共查询到20条相似文献,搜索用时 0 毫秒
1.
Joseph P. S. Kung 《Annals of Combinatorics》2008,12(2):183-194
Using matroid duality and the critical problem, we show that certain evaluations of the Tutte polynomial of a matroid represented
as a matrix over a finite field GF(q) can be interpreted as weighted sums over pairs f , g of functions defined from the ground set to GF(q) whose difference f – g is the restriction of a linear functional on the column space of the matrix. Similar interpretations are given for the characteristic
polynomial evaluated at q. These interpretations extend and elaborate interpretations for Tutte and chromatic polynomials of graphs due to Goodall
and Matiyasevich.
Received July 14, 2006 相似文献
2.
The theory of functions with values in the algebra of quaternions shows a lot of analogies to the function theory in the complex
one-dimensional case. The class of holomorphic functions is replaced by the set of null solutions of a generalized Cauchy-Riemann
system, the class of monogenic functions. R. Delanghe described in “On Primitives of Monogenic Functions”, Complex Variables and Elliptic Equations, 51, No. 8-11 (2006) the basic ideas of an algorithm to construct monogenic primitives
of the Fueter polynomials. Main goal of this paper is to complete the proposed algorithm for the anti-derivation and to calculate
the primitives explicitly. 相似文献
3.
A. Kananthai 《Southeast Asian Bulletin of Mathematics》2001,25(1):129-134
Consider the Differential Equation of the form ty(n)(t) + my(n–1)(t) + ty(t) = 0 (1) where m is any integer and n 2 for t (–, ). It is found that the values of m make the solutions of (1) to be classical, that is the solutions in the space C(–, ) of continuous functions, or the Distributions which are the solutions in the space DR of Distributions whose supports are bounded on the left.AMS Subject Classification (1991) 46F10 相似文献
4.
S. P. Eveson 《Integral Equations and Operator Theory》2008,62(4):585-589
We show that if V
α (α > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L
2(0, 1) which commutes with V , then TV
α is not supercyclic on L
2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used
by Gallardo-Gutiérrez and Montes-Rodríguez to show that V is not supercyclic. 相似文献
5.
Shuichi Sato 《Integral Equations and Operator Theory》2008,62(3):429-440
We prove certain L
p
-estimates for Littlewood-Paley functions arising from rough kernels. The estimates are useful for extrapolation to prove
L
p
-boundedness of the Littlewood-Paley functions under a sharp kernel condition.
相似文献
6.
Let f be an integral homogeneous polynomial of degree d, and
let
be the level set for each
. For a compact
subset in
), set
We define the notion of Hardy-Littlewood system for the sequence {Vm},
according as the asymptotic of
as
coincides
with the one
predicted by Hardy-Littlewood circle method. Using a recent work of Eskin
and Oh [EO], we then show for a large family of invariant polynomialsf,
the level sets {Vm} are Hardy-Littlewood. In particular, our results yield
a new proof of Siegel mass formula for quadratic forms. 相似文献
7.
Chiung-Jue Sung 《Journal of Geometric Analysis》1998,8(1):143-161
Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside a compact subset. Let h be another
Riemannian metric which is uniformly equivalent to g. It was shown that the dimension of the space of bounded harmonic functions
on (M, h) is finite and is the same as of that under metric g, and the dimension of the space spanned by nonnegative harmonic
functions on (M, h) is also finite and is the same as of that under metric g. Moreover, bases were constructed for both spaces
on (M, h) and precise estimates were established on the asymptotic behavior at infinity for those basic functions. 相似文献
8.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
9.
Thomas A. Willging 《Archiv der Mathematik》2008,91(4):323-329
In this work we discuss Schmutz’s conjecture that in dimension 2 to 8 the distinct norms that occur in the lattices with the
best known sphere packings are strictly greater than those in any other lattice of the same covolume. We see that the ternary
conjecture is not true. However, it seems that there is but one exception: one lattice, where for one length the conjecture
fails.
Received: 11 February 2008, Revised: 20 May 2008 相似文献
10.
Makoto Sakai 《Complex Analysis and Operator Theory》2009,3(2):525-549
We discuss quadrature domains for subharmonic functions and prove the existence of core quadrature domains for certain positive
measures. The core quadrature domains are the smallest quadrature domains as measures and inherit good properties from quadrature
domains with finite volume. We next discuss new balayage for the class of harmonic functions integrable in a neighborhood
of ∞. We give several estimates of balayage measures. The new balayage is introduced to construct quadrature domains for harmonic
functions.
Submitted: June 26, 2008. Accepted: July 24, 2008. 相似文献
11.
A. M. Vershik 《Journal of Fixed Point Theory and Applications》2008,3(2):317-329
We consider the sequence of the hyperspheres M
n
, i.e., the homogeneous transitive spaces of the Cartan subgroup of the group and study the normalized limit of the corresponding sequence of invariant measures m
n
on those spaces. In the case of compact groups and homogeneous spaces, for example, for the classical pairs (SO(n), S
n-1), n = 1, 2, … , the limit of the corresponding measures is the classical infinite-dimensional Gaussian measure; this is the well-known
Maxwell-Poincaré lemma. Simultaneously the Gaussian measure is a unique (up to a scalar) invariant measure with respect to
the action of the infinite orthogonal group O(∞). This coincidence implies the asymptotic equivalence between grand and small canonical ensembles for the series of the
pairs (SO(n), S
n-1). Our main result shows that the situation for noncompact groups, for example for the case , is completely different: the limit of the measures m
n
does not exist in the literal sense, and we show that only a normalized logarithmic limit of the Laplace transforms of those
measures does exist. At the same time, there exists a measure which is invariant with respect to a continuous analogue of
the Cartan subgroup of the group GL(∞), the so-called infinite-dimensional Lebesgue measure (see [7]). This difference is an evidence for non-equivalence between
the grand and small canonical ensembles in the noncompact case.
To my friend Dima Arnold 相似文献
12.
Serdar Beji 《Mediterranean Journal of Mathematics》2008,5(2):163-172
A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial
of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution
for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel’s proof,
the method produces no solution for the quintic equation.
相似文献
13.
Suppose that
is a 0-symmetric convex body
which denes the usual norm
on
. Let also
be a measurable set of positive upper density .
We show that if the body K is not a polytope, or if it is a polytope with
many faces (depending on ), then the distance set
contains all points t t0 for some positive number t0 . This was proved
by Furstenberg, Katznelson and Weiss, by Falconer and Marstrand and
by Bourgain in the case where K is the Euclidean ball in any dimension
greater than 1. As corollaries we obtain (a) an extension to any dimension
of a theorem of Iosevich and Laba regarding distance sets with respect to
convex bodies of well-distributed sets in the plane, and also (b) a new proof
of a theorem of Iosevich, Katz and Tao about the nonexistence of Fourier
spectra for smooth convex bodies with positive curvature. 相似文献
14.
The classical Fischer decomposition of polynomials on Euclidean space makes it possible to express any polynomial as a sum
of harmonic polynomials multiplied by powers of |x|2. A deformation of the Laplace operator was recently introduced by Ch.F. Dunkl. It has the property that the symmetry with
respect to the orthogonal group is broken to a finite subgroup generated by reflections (a Coxeter group). It was shown by
B. ?rsted and S. Ben Said that there is a deformation of the Fischer decomposition for polynomials with respect to the Dunkl
harmonic functions. In Clifford analysis, a Dunkl version of the Dirac operator was introduced and studied by P. Cerejeiras,
U. K?hler and G. Ren. The aim of the article is to describe an analogue of the Fischer decomposition for solutions of the
Dunkl Dirac operator. The main methods used are coming from representation theory, in particular, from ideas connected with
Howe dual pairs.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš to recall our long lasting cooperation on
many topics in mathematics
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117.
Received: October, 2007. Accepted: February, 2008. 相似文献
15.
C. J. Maxson 《Archiv der Mathematik》2008,91(5):385-391
For a group G, let M(G) denote the near-ring of functions on G. We characterize all maximal subnear-rings of M(G) and show that for many classes of groups, E(G), the near-ring generated by the semigroup, End(G) of G, is never maximal as a subnear-ring of M
0 (G).
Received: 25 April 2008 相似文献
16.
The exact bounds are obtained for the norm of the singular integral operator S on the family of rays originating at the same point. These bounds, with the use of the localization technique, are then extended
to the essential norm of S on piecewise smooth curves with finitely many points of self intersection.
Submitted: April 13, 2007. Accepted: September 19, 2007. 相似文献
17.
Flower snarks and Goldberg snarks are two infinite families of cyclically 5–edge–connected cubic graphs with girth at least
five and chromatic index four. For any odd integer k, k > 3, there is a Flower snark, say J
k
, of order 4k and a Goldberg snark, say B
k
, of order 8k. We determine the automorphism groups of J
k
and B
k
for every k and prove that they are isomorphic to the dihedral group D
4k
of order 4k.
Research performed within the activity of INdAM–GNSAGA with the financial support of the Italian Ministry MIUR, project “Strutture
Geometriche, Combinatoria e loro Applicazioni”. 相似文献
18.
Cláudia F. R. Concordido Dinamérico P. Pombo 《Rendiconti del Circolo Matematico di Palermo》2002,51(2):213-236
Criteria for the equicontinuity of sets of multilinear mappings between topological modules are studied, as well as topological
modules of continuous multilinear mappings. As a consequence, criteria for the equicontinuity of sets of homogeneous polynomials
between topological modules are also studied, as well as topological modules of continuous homogeneous polynomials. 相似文献
19.
Hiroyuki Chihara 《Integral Equations and Operator Theory》2009,63(3):321-335
We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex
n-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj?strand. We also obtain
the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order
three are in the Wiener algebra of Sj?strand. Our method of proofs is based on the pseudodifferential calculus and the heat
flow determined by the phase function of the Bargmann transform.
Supported by the JSPS Grant-in-Aid for Scientific Research #20540151. 相似文献
20.
Trieu Le 《Integral Equations and Operator Theory》2009,63(4):547-555
For any α > −1, let A2α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|2)α. We show that if all except possibly one of the Toeplitz operators are diagonal with respect to the standard orthonormal basis of A2α and has finite rank, then one of the functions must be the zero function.
相似文献