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1.
For a fixed multigraph H with vertices w1,…, wm, a graph G is H- linked if for every choice of vertices v1,…, vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs.Given a connected multigraph H with k edges and minimum degree at least two and n7.5 k, we determine the least integer d such that every n-vertex simple graph with minimum degree at least d is H-linked. This value D( H, n) appears to equal the least integer d′ such that every n-vertex graph with minimum degree at least d′ is b( H)-connected, where b( H) is the maximum number of edges in a bipartite subgraph of H. 相似文献
2.
For integer r≥2, the infinite r-path P∞( r) is the graph on vertices … v−3, v−2, v−1, v0, v1, v2, v3… such that vs is adjacent to vt if and only if | s− t|≤ r−1. The r-path on n vertices is the subgraph of P∞( r) induced by vertices v0, v1, v2,…, vn−1. For non-negative reals x1 and x2, a λx1,x2-labeling of a simple graph G is an assignment of non-negative reals to the vertices of G such that adjacent vertices receive reals that differ by at least x1, vertices at distance two receive reals that differ by at least x2, and the absolute difference between the largest and smallest assigned reals is minimized. With λx1,x2( G) denoting that minimum difference, we derive λx1,x2( Pn( r)) for r≥3, 1≤ n≤ ∞, and . For , we obtain upper bounds on λx1,x2( P∞( r)) and use them to give λx1,x2( P∞( r)) for r≥5 and . We also determine λx1,x2( P∞(3)) and λx1,x2( P∞(4)) for all . 相似文献
3.
This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W= e-Q, which are given as follows. Let an= an( Q) be the nth Mhaskar–Rahmanov–Saff number, φn( x)=max{ n-2/3,1-| x|/ an}, and d>0. Assume that QC( R) is even, , and for some A, B>1 Then for xRand for | x| an(1+ dn-2/3) 相似文献
4.
For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn, let be the family of all fuzzy sets of Rn, which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space with the topology of endograph metric is homeomorphic to the Hilbert cube Q=[-1,1] ω iff Y is compact; and the space is homeomorphic to {( xn) Q:sup| xn|<1} iff Y is non-compact and locally compact. 相似文献
5.
In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with delays of the form x(n)(t)+f(t,x(n−1)(t))+g(t,x(t−τ(t)))=e(t). | 相似文献
6.
In 1990, Acharya and Hegde introduced the concept of strongly
k-indexable graphs: A (
p,
q)-graph
G=(
V,
E) is said to be
strongly k-
indexable if its vertices can be assigned distinct numbers 0,1,2,…,
p−1 so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices form an arithmetic progression
k,
k+1,
k+2,…,
k+(
q−1). When
k=1, a strongly
k-indexable graph is simply called a strongly indexable graph. In this paper, we report some results on strongly
k-indexable graphs and give an application of strongly
k-indexable graphs to
plane geometry, viz;
construction of polygons of same internal angles and sides of distinct lengths.
相似文献
7.
Consider Robin problem involving the
p(
x)-Laplacian on a smooth bounded domain
Ω as follows
Applying the sub-supersolution method and the variational method, under appropriate assumptions on
f, we prove that there exists
λ*>0 such that the problem has at least two positive solutions if
λ(0,
λ*), has at least one positive solution if
λ=
λ*<+∞ and has no positive solution if
λ>
λ*. To prove the results, we prove a norm on
W1,p(x)(
Ω) without the part of ||
Lp(x)(Ω) which is equivalent to usual one and establish a special strong comparison principle for Robin problem.
相似文献
8.
For integers
,
n≥
k and
r≥
s, let
m(
n,
r,
s,
k) be the largest (in order)
k-connected component with at most
s colours one can find in
any r-colouring of the edges of the complete graph
Kn on
n vertices. Bollobás asked for the determination of
m(
n,
r,
s,
k).Here, bounds are obtained in the cases
s=1,2 and
k=
o(
n), which extend results of Liu, Morris and Prince. Our techniques use Szemerédi’s Regularity Lemma for many colours.We shall also study a similar question for bipartite graphs.
相似文献
9.
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
10.
A
μ-algebra is a model of a first-order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms (
f,
μx.
f) where
μx.
f is axiomatized as the least prefixed point of
f, whose axioms are equations or equational implications.Standard
μ-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any nontrivial quasivariety of
μ-algebras contains a
μ-algebra that has no embedding into a complete
μ-algebra.We then focus on modal
μ-algebras, i.e. algebraic models of the propositional modal
μ-calculus. We prove that free modal
μ-algebras satisfy a condition–reminiscent of Whitman’s condition for free lattices–which allows us to prove that (i) modal operators are adjoints on free modal
μ-algebras, (ii) least prefixed points of
Σ1-operations satisfy the constructive relation
μx.
f=
n≥0fn(). These properties imply the following statement:
the MacNeille–Dedekind completion of a free modal μ-
algebra is a complete modal μ-
algebra and moreover the canonical embedding preserves all the operations in the class of the fixed point alternation hierarchy. 相似文献
11.
Let
Ak,
k=0,1,2,…, be a sequence of real nonsingular
n×
n matrices which converge to a nonsingular matrix
A. Suppose that
A has exactly one positive eigenvalue
λ and there exists a unique nonnegative vector
u with properties
Au=
λu and
u=1. Under further additional conditions on the spectrum of
A, it is shown that if
x0≠0 and the iterates
are nonnegative, then
converges to
u and
converges to
λ as
k→
∞.
相似文献
13.
Let
G be an edge weighted graph with
n nodes, and let
A(3,
G) be the average weight of a triangle in
G. We show that the number of triangles with weight at most equal to
A(3,
G) is at least (
n−2) and that this bound is sharp for all
n≥7. Extensions of this result to cliques of cardinality
k>3 are also discussed.
相似文献
14.
This study concerns the existence of positive solutions to the boundary value problemwhere
ξi(0,1) with 0<
ξ1<
ξ2<<
ξn-2<1,
ai,
bi[0,∞) with and . By applying the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general
n-point boundary value problem.
相似文献
15.
In a previous paper [H. Tsuiki, Y. Hattori, Lawson topology of the space of formal balls and the hyperbolic topology of a metric space, Theoret. Comput. Sci. 405 (2008) 198–205], the authors introduced the hyperbolic topology on a metric space, which is weaker than the metric topology and naturally derived from the Lawson topology on the space of formal balls. In this paper, we characterize spaces
Lp(
Ω,
Σ,
μ) on which the hyperbolic topology induced by the norm
p coincides with the norm topology. We show the following:
(1) The hyperbolic topology and the norm topology coincide for 1<p<∞.
(2) They coincide on L1(Ω,Σ,μ) if and only if μ(Ω)=0 or Ω has a finite partition by atoms.
(3) They coincide on L∞(Ω,Σ,μ) if and only if μ(Ω)=0 or there is an atom in Σ.
Keywords: Normed linear space;
Lp; Uniformly rotund (convex); Locally uniformly rotund (convex); Atom; Metric space; Hyperbolic topology; Norm topology; Formal ball; Lawson topology
相似文献
16.
Let
be a sequence of polynomials with real coefficients such that
uniformly for
[
α-
δ,
β+
δ] with
G(
ei)≠0 on [
α,
β], where 0
α<
βπ and
δ>0. First it is shown that the zeros of
are dense in [
α,
β], have spacing of precise order
π/
n and are interlacing with the zeros of
pn+1(cos
) on [
α,
β] for every
nn0. Let
be another sequence of real polynomials with
uniformly on [
α-
δ,
β+
δ] and
on [
α,
β]. It is demonstrated that for all sufficiently large
n the zeros of
pn(cos
) and
strictly interlace on [
α,
β] if
on [
α,
β]. If the last expression is zero then a weaker kind of interlacing holds. These interlacing properties of the zeros are new for orthogonal polynomials also. For instance, for large
n a simple criteria for interlacing of zeros of Jacobi polynomials on [-1+
,1-
],
>0, is obtained. Finally it is shown that the results hold for wide classes of weighted
Lq-minimal polynomials,
q[1,∞], linear combinations and products of orthogonal polynomials, etc.
相似文献
17.
Jackson’s theorem is established in a new kind of holomorphic function space
Qμ related to measures in any starlike circular domain in
. Particularly, the result covers many spaces including
BMOA,
Qp,
QK, and
F(
p,
q,
s) spaces in the unit ball of
. Moreover, we construct integral operators which give pointwise estimates for the gradient of the difference in terms of the gradient on the boundary. The gradient estimates are independent of the measures in question and give rise to Jackson’s theorem.
相似文献
18.
The core of a game
v on
N, which is the set of additive games
φ dominating
v such that
φ(
N)=
v(
N), is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the
k-additive core by replacing additive games by
k-additive games in the definition of the core, where
k-additive games are those games whose Möbius transform vanishes for subsets of more than
k elements. For a sufficiently high value of
k, the
k-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds’ theorem for the greedy algorithm), which characterize the vertices of the core.
相似文献
19.
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 0
ρ(
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 0
ρ(
A).
相似文献
20.
We prove a Strong Haagerup inequality with operator coefficients. If for an integer
d,
denotes the subspace of the von Neumann algebra of a free group
FI spanned by the words of length
d in the generators (but not their inverses), then we provide in this paper an explicit upper bound on the norm on
, which improves and generalizes previous results by Kemp–Speicher (in the scalar case) and Buchholz and Parcet–Pisier (in the non-holomorphic setting). Namely the norm of an element of the form ∑
i=(i1,…,id)aiλ(
gi1gid) is less than
, where
M0,…,
Md are
d+1 different block-matrices naturally constructed from the family (
ai)
iId for each decomposition of
IdIl×
Id−l with
l=0,…,
d. It is also proved that the same inequality holds for the norms in the associated non-commutative
Lp spaces when
p is an even integer,
pd and when the generators of the free group are more generally replaced by *-free
-diagonal operators. In particular it applies to the case of free circular operators. We also get inequalities for the non-holomorphic case, with a rate of growth of order
d+1 as for the classical Haagerup inequality. The proof is of combinatorial nature and is based on the definition and study of a symmetrization process for partitions.
相似文献