the condition (BB)
i
holds for all i with 1 ≤ i ≤ m. Similarly we can show that the condition (CA)
i
holds for all i with 1 ≤ i ≤ m. In this paper we prove that if the conditions (BB)
i
and (CA)
i
hold for all i with 1 ≤ i ≤ m, then the condition (SC)
m
holds. Applying this result we give a sufficient condition for the existence of a dual polar graph as a strongly closed subgraph
in Γ. 相似文献
(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 ∂ Γ (x, y) = 2, ∂ Γ (x, z) = ∂ Γ (y, z) = m and |C(z, x) ∩ C(z, y)| ≥ 2. Then C(x, z) ∪ A(x, z) = C(y, z) ∪ A(y, z). |
9.
Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J1-topology of a sequence (xn) in D([0, 1]; E) does not imply convergence of a sequence (
n) of averages. Convergence in the J1-topology of a sequence (
n) of averages is shown, under the growth condition xn ∞ = o(n), to be equivalent to the convergence of (
n) in the uniform topology. Convergence of a sequence (xn,) is shown to imply convergence of the sequence (
n) of averages in the M1 and M2 topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent. 相似文献
10.
Sequential retractivities and regularity on inductive limits 总被引:2,自引:0,他引:2
Qiu Jing-Hui 《Czechoslovak Mathematical Journal》2000,50(4):847-851
11.
A quasigroup (Q,) satisfying the identityx(yx) =y (or the equivalent identity (xy)x =y) is called semisymmetric. Ann-quasigroup (Q, A) satisfying the identityA(A(x
1, ...,x
n
),x
1, ...,x
n–1) =x
n
is called cyclic. So, cyclicn-quasigroups are a generalization of semisymmetric quasigroups. In this paper, self-orthogonal cyclicn-quasigroups (SOCnQs) are considered. Some constructions ofSOCnQs are described and the spectrum of suchn-quasigroups investigated. 相似文献
12.
Jan Goncerzewicz 《Mathematical Methods in the Applied Sciences》1992,15(5):299-314
The initial-boundary value problem in a semi-infinite strip (0, ∞)×(0, T) for a degenerate parabolic equation of the form u, t= φ(u)xx + b(x)φ(u)x is considered. The properties of solutions in the case where the initial function is compactly supported and for constant initial and boundary data are investigated. 相似文献
13.
《Quaestiones Mathematicae》2013,36(3-4):219-234
Abstract For a unital module V over a commutative ring R, let C denote the collection of cyclic submodules. The ring ?R(V;C) = {f ε EndR V |f(C) ?C, ?C εR (V;C) has been the object of several recent studies in which the structure of ?R(V;C) is related to the triple (V, R,C). Here we introduce a new ring HR(V;C) containing ?(V;C) and investigate its structure in terms of the parameters (V, R, C). 相似文献
14.
A (k; g)-graph is a k-regular graph with girth g. Let f(k; g) be the smallest integer v such there exists a (k; g)-graph with v vertices. A (k; g)-cage is a (k; g)-graph with f(k; g) vertices. In this paper we prove that the cages are monotonic in that f(k; g1) < f(k; g2) for all k ≥ 3 and 3 ≥ g1 < g2. We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k. © 1997 John Wiley & Sons, Inc. 相似文献
15.
Eduard Boďa 《Mathematica Slovaca》2008,58(2):173-176
Let (R,m) = k[x
1,..., x
n
](x
1,...,x
n
) be a local polynomial ring (k being an algebraically closed field), and Q:= (F
1,..., F
r
)R be a primary ideal in R with respect to a maximal ideal m ⊂ R. In this short note we give a formula for the multiplicity e
0 (QR/(F
1)R, R/(F
1)R).
The author was supported by the grant No. 1/0262/03) of the Slovak Ministry of Education. 相似文献
16.
An operator T ∈ L(E, F) factors over G if T = RS for some S ∈ L(E, G) and R ∈ L(G, F); the set of such operators is denoted by LG(E, F). A triple (E, G, F) satisfies bounded factorization property (shortly, (E, G, F) ∈ ???) if LG(E, F) ? LB(E, F), where LB(E, F) is the set of all bounded linear operators from E to F. The relationship (E, G, F) ∈ ??? is characterized in the spirit of Vogt's characterisation of the relationship L(E, F) = LB(E, F) [23]. For triples of K?othe spaces the property ??? is characterized in terms of their K?othe matrices. As an application we prove that in certain cases the relations L(E, G1) = LB(E, G1) and L(G2, F) = LB(G2, F) imply (E, G, F) ∈ ??? where G is a tensor product of G1 and G2. 相似文献
17.
Let t(n) denote the greatest number of arcs in a diagraph of orders n which does not contain any antidrected cycles. We show that [16/5(n ? 1)] ≤ t(n) ≤ 1/2 (n ? 1) for n ≥ 5. Let tr (n) denote the corresponding quantity for r-colorable digraphs. We show that [16/5(n ? 1)] ≤ t5(n) ≤ t6(n) ≤ 10/3(n ? 1) for n ≥ 5 and that t4(n) = 3(n ? 1) for n ≥ 3. 相似文献
18.
Noômen Jarboui 《Archiv der Mathematik》2008,90(2):133-135
We answer a question raised by Othman Echi: Is an E
1 (resp., a C
1) ring an E (resp., a C) ring? We construct a C
1 (thus E
1) ring which is not an E
2 (thus not a C
2) ring.
Received: 11 June 2007 相似文献
19.
S. K. Chatterjea 《Annali dell'Universita di Ferrara》1961,10(1):13-16
Summary Defining the function Δn, 1,k;x(J) asΔn, 1,k;x(J)=J
n+1(x)−J
n(x)J
n+k+1(x) associated with the Bessel functionJ
n(x), we derive a series of products of Bessel functions for Δn, f, k, x (J). Whenk=1,k;x (J) becomes Turàn expression for Bessel functions. Some consequences have been pointed out.
Riassunto Definita la Δn, f, k, x (J) come Δn, f, k, x, (J)=J n+1(x)J n+k(x)-J n(n+k+1)(x) associata alla funzioneJ n(x) di Bessel, si ricava una serie di prodotti di funzioni di Bessel per Δn, f, k, x, (J). 3 Quandok=1, Δn, f, k, x, (J) diventa una espressione di Turàn per le funzioni di 2 Bessel, vengono inoltre indicate alcune altre conseguenze.相似文献
20.
J. Hoffmann-Jørgensen 《Journal of Theoretical Probability》1999,12(1):131-145
Let N
n denote the number of positive sums in the first n trials in a random walk (S
i) and let L
n denote the first time we obtain the maximum in S
0,..., S
n. Then the classical equivalence principle states that N
n and L
n have the same distribution and the classical arcsine law gives necessary and sufficient condition for (1/n) L
n or (1/n) N
n to converge in law to the arcsine distribution. The objective of this note is to provide a simple and elementary proof of the arcsine law for a general class of integer valued random variables (T
n) and to provide a simple an elementary proof of the equivalence principle for a general class of integer valued random vectors (N
n, L
n). 相似文献