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951.
An explicit coloring of the edges of Kn is constructed such that every copy of K4 has at least four colors on its edges. As n , the number of colors used is n1/2+o(1). This improves upon the previous bound of O(n2/3) due to Erds and Gyárfás obtained by probabilistic methods. The exponent 1/2 is optimal, since it is known that at least (n1/2) colors are required in such a coloring.The coloring is related to constructions giving lower bounds for the multicolor Ramsey number rk(C4). It is more complicated however, because of restrictions imposed on interactions between color classes.* Research supported in part by NSF Grant No. DMS–9970325. 相似文献
952.
We consider the poset SO(n) of all words over an n-element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i. e. there is a theorem of Kruskal–Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip-order can be chosen.Daykin introduced the V-order which generalizes the vip-order to the n2 case. He conjectured that the V-order gives a Kruskal–Katona type theorem for SO(n).We show that this conjecture fails for all n3 by explicitly giving a counterexample. Based on this, we prove that for no n3 the subword order SO(n) is a Macaulay poset. 相似文献
953.
There exists a constant C such that for every d-degenerate graphs G
1 and G
2 on n vertices, Ramsey number R(G
1,G
2) is at most Cn, where is the minimum of the maximum degrees of G
1 and G
2.* The work of this author was supported by the grants 99-01-00581 and 00-01-00916 of the Russian Foundation for Fundamental Research and the Dutch-Russian Grant NWO-047-008-006. The work of this author was supported by the NSF grant DMS-9704114. 相似文献
954.
Philippe?RambourEmail author Abdellatif?Seghier 《Integral Equations and Operator Theory》2004,50(1):83-114
We consider large finite Toeplitz matrices with symbols of the form (1– cos )p f() where p is a natural number and f is a sufficiently smooth positive function. By employing techniques based on the use of predictor polynomials, we derive exact and asymptotic formulas for the entries of the inverses of these matrices. We show in particular that asymptotically the inverse matrix mimics the Green kernel of a boundary value problem for the differential operator
Submitted: June 20, 2003 相似文献
955.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
956.
We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants. 相似文献
957.
In this paper we consider a class of integral operators whose kernels
satisfy certain generalizations of Hörmander condition and establish their
regularity results. 相似文献
958.
Fabiano?B.?BritoEmail author Pablo?M.?Chacón A. M.?Naveira 《Commentarii Mathematici Helvetici》2004,79(2):300-316
A unit vector field X on
a Riemannian manifold determines a submanifold in the unit
tangent bundle. The volume of X is
the volume of this submanifold for the induced
Sasaki metric. It is known that the parallel fields are the trivial minima.
In this paper, we obtain a lower bound for the volume in terms
of the integrals of the 2i-symmetric
functions of the second fundamental form of the
orthogonal distribution to the field X.
In the spheres ${\textbf {S}}^{2k+1}$, this lower bound is independent of
X.
Consequently, the volume of a unit vector
field on an odd-sphere is always greater than the volume of the radial field.
The main theorem on volumes is applied also to hyperbolic
compact spaces, giving a non-trivial lower bound of the volume of unit fields. 相似文献
959.
We study a continuum model for epitaxial growth of thin films in which the slope of mound structure of film surface increases. This model is a diffusion equation for the surface height profile h which is assumed to satisfy the periodic boundary condition. The equation happens to possess a Liapunov or free-energy functional. This functional consists of the term | h|2, which represents the surface diffusion, and - log (1 + | h|2), which describes the effect of kinetic asymmetry in the adatom attachment-detachment. We first prove for large time t that the interface width---the standard deviation of the height profile---is bounded above by O(t1/2), the averaged gradient is bounded above by O(t1/4), and the averaged energy is bounded below by O(- log t). We then consider a small coefficient 2 of | h|2 with = 1/L and L the linear size of the underlying system, and study the energy asymptotics in the large system limit 0. We show that global minimizers of the free-energy functional exist for each > 0, the L2-norm of the gradient of any global minimizer scales as O(1/), and the global minimum energy scales as O( log ). The existence of global energy minimizers and a scaling argument are used to construct a sequence of equilibrium solutions with different wavelengths. Finally, we apply our minimum energy estimates to derive bounds in terms of the linear system size L for the saturation interface width and the corresponding saturation time. 相似文献
960.
Louis?Dupaigne Augusto?C.?Ponceaugponce@math.rutgers.edu" title="ponce@ann.jussieu.fr augponce@math.rutgers.edu" itemprop="email" data-track="click" data-track-action="Email author" data-track-label="">Email author 《Selecta Mathematica, New Series》2004,10(3):341-358
We present several extensions of the Brezis–Lions Lemma on removable singularities. We also give a positive answer to a question raised by H. Brezis and M. Marcus about an inverse maximum principle for the Laplacian. 相似文献