共查询到20条相似文献,搜索用时 93 毫秒
1.
Tetsushi Matsui Akihiro Higashitani Yuuki Nagazawa Hidefumi Ohsugi Takayuki Hibi 《Journal of Algebraic Combinatorics》2011,34(4):721-749
Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of
the Ehrhart polynomials not merely supports the conjecture of Beck et al. that all roots α of Ehrhart polynomials of polytopes of dimension D satisfy −D≤Re(α)≤D−1, but also reveals some interesting phenomena for each type of polytope. Here we present two new conjectures: (1) the roots
of the Ehrhart polynomial of an edge polytope for a complete multipartite graph of order d lie in the circle
|z+\fracd4| £ \fracd4|z+\frac{d}{4}| \le \frac{d}{4} or are negative integers, and (2) a Gorenstein Fano polytope of dimension D has the roots of its Ehrhart polynomial in the narrower strip
-\fracD2 £ Re(a) £ \fracD2-1-\frac{D}{2} \leq \mathrm{Re}(\alpha) \leq \frac{D}{2}-1. Some rigorous results to support them are obtained as well as for the original conjecture. The root distribution of Ehrhart
polynomials of each type of polytope is plotted in figures. 相似文献
2.
Regularizing and decay rate estimates for solutions to the Cauchy problem of the Debye–Hückel system
Jihong Zhao Qiao Liu Shangbin Cui 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(1):1-18
In this paper we establish some regularizing and decay rate estimates for mild solutions of the Debye–Hückel system. We prove
that if the initial data belong to the critical Lebesgue space
L\fracn2(\mathbbRn){L^{\frac{n}{2}}(\mathbb{R}^{n})} , then the L
q
-norm (
\fracn2 £ q £ ¥{\frac{n}{2} \leq q \leq \infty}) of the βth order spatial derivative of mild solutions are majorized by
K1(K2|b|)|b|t-\frac|b|2-1+\fracn2q{K_{1}(K_{2}|\beta|)^{|\beta|}t^{-\frac{|\beta|}{2}-1+\frac{n}{2q}}} for some constants K
1 and K
2. These estimates particularly imply that mild solutions are analytic in the space variable, and provide decay estimates in
the time variable for higher-order derivatives of mild solutions. We also prove that similar estimates also hold for mild
solutions whose initial data belong to the critical homogeneous Besov space
[(B)\dot]-2+\fracnpp,¥(\mathbbRn){\dot{B}^{-2+\frac{n}{p}}_{p,\infty}(\mathbb{R}^n)} (
\fracn2 < p < n{\frac{n}{2} < p < n}). 相似文献
4.
In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if
div( \fracu|u|) \mathrm{div}( \frac{u}{|u|}) belongs to
L\frac21-r( 0,T;[(X)\dot]r( \mathbbR3) ) L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) with 0≤r≤1, then the weak solution actually is regular and unique. 相似文献
5.
Let S be a set of n points in ℝ3, no three collinear and not all coplanar. If at most n−k are coplanar and n is sufficiently large, the total number of planes determined is at least
1+k\binomn-k2-\binomk2(\fracn-k2)1+k\binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2}). For similar conditions and sufficiently large n, (inspired by the work of P.D.T.A. Elliott in Acta Math. Sci. Hung. 18:181–188, 1967) we also show that the number of spheres determined by n points is at least
1+\binomn-13-t3orchard(n-1)1+\binom{n-1}{3}-t_{3}^{\mathrm{orchard}}(n-1), and this bound is best possible under its hypothesis. (By t3orchard(n)t_{3}^{\mathrm{orchard}}(n), we are denoting the maximum number of three-point lines attainable by a configuration of n points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines
and circles. 相似文献
6.
Jan A. van Casteren 《Journal of Evolution Equations》2011,11(2):457-476
Let
(tj)j ? \mathbbN{\left(\tau_j\right)_{j\in\mathbb{N}}} be a sequence of strictly positive real numbers, and let A be the generator of a bounded analytic semigroup in a Banach space X. Put
An=?j=1n(I+\frac12 tjA) (I-\frac12 tjA)-1{A_n=\prod_{j=1}^n\left(I+\frac{1}{2} \tau_jA\right) \left(I-\frac{1}{2} \tau_jA\right)^{-1}}, and let x ? X{x\in X}. Define the sequence
(xn)n ? \mathbbN ì X{\left(x_n\right)_{n\in\mathbb{N}}\subset X} by the Crank–Nicolson scheme: x
n
= A
n
x. In this paper, it is proved that the Crank–Nicolson scheme is stable in the sense that
supn ? \mathbbN||Anx|| < ¥{\sup_{n\in\mathbb{N}}\left\Vert A_nx\right\Vert<\infty}. Some convergence results are also given. 相似文献
7.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
\frac1j(N) ? 0 £ m < Ngcd(m,N)=1 |S(m,N)|\frac{1}{\varphi(N)} \sum_{\mathop{\mathop{ 0 \le m< N}}\limits_{\gcd(m,N)=1}} \vert S(m,N)\vert
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
Ah(Q)=\frac1?\fracaq ? FQh(\fracaq) ×?\fracaq ? FQh(\fracaq) |s(a¢,q¢)-s(a,q)|A_{h}(Q)=\frac{1}{\sum_{\frac{a}{q} \in {\cal F}_{Q}}h\left(\frac{a}{q}\right)} \times \sum_{\frac{a}{q} \in {\cal F}_{\!Q}}h\left(\frac{a}{q}\right) \vert s(a^{\prime},q^{\prime})-s(a,q)\vert
, where
h:[0,1] ? \Bbb Ch:[0,1] \rightarrow {\Bbb C}
is a continuous function with
ò01 h(t) d t 1 0\int_0^1 h(t) \, {\rm d} t \ne 0
,
\fracaq{\frac{a}{q}}
runs over
FQ{\cal F}_{\!Q}
, the set of Farey fractions of order Q in the unit interval [0,1] and
\fracaq < \fraca¢q¢{\frac{a}{q}}<\frac{a^{\prime}}{q^{\prime}}
are consecutive elements of
FQ{\cal F}_{\!Q}
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
8.
In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi.
Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan’s congruences for the unrestricted
partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0,
pod(32a+3n+\frac23×32a+2+18) o 0 (mod 3).\mathrm{pod}\biggl(3^{2\alpha+3}n+\frac{23\times3^{2\alpha+2}+1}{8}\biggr)\equiv 0\ (\mathrm{mod}\ 3). 相似文献
9.
The class of finitely presented groups
is an extension of the class of triangle groups studied recently. These groups are finite and their orders depend on the Lucas
numbers. In this paper, by considering the three presentations
10.
Alina Sîntămărian 《Numerical Algorithms》2007,46(2):141-151
The purpose of this paper is to evaluate the limit γ(a) of the sequence , where a ∈ (0, + ∞ ).
相似文献
11.
The polynomial null solutions are studied of the higher spin Dirac operator Q k,l acting on functions taking values in an irreducible representation space for Spin(m) with highest weight ${(k + \frac{1}{2},l+\frac{1}{2},\frac{1}{2},\ldots,\frac{1}{2})}
12.
In this paper we consider the Cauchy problem for a higher order modified Camassa–Holm equation. By using the Fourier restriction
norm method introduced by Bourgain, we establish the local well-posedness for the initial data in the H
s
(R) with ${s > -n+\frac{5}{4},\,n\in {\bf N}^{+}.}${s > -n+\frac{5}{4},\,n\in {\bf N}^{+}.} As a consequence of the conservation of the energy ||u||H1(R),{{||u||_{H^{1}(R)},}} we have the global well-posedness for the initial data in H
1(R). 相似文献
13.
This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form
, where A generates a strongly continuous semigroup in a Banach space
, F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e
2π
iℳ(f)⊂e
2π
iℳ(u). If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given. 相似文献
14.
Y. C. Wang 《Acta Mathematica Hungarica》2012,135(3):248-269
Let Hk\mathcal{H}_{k} denote the set {n∣2|n,
n\not o 1 (mod p)n\not\equiv 1\ (\mathrm{mod}\ p) ∀ p>2 with p−1|k}. We prove that when
X\frac1120(1-\frac12k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X, almost all integers
n ? \allowbreak Hk ?(X, X+H]n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]} can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when
X\frac1120(1-\frac1k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X, almost all integers n∈(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3. 相似文献
15.
Nikolaos Bournaveas Timothy Candy 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(1):67-78
It is known from Czubak (Anal PDE 3(2):151–174, 2010) that the space–time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} for ${s>\frac{1}{4}}${s>\frac{1}{4}}. Here we prove local well-posedness for arbitrary initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} with ${s>\frac{1}{4}}${s>\frac{1}{4}} in the Lorenz gauge. 相似文献
16.
We prove that if u
1,u
2:(0,∞)×ℝ
d
→(0,∞) are sufficiently well-behaved solutions to certain heat inequalities on ℝ
d
then the function u:(0,∞)×ℝ
d
→(0,∞) given by
also satisfies a heat inequality of a similar type provided
. On iterating, this result leads to an analogous statement concerning n-fold convolutions. As a corollary, we give a direct heat-flow proof of the sharp n-fold Young convolution inequality and its reverse form.
Both authors were supported by EPSRC grant EP/E022340/1. 相似文献
17.
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter–Reissner–Nordstr?m black holes.
We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering
matrix S(λ) at a fixed energy λ ≠ 0. More precisely, we consider the partial wave scattering matrices S(λ, n) (here λ ≠ 0 is the fixed energy and
n ? \mathbbN*{n \in \mathbb{N}^{*}} denotes the angular momentum) defined as the restrictions of the full scattering matrix on a well chosen basis of spin-weighted
spherical harmonics. We prove that the mass M, the square of the charge Q
2 and the cosmological constant Λ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge
of either the transmission coefficients T(λ, n), or the reflexion coefficients R(λ, n) (resp. L(λ, n)), for all n ? L{n \in {\mathcal{L}}} where L{\mathcal{L}} is a subset of
\mathbbN*{\mathbb{N}^{*}} that satisfies the Müntz condition
?n ? L\frac1n = +¥{\sum_{n \in{\mathcal{L}}}\frac{1}{n} = +\infty} . Our main tool consists in complexifying the angular momentum n and in studying the analytic properties of the “unphysical” scattering matrix S(λ, z) in the complex variable z. We show, in particular, that the quantities
\frac1T(l,z){\frac{1}{T(\lambda,z)}},
\fracR(l,z)T(l,z){\frac{R(\lambda,z)}{T(\lambda,z)}} and
\fracL(l,z)T(l,z){\frac{L(\lambda,z)}{T(\lambda,z)}} belong to the Nevanlinna class in the region ${\{z \in \mathbb{C}, Re(z) > 0 \}}${\{z \in \mathbb{C}, Re(z) > 0 \}} for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstruction
formulae for the surface gravities of the event and cosmological horizons of the black hole which have an important physical
meaning in the Hawking effect. 相似文献
18.
András Kroó 《Constructive Approximation》2012,35(2):181-200
We consider the problem of the approximation of regular convex bodies in ℝ
d
by level surfaces of convex algebraic polynomials. Hammer (in Mathematika 10, 67–71, 1963) verified that any convex body in ℝ
d
can be approximated by a level surface of a convex algebraic polynomial. In Jaen J. Approx. 1, 97–109, 2009 and subsequently in J. Approx. Theory 162, 628–637, 2010 a quantitative version of Hammer’s approximation theorem was given by showing that the order of approximation of convex bodies
by convex algebraic level surfaces of degree n is
\frac1n\frac{1}{n}. Moreover, it was also shown that whenever the convex body is not
regular (that is, there exists a point on its boundary at which the convex body possesses two distinct supporting hyperplanes), then
\frac1n\frac{1}{n} is essentially the sharp rate of approximation. This leads to the natural question whether this rate of approximation can
be improved further when the convex body is regular. In this paper we shall give an affirmative answer to this question. It
turns out that for regular convex bodies a o(1/n) rate of convergence holds. In addition, if the body satisfies the condition of C
2-smoothness the rate of approximation is
O(\frac1n2)O(\frac{1}{n^{2}}). 相似文献
19.
Li Wang 《Journal of Theoretical Probability》2010,23(2):401-416
We establish an almost sure scaling limit theorem for super-Brownian motion on ℝ
d
associated with the semi-linear equation
ut=\frac12Du+bu-au2u_{t}=\frac{1}{2}\Delta u+\beta u-\alpha u^{2}
, where α and β are positive constants. In this case, the spectral theoretical assumptions required in Chen et al. (J. Funct. Anal. 254:1988–2019,
2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in ℝ
d
. 相似文献
20.
Sergey Bereg Prosenjit Bose Adrian Dumitrescu Ferran Hurtado Pavel Valtr 《Discrete and Computational Geometry》2009,41(4):513-532
Given a finite set of points S in ℝ
d
, consider visiting the points in S with a polygonal path which makes a minimum number of turns, or equivalently, has the minimum number of segments (links).
We call this minimization problem the minimum link spanning path problem. This natural problem has appeared several times in the literature under different variants. The simplest one is
that in which the allowed paths are axis-aligned. Let L(S) be the minimum number of links of an axis-aligned path for S, and let G
n
d
be an n×…×n grid in ℤ
d
. Kranakis et al. (Ars Comb. 38:177–192, 1994) showed that L(G
n
2)=2n−1 and
and conjectured that, for all d≥3,
We prove the conjecture for d=3 by showing the lower bound for L(G
n
3). For d=4, we prove that
For general d, we give new estimates on L(G
n
d
) that are very close to the conjectured value. The new lower bound of
improves previous result by Collins and Moret (Inf. Process. Lett. 68:317–319, 1998), while the new upper bound of
differs from the conjectured value only in the lower order terms.
For arbitrary point sets, we include an exact bound on the minimum number of links needed in an axis-aligned path traversing
any planar n-point set. We obtain similar tight estimates (within 1) in any number of dimensions d. For the general problem of traversing an arbitrary set of points in ℝ
d
with an axis-aligned spanning path having a minimum number of links, we present a constant ratio (depending on the dimension d) approximation algorithm.
Work by A. Dumitrescu was partially supported by NSF CAREER grant CCF-0444188.
Work by F. Hurtado was partially supported by projects MECMTM2006-01267 and Gen. Cat. 2005SGR00692.
Work by P. Valtr was partially supported by the project 1M0545 of the Ministry of Education of the Czech Republic. 相似文献
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