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1.
An Improved Upper Bound for Leo Moser's Worm Problem 总被引:1,自引:0,他引:1
Abstract. A worm ω is a continuous rectifiable arc of unit length in the Cartesian plane. Let W denote the class of all worms. A planar region C is called a cover for W if it contains a copy of every worm in W . That is, C will cover or contain any member ω of W after an appropriate translation and/ or rotation of ω is completed (no reflections). The open problem of determining a cover C of smallest area is attributed to Leo Moser [7], [8]. This paper reduces the smallest known upper bound for this area from
0.275237 [10] to 0.260437. 相似文献
2.
Erdélyi 《Constructive Approximation》2008,19(3):329-338
Abstract. Various important, weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc., have
been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most cases this
minimal assumption is the doubling condition. Here, based on a recently proved Bernstein-type inequality by D. S. Lubinsky,
we establish Markov—Bernstein-type inequalities for trigonometric polynomials with respect to doubling weights on [-ω,ω] . Namely, we show the theorem below.
Theorem
Let p ∈ [1,∞) and ω ∈ (0, 1/2] . Suppose W is a weight function on [-ω,ω] such that W(ω cos t) is a doubling weight. Then there is a constant C depending only on p and the doubling constant L so that
holds for every T
n
∈ T
n
, where T
n
denotes the class of all real trigonometric polynomials of degree at most n . 相似文献
3.
For an arbitrary continuous, increasing function ω : [0, ∈fty) →
C of finite exponential type, we characterize Laplace-Stieltjes transforms of Banach-space-valued functions that are O(ω) , and use this to establish a Hille-Yosida type theorem for strongly continuous semigroups that are O(ω) . Corollaries include characterizing generators of strongly continuous semigroups that are , for d > 1 , in addition to the already known examples of exponential or polynomial growth.
January 27, 1999 相似文献
4.
Narong Punnim 《Graphs and Combinatorics》2002,18(4):781-785
Let ω(G) be the clique number of a graph G. We prove that if G runs over the set of graphs with a fixed degree sequence d, then the values ω(G) completely cover a line segment [a,b] of positive integers. For an arbitrary graphic degree sequence d, we define min(ω,d) and max(ω,d) as follows:
where is the graph of realizations of d.
Thus the two invariants a:=min(ω,d) and b:=max(ω,d) naturally arise. For a graphic degree sequence d=r
n
:=(r,r,…,r) where r is the vertex degree and n is the number of vertices, the exact values of a and b are found in all situations. Since the independence number, α(G)=ω(Gˉ), we obtain parallel results for the independence number of graphs.
Received: October, 2001 Final version received: July 25, 2002
RID="*"
ID="*" Work supported by The Thailand Research Fund, under the grant number BRG/09/2545 相似文献
5.
LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X
ω
), where X
ω
are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X
ω
), where X
ω
are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties
with respect to the link operator and specialization.
Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN
610/P3/94. 相似文献
6.
O. Ascenzi 《Annali dell'Universita di Ferrara》2001,47(1):41-56
In this work I consider the expression of the stress intensity factor for convex bounded sets proposed by Ore and Burns [4],
and we will study its properties. In particular we will show that the stress intensity factor defined in ω is well defined
whether ϖω isC
2 or ω is a polygon.
Sunto In questo lavoro considero l'espressione dello stress intensity factor proposto da Ore e Burns in [4], e ne studierò le sue proprietà. In particolare dimostrerò che lo stress intensity factor è finito sia se l'insieme di definizione ω è un convesso con bordoC 2 sia se è un poligono.相似文献
7.
Bogdan Szal 《Proceedings Mathematical Sciences》2010,120(5):563-582
We consider the embedding relation between the class W
q
H
β
ω
, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions.
We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl.
11(4) (2008) 749–756] which is a generalization of Tikhonov’s results [Anal. Math.
31 (2005) 183–194]. We also extend the Leindler theorem [Anal. Math.
31 (2005) 175–182] concerning sequences of Fourier coefficients. 相似文献
8.
Ralph deLaubenfels 《Israel Journal of Mathematics》1993,81(1-2):227-255
We show that, whenA generates aC-semigroup, then there existsY such that [M(C)] →Y →X, andA|
Y
, the restriction ofA toY, generates a strongly continuous semigroup, where ↪ means “is continuously embedded in” and ‖x‖[Im(C)]≡‖C
−1
x‖. There also existsW such that [C(W)] →X →W, and an operatorB such thatA=B|
X
andB generates a strongly continuous semigroup onW. If theC-semigroup is exponentially bounded, thenY andW may be chosen to be Banach spaces; in general,Y andW are Frechet spaces. If ρ(A) is nonempty, the converse is also true.
We construct fractional powers of generators of boundedC-semigroups.
We would like to thank R. Bürger for sending preprints, and the referee for pointing out reference [37]. This research was
supported by an Ohio University Research Grant. 相似文献
9.
LetK be a number field. Denote byV
3 a split Del Pezzo surface of degree six overK and by ω its canonical divisor. Denote byW
3 the open complement of the exceptional lines inV
3. LetN
W
s(−ω, X) be the number ofK-rational points onW
3 whose anticanonical heightH
−ω is bounded byX. Manin has conjectured that asymptoticallyN
W
3(−ω, X) tends tocX(logX)3, wherec is a constant depending only on the number field and on the normalization of the height. Our goal is to prove the following
theorem: For each number fieldK there exists a constantc
K such thatN
W
3(−ω, X)≤cKX(logX)3+2r
, wherer is the rank of the group of units ofO
K. The constantc
K is far from being optimal. However, ifK is a purely imaginary quadratic field, this proves an upper bound with a correct power of logX. The proof of Manin's conjecture for arbitrary number fields and a precise treatment of the constants would require a more
sophisticated setting, like the one used by [Peyre] to prove Manin's conjecture and to compute the correct asymptotic constant
(in some normalization) in the caseK=ℚ. Up to now the best result for arbitraryK goes back, as far as we know, to [Manin-Tschinkel], who gives an upper boundN
W
3(−ω,X)≤cXl+ε.
The author would like to express his gratitude to Daniel Coray and Per Salberger for their generous and indispensable support. 相似文献
10.
Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the
group is irreducible andΠ
1 andΠ
2 any two bases of the root system ofW, thenΠ
2 = ±ωΠ
1 for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and
Howlett.
This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991. 相似文献
11.
Samy Abbes 《Semigroup Forum》2008,77(3):482-499
A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a
natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect to congruences are two operations that commute with each other. This contrasts with
the case of general partially ordered sets. 相似文献
12.
Y. Benyamini 《Israel Journal of Mathematics》1978,29(1):24-30
We construct a totally disconnected ω*, norming subsetF of the unit ballB
* of an arbitrary separable Banach space,X, and an operator fromC(F) toC(B*) that “amost” commutes with the natural embeddings ofX. This is used to give a new proof of Milutin's theorem and to prove some new results on complemented subspaces ofC[0, 1] with separable dual. In particular we show that a complemented subspace ofC(ωω), is either isomorphic toC(ωω) or toc
u. 相似文献
13.
Antonio Leaci 《manuscripta mathematica》1992,75(1):429-441
We prove the existence of a minimizing pair for the functionalG defined for every closed setK ⊂R
2 and for every functionu ∈C
1(ω/K) by
where ω is an open set inR
2, λ, μ>0,q≥1,g ∈L
q
(ω) ∩L
p
(ω) withp>2q andH
1 is the 1-dimensional Hausdorff measure. 相似文献
14.
Kazumasa Nomura 《Graphs and Combinatorics》1999,15(1):79-92
. A type II matrix is an n×n matrix W with non-zero entries W
i,j which satisfies , i, j=1, …, n. Two type II matrices W, W′ are said to be equivalent if W′=P
1Δ1
WΔ2
P
2 holds for some permutation matrices P
1, P
2 and for some non-singular diagonal matrices Δ1, Δ2. In the present paper, it is shown that there are up to equivalence exactly three type II matrices in M
5(C).
Received: August 15, 1996 Revised: May 16, 1997 相似文献
15.
We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs
and apply, in Sect. 2, to two situations. First, let W\mathcal{W} be a wedge of ℂ
n
with C
ω
, generic edge ℰ: a holomorphic function f on W\mathcal{W} has always a generalized (hyperfunction) boundary value bv(f) on ℰ, and this coincides with the collection of the boundary values along the discs which have C
ω
transversal intersection with ℰ. Thus Sect. 1 can be applied and yields the uniform continuity at ℰ of f when bv(f) is (separately) continuous. When W\mathcal{W} is only smooth, an additional property, the temperateness of f at ℰ, characterizes the existence of boundary value bv(f) as a distribution on ℰ. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again
the uniform continuity at ℰ of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63–72, 1986), in whose original proof the method of “slicing” by discs is not used. 相似文献
16.
Sonia Natale 《Israel Journal of Mathematics》2007,162(1):253-273
We describe the exponent of a group-theoretical fusion category C = C(G, ω, F, α) associated to a finite group G in terms of group cohomology. We show that the exponent of C divides both e(ω)expG and (expG)2, where e(ω) is the cohomological order of the 3-cocycle ω. In particular, expC divides (dim C)2.
This work was partially supported by CONICET, Fundación Antorchas, Agencia Córdoba Ciencia, ANPCyT and Secyt (UNC). 相似文献
17.
Eugene Wesley 《Israel Journal of Mathematics》1973,14(1):104-114
Using the method of forcing of set theory, we prove the following two theorems on the existence of measurable choice functions:
LetT be the closed unit interval [0,1] and letm be the usual Lebesgue measure defined on the Borel subsets ofT. Theorem1. LetS⊂T×T be a Borel set such that for alltεT,S
t
def={x|(t,x)εS} is countable and non-empty. Then there exists a countable series of Lebesgue-measurable functionsf
n: T→T such thatS
t={fn(t)|nεω} for alltε[0,1],W
x={y|(x,y)εW} is uncountable. Then there exists a functionh:[0,1]×[0,1]→W with the following properties: (a) for each xε[0,1], the functionh(x,·) is one-one and ontoW
x and is Borel measurable; (b) for eachy, h(·, y) is Lebesgue measurable; (c) the functionh is Lebesgue measurable. 相似文献
18.
V. P. Motornyi 《Ukrainian Mathematical Journal》2008,60(8):1270-1284
We obtain a correction to the estimate of approximation of functions from the class W
r
H
ω
, where ω(t) is a convex modulus of continuity such that tω′(t) is nondecreasing, by algebraic polynomials with regard for the location of a point on a segment.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1087–1098, August, 2008. 相似文献
19.
Let X be a compact Riemann surface of genus at most 1, i.e., the Riemann sphere or a torus, and let W ⊊ X be an arbitrary domain. We construct a variety of examples of holomorphic functions g: W → X that satisfy Epstein’s Ahlfors islands property and that have “pathological” dynamical behaviour. In particular, we show that the accumulation set of any curve tending to the boundary of W can be realized as the ω-limit set of a Baker domain of such a function. We furthermore construct Ahlfors islands maps
• | with wandering domains having prescribed ω-limit sets 相似文献
20.
M.M. Cavalcanti V.N. Domingos Cavalcanti 《NoDEA : Nonlinear Differential Equations and Applications》2000,7(3):285-307
This paper is concerned to the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordon-Schr?dinger
damped equations
where ω is a bounded domain of R
n
, n≤ 3, F : R
2→R is a C
1-function; γ, β; θ are constants such that γ, β > 0 and 1 ≤ 2θ≤ 2.
Received January 1999 – Accepted October 1999 相似文献
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