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1.
Vizing and Behzad independently conjectured that every graph is (Δ + 2)-totally-colorable, where Δ denotes the maximum degree
of G. This conjecture has not been settled yet even for planar graphs. The only open case is Δ = 6. It is known that planar graphs
with Δ ≥ 9 are (Δ + 1)-totally-colorable. We conjecture that planar graphs with 4 ≤ Δ ≤ 8 are also (Δ + 1)-totally-colorable.
In addition to some known results supporting this conjecture, we prove that planar graphs with Δ = 6 and without 4-cycles
are 7-totally-colorable.
Supported by the Natural Science Foundation of Department of Education of Zhejiang Province, China, Grant No. 20070441. 相似文献
2.
S. A. Nazarov 《Journal of Applied and Industrial Mathematics》2009,3(3):377-390
Taking various viewpoints, we study the selfadjoint extensions $
\mathcal{A}
$
\mathcal{A}
of the operator A of the Dirichlet problem in a 3-dimensional region Ω with an edge Γ. We identify the infinite dimensional nullspace def A with the Sobolev space H
−ϰ(Γ) on Γ with variable smoothness exponent −ϰ ∈ (−1, 0); while the selfadjoint extensions, with selfadjoint operators $
\mathcal{T}
$
\mathcal{T}
on the subspaces of H
−ϰ(Γ). To the boundary value problem in the region with a “smoothed” edge we associate a concrete extension, which yields a
more precise approximate solution to the singularly perturbed problem. 相似文献
3.
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with
high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction whether the
event occurs. On the other hand, weighted majority functions are shown to be noise-stable. Several necessary and sufficient
conditions for noise sensitivity and stability are given.
Consider, for example, bond percolation on ann+1 byn grid. A configuration is a function that assigns to every edge the value 0 or 1. Let ω be a random configuration, selected
according to the uniform measure. A crossing is a path that joins the left and right sides of the rectangle, and consists
entirely of edges ℓ with ω(ℓ)=1. By duality, the probability for having a crossing is 1/2. Fix an ɛ ∈ (0, 1). For each edge
ℓ, let ω′(ℓ)=ω(ℓ) with probability 1 − ɛ, and ω′(ℓ)=1 − ω(ℓ) with probability ɛ, independently of the other edges. Letp(τ) be the probability for having a crossing in ω, conditioned on ω′ = τ. Then for alln sufficiently large,P{τ : |p(τ) − 1/2| > ɛ}<ɛ. 相似文献
4.
S. A. Nazarov 《Journal of Mathematical Sciences》2010,167(5):713-725
An asymptotic model is found for the Neumann problem for the second-order differential equation with piecewise constant coefficients
in a composite domain Ω∪ω, which are small, of order ε, in the subdomain ω. Namely, a domain Ω(ε) with a singular perturbed
boundary is constructed, the solution for which provides a two-term asymptotic, that is, of increased accuracy O(ε2| log ε|3/2), approximation to the restriction to Ω of the solution of the original problem. As opposed to other singularly perturbed
problems, in the case of contrasting stiffness, the modeling requires the construction of a contour ∂Ω(ε) with ledges, i.e.,
with boundary fragments of curvature O(ε−1). Bibliography: 33 titles. 相似文献
5.
设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2([0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作. 相似文献
6.
In the present paper, the embedding problem is considered for number fields with p-groups whose kernel is either of two groups
with two generators α and β and with the following relations: (1) αρ=1, αρ=1, [α,β,β]=1, [α,β,α,α]=1, or (2) αρ=[α, β α], βρ=1, [α,β,β]=1. It is shown that for the solvability of the original embedding problem it is necessary and sufficient to have the solvability
of the associated Abelian and local problems for all completions of the base fields. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 120–126.
Translated by V. V. Ishkhanov. 相似文献
7.
In a recent paper, Pawale (Des Codes Cryptogr, 2010) investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x + 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D{\mathcal{D}} is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper,
quasi-symmetric designs with y − x = 3 are investigated. It is shown that such a design or its complement has parameter set which is one of finitely many which
are listed explicitly or λ ≤ x + 4 or 0 ≤ x ≤ 1 or the pair (λ, x) is one of (7, 2), (8, 2), (9, 2), (10, 2), (8, 3), (9, 3), (9, 4) and (10, 5). It is also shown that there are no triangle-free
quasi-symmetric designs with positive intersection numbers x and y with y = x + 3. 相似文献
8.
LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the
basic problems is how to characterize the class of rings which have the property that every (weakly) invertible linear finite
automaton ℳ with delay τ over R has a linear finite automaton ℳ′ over R which is a (weak) inverse with delay τ of ℳ. The rings
and linear finite automata are studied by means of modules and it is proved that *-rings are equivalent to self-injective
rings, and the unsolved problem (for τ=0) is solved. Moreover, a further problem of how to characterize the class of rings
which have the property that every invertible with delay τ linear finite automaton ℳ overR has a linear finite automaton ℳ′ over R which is an inverse with delay τ′ for some τ′⩾τ is studied and solved.
Project supported by the National Natural Science Foundation of China(Grant No. 69773015). 相似文献
9.
In the case of number fields the embedding problem of a p-extension with non-Abelian kernel of order p4 is studied. The two kernels of order 34 with generators α, γ and relations α9 = 1, [α,α]3=1,[α,αγγ]==1,[αγγ]=α3,γ3=1 or γ3=α3 and the kernel of order 24 with generators α, β, γ and relations α4=1 β2,[αγ]=1, [α,γ]=1,[βγ]=α2 are considered. For kernels of odd order the embedding problem is always solvable. For the kernel of order 16 the solvability
conditions are reduced to those for the associated problems at the Archimedean points, and to the compatibility condition.
Bibliography: 9 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 74–82. 相似文献
10.
V. V. Arestov 《Ukrainian Mathematical Journal》2010,62(3):331-342
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment
[–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫–11 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞). 相似文献
11.
Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the
following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most (n − 3)/(δ − 1) components, unless G is a complete graph. These bounds are best possible in the sense that we cannot replace 5/18 by a smaller quotient and we
cannot replace δ − 1 by δ, respectively. 相似文献
12.
Arthur W. Apter 《Archive for Mathematical Logic》2008,47(2):101-110
If κ < λ are such that κ is indestructibly supercompact and λ is measurable, then we show that both A = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries the maximal number of normal measures} and B = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries fewer than the maximal number of normal measures} are unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and
sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal
κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must carry fewer than the maximal number of normal measures. We also, however, show how to construct a model with an indestructibly
supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must carry the maximal number of normal measures. If we weaken the requirements on indestructibility, then this last result
can be improved to obtain a model with an indestructibly supercompact cardinal κ in which every measurable cardinal δ < κ carries the maximal number of normal measures.
A. W. Apter’s research was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive grants. In addition, the
author wishes to thank the referee, for helpful comments, corrections, and suggestions which have been incorporated into the
current version of the paper. 相似文献
13.
This paper aims to study the local convergence of a family of Euler-Halley type methods with a parameter α for solving nonlinear operator equations under the second-order generalized Lipschitz assumption. The radius r
α
of the optimal convergence ball and the error estimation of the method corresponding to α are estimated for each α ∈ ( − ∞ , + ∞ ). For each α > 0, we get r
α
≥ r
− α
and the upper bound of the error estimation of the method with α > 0 is not larger than the one with α < 0. For each α ≤ 0, we get the precise value of r
α
, which is closely linked to the dynamical property of the method applied to a real or a complex function, and the optimal
error estimation, which decreases when α→0 − . Results show that the method corresponding to α is better than the one corresponding to − α for each α > 0 and the Chebyshev-Euler method is the best among all methods in the family with α ∈ ( − ∞ , 0] from the view of both safe choice of the initial point and error estimation. 相似文献
14.
15.
In this paper, by using probabilistic methods, we establish sharp two-sided large time estimates for the transition densities
of relativistic α-stable processes with mass m ∈ (0, 1] (i.e., for the Dirichlet heat kernels of m − (m
2/α
− Δ)
α/2 with m ∈ (0, 1]) in half-space-like C
1, 1 open sets. The estimates are uniform in m in the sense that the constants are independent of m ∈ (0, 1]. Combining with the sharp two-sided small time estimates, established in Chen et al. (Ann Probab, 2011), valid for all C
1, 1 open sets, we have now sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m ∈ (0, 1] in half-space-like C
1, 1 open sets for all times. Integrating the heat kernel estimates with respect to the time variable, one can recover the sharp
two-sided Green function estimates for relativistic α-stable processes with mass m ∈ (0, 1] in half-space-like C
1, 1 open sets established recently in Chen et al. (Stoch Process their Appl, 2011). 相似文献
16.
Dian K. Palagachev 《Journal of Global Optimization》2008,40(1-3):305-318
We derive W
2,p
(Ω)-a priori estimates with arbitrary
p ∈(1, ∞), for the solutions of a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular
coefficients. The boundary operator is given in terms of directional derivative with respect to a vector field ℓ that is tangent
to ∂Ω at the points of a non-empty set ε ⊂ ∂Ω and is of emergent type on ∂Ω.
相似文献
17.
Vladimir Semenovich Korolyuk 《Journal of Mathematical Sciences》2011,179(2):273-289
Three main schemes of limit theorems for random evolutions are discussed: averaging, diffusion approximation, and the asymptotics
of large deviations. Markov stochastic evolutions with locally independent increments on increasing time intervals T
ε
= t/ε → ∞, ε → 0, are considered. The asymptotic behavior of random evolutions is investigated with the use of solutions of the singular perturbation
problems for reducibly invertible operators. 相似文献
18.
M. S. Nikulin 《Journal of Mathematical Sciences》1995,75(2):1516-1517
The best (in the sense of quadratic risk) unbiased estimators are constructed for the function f(x)=σ(2x/(n+1)−1)+μ from a
sample of size n from the uniform distribution over [μ−σ, μ+σ] with unknown μ and σ. The best unbiased estimator for σ with
μ being known is also presented.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 36–39, Perm, 1991. 相似文献
19.
Lattice-universal Orlicz function spacesL
F
α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL
F
α,β[0, 1] with indices α and β such that every Orlicz function spaceL
G
[0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL
F
α,β[0, 1]. The existence of classes of universal Orlicz spacesl
Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case.
Partially supported by BFM2001-1284. 相似文献
20.
B. Farkas 《Acta Mathematica Hungarica》2003,98(1-2):71-77
Given a measure space < Ω,m,μ >, a locally bounded, Hausdorff topological linear space < X, τ > and a real number 0<p<1, one can define the space Lp(Ω,m,μ,X), which is, under certain assumptions, a Fréchet space if endowed with a suitable topology. M.M. Day [1] has given a necessary
and sufficient condition, in terms of the properties of the measure space < Ω,m,μ >, for the dual of Lp(Ω,m,μ,C) to be trivial. In this paper a different proof along with a slight generalization is given for this result, using standard
and elementary measure theoretic arguments.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献