共查询到20条相似文献,搜索用时 296 毫秒
1.
We prove weighted mixed-norm Lqt(W2,px)and Lqt(C2,αx)estimates for 1
0,x∈Rn.x∈Rn,The coefficients a(t)=(aij(t))are just bounded,measurable,symmetric and uniformly elliptic.Furthermore,we show strong,weak type and BMO-Sobolev estimates with parabolic Muckenhoupt weights.It is quite remarkable that most of our results are new even for the classical heat equation?tu?Δu+u=f. 相似文献
2.
Ukrainian Mathematical Journal - We prove that, for any 0 < ?? < 1, there exists a measurable set E?? ? [0, 1], mes (E??) > 1... 相似文献
3.
M. Aguiar 《Discrete and Computational Geometry》2002,27(1):3-28
Infinitesimal bialgebras were introduced by Joni and Rota [JR]. The basic theory of these objects was developed in [Aff1] and [Aff2]. In this paper we present a simple proof of the existence of the cd -index of polytopes, based on the theory of infinitesimal Hopf algebras.For the purpose of this work, the main examples of infinitesimal Hopf algebras are provided by the algebra \ppp of all posets and the algebra k &;lt;ab &;gt; of noncommutative polynomials. We show that k &;lt;ab &;gt; satisfies the following universal property: given a graded infinitesimal bialgebra A and a morphism of algebras ζ A \colon A→ k , there exists a unique morphism of graded infinitesimal bialgebras ψ\colon A → k&;lt;ab &;gt; such that ζ_{1,0}ψ=ζ_A, where ζ_{1,0} is evaluation at (1,0). When the universal property is applied to the algebra of posets and the usual zeta function ζ_{\ppp}(P)=1, one obtains the \abindex of posets ψ\colon \ppp→k &;lt;ab &;gt;.The notion of antipode is used to define an analog of the Möbius function of posets for more general infinitesimal Hopf algebras than \ppp , and this in turn is used to define a canonical infinitesimal Hopf subalgebra, called the eulerian subalgebra. All eulerian posets belong to the eulerian subalgebra of \ppp . The eulerian subalgebra of k &;lt;ab &;gt; is precisely the algebra spanned by c=a+b and d=ab+ba . The existence of the cd -index of eulerian posets is then an immediate consequence of the simple fact that eulerian subalgebras are preserved under morphisms of infinitesimal Hopf algebras.The theory also provides a version of the generalized Dehn—Sommerville equations for more general infinitesimal Hopf algebras than k &;lt;ab &;gt;. 相似文献
4.
For stable FIFO GI/GI/s queues, s ≥ 2, we show that finite (k+1)st moment of service time, S, is not in general necessary for finite kth moment of steady-state customer delay, D, thus weakening some classical conditions of Kiefer and Wolfowitz (1956). Further, we demonstrate that the conditions required
for E[D
k]<∞ are closely related to the magnitude of traffic intensity ρ (defined to be the ratio of the expected service time to the
expected interarrival time). In particular, if ρ is less than the integer part of s/2, then E[D] < ∞ if E[S3/2]<∞, and E[Dk]<∞ if E[Sk]<∞, k≥ 2. On the other hand, if s-1 < ρ < s, then E[Dk]<∞ if and only if E[Sk+1]<∞, k ≥ 1. Our method of proof involves three key elements: a novel recursion for delay which reduces the problem to that of a
reflected random walk with dependent increments, a new theorem for proving the existence of finite moments of the steady-state
distribution of reflected random walks with stationary increments, and use of the classic Kiefer and Wolfowitz conditions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Most bounds for expected delay, E[D], in GI/GI/c queues are modifications of bounds for the GI/GI/1 case. In this paper we exploit a new delay recursion for the GI/GI/c queue to produce bounds of a different sort when the traffic intensity p = λ/μ = E[S]/E[T] is less than the integer portion of the number of servers divided by two. (S AND T denote generic service
and interarrival times, respectively.) We derive two different families of new bounds for expected delay, both in terms of
moments of S AND T. Our first bound is applicable when E[S2] < ∞. Our second bound for the first time does not require finite variance of S; it only involves terms of the form E[Sβ], where 1 < β < 2. We conclude by comparing our bounds to the best known bound of this type, as well as values obtained from
simulation.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Bruno de Malafosse 《Acta Mathematica Hungarica》2006,113(4):289-311
Summary We are interested in the study of the sum <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"10"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"11"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"12"><EquationSource
Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>E+F$
and the product $E*F$, when $E$ and $F$ are of the form $s_{\xi}$, or $s_{\xi}^{\circ}$, or $s_{\xi}^{(c)}$. Then we deal
with the identities $(E+F) (\Delta^{q}) \eg E$ and $(E+F) (\Delta^{q}) \eg F$. Finally we consider matrix transformations
in the previous sets and study the identities $\big((E^{p_{1}}+F^{p_{2}}) (\Delta^{q}),s_{\mu}\big) \eg S_{\alpha^{p_{1}}\pl
\beta^{p_{2}},\mu}$ and $\big(E+F(\Delta^{q}),s_{\gamma}\big) \eg S_{\beta,\gamma}$. 相似文献
7.
Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal
{X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and
fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular
properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed
components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of
the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities
or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and
of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995). 相似文献
8.
Fang Ainong 《数学学报(英文版)》1993,9(3):231-239
We will solve several fundamental problems of Möbius groupsM(R n) which have been matters of interest such as the conjugate classification, the establishment of a standard form without finding the fixed points and a simple discrimination method. Let \(g = \left[ {\begin{array}{*{20}c} a &; b \\ c &; d \\ \end{array} } \right]\) be a Clifford matrix of dimensionn, c ≠ 0. We give a complete conjugate classification and prove the following necessary and sufficient conditions:g is f.p.f. (fixed points free) iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; 0 \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α|<1 and |E?AE 1| ≠ 0;g is elliptic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; \beta \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α| <1 and |E?AE 1|=0;g is parabolic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; 0 \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α|=1; andg is loxodromic iff \(g \sim \left[ {\begin{array}{*{20}c} \alpha &; \beta \\ c &; {\alpha '} \\ \end{array} } \right]\) , |α| >1 or rank (E?AE 1) ≠ rank (E?AE 1,ac ?1+c ?1 d), where α is represented by the solutions of certain linear algebraic equations and satisfies $\left| {c^{ - 1} \alpha '} \right| = \left| {\left( {E - AE^1 } \right)^{ - 1} \left( {\alpha c^{ - 1} + c^{ - 1} \alpha '} \right)} \right|.$ 相似文献
9.
Summary We prove that the mininum surface area of a Voronoi cell in a unit ball
packing in <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\mathbb
E}^3$ is at least $16.1977$. This result provides further
support for the Strong Dodecahedral Conjecture according to which the minimum
surface area of a Voronoi cell in a $3$-dimensional unit ball packing is at
least as large as the surface area of a regular dodecahedron of inradius $1$,
which is about $16.6508\ldots\,$. 相似文献
10.
Alexej P. Pynko 《Archive for Mathematical Logic》2002,41(3):299-307
As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices
with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties
of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply
this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties,
we prove that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the
least non-paraconsistent extension of it and the classical logic.
RID="ID=" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10 RID="ID=" <E5>Key words or phrases:</E5>
Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice
Received 12 August 2000 / Published online: 25 February 2002
RID="
ID=" <E5>Mathematics Subject Classification (2000):</E5> 03B50, 03B53, 03G10
RID="
ID=" <E5>Key words or phrases:</E5> Many-valued logic – Paraconsistent logic – Extension – Prevariety –
Distributive lattice 相似文献
11.
Károly Böröczky Károly Böröczky Jr. Gergely Wintsche 《Periodica Mathematica Hungarica》2006,53(1-2):83-102
Summary Given <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>r>1$,
we search for the convex body of minimal volume in
$\mathbb{E}^3$ that contains a unit ball, and whose extreme points are of
distance at least $r$ from the centre of the unit ball. It is known that the
extremal body is the regular octahedron and icosahedron for suitable values of
$r$. In this paper we prove that if $r$ is close to one then the typical faces
of the extremal body are asymptotically regular triangles. In addition we prove
the analogous statement for the extremal bodies with respect to the surface
area and the mean width. 相似文献
12.
A. Yu. Solynin 《Journal of Mathematical Sciences》1996,78(2):218-222
Theorem 2
Let f(z) ∈ $\mathcal{F}(\rho ,r)$ , f(z) ≠ eiα f(z;pr), α ∈ ?, and let ?(t) be a strictly convex monotone function of t>0. Then $$\int\limits_0^{2\pi } {\Phi (|f'(e^{i\theta } )|)d\theta< } \int\limits_0^{2\pi } {\Phi (|f'(e^{i\theta } ;\rho ,r)|)d\theta } $$ . The proof of this theorem is based on the Golusin-Komatu equation. If E is a continuum in the disk UR={z:|z|<R}, then M (R, E) denotes the conformal module of the doubly connected component of UR/E; let $\varepsilon (m) = \{ E:\overline U _r \subset E \subset U_1 , M(1,E) = M^{ - 1} \} $ .Problem 3
Find the maximum of M(R, E), R>1, and the minimum of cap E over all E in ε(m). This problem was posed by V. V. Kozevnikov in a lecture to the Seminar on Geometric Function Theory at the Kuban University in 1980, and by D. Gaier (see [2]). The solution of this problem is given by the following theorem.Theorem 3
Let $E^* = \underline U _m \cup [m,s]$ . If R>1; E, E* ∈ ε(m) and E ≠ eiα E*, α ∈ ?, then M(R, E)<M(R, E*), capE*<capE. A similar statement is also proved for continua lying in the half-plane. Bibliography: 7 titles. 相似文献13.
14.
Morton E. Harris 《代数通讯》2013,41(8):3668-3671
At some point, after publication, the author realized that the proof of [3, Theorem 5.2] is incorrect. This proof incorrectly adapts the proof of [1, Theorem 4.8] since [3, (5.5)] is incorrect. Using the same proof outline, we correct the proof of [3, Theorem 5.2]. 相似文献
15.
16.
D. A. S. Rees 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(3):437-448
17.
For Brownian motion B denote by Bδ its polygonal approximation corresponding to a partition δ of [0,1]. It is proved that if E(f1|Xt|p dt<∞ for some p>2 then converges to in mean as the mesh |Δ|→0 provided the symmetric (Stratonovich) stochastic integral is determined (in the sense given in [4]) 相似文献
18.
Summary We provide uniform rates of convergence in the central limit theorem for linear negative quadrant dependent (LNQD) random
variables. Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\{X_{n},\allowbreak
n\ge1\}$ be a LNQD sequence of random variables with $EX_{n}=0$, set $S_{n}=\sum_{j=1}^{n}X_{j}$ and $B_{n}^{2}=\Var\, (S_{n})$.
We show that \begin{gather*} \sup_{x} \left|P\left(\frac{S_{n}}{B_{n}}<x\right)-\Phi(x)\right|= O\bigg(n^{-\delta/(2+3\delta)}\vee
\frac{n^{3\delta^{2}/(4+6\delta)}}{B^{2+\delta}_{n}} \sum_{i=1}^{n} E{|X_{i}|}^{2+\delta}\bigg) \end{gather*} under finite
$(2+\delta)$th moment and a power decay rate of covariances. Moreover, by the truncation method, we obtain a Berry--Esseen
type estimate for negatively associated (NA) random variables with only finite second moment. As applications, we obtain another
convergence rate result in the central limit theorem and precise asymptotics in the law of the iterated logarithm for NA sequences,
and also for LNQD sequences. 相似文献
19.
Periodica Mathematica Hungarica - Let a1&;lt;... be an infinite sequence of positive integers, let k≥2 be a fixed integer and denote by Rk(n) the number of solutions of n=ai1+ai2+...+aik.... 相似文献
20.
Xu Shusheng 《分析论及其应用》1989,5(1):33-45
We denote En(f) and E
k
n
(f) the best uniform approximations to a continuous function f defined on [a,b] by the sets of algebraic polynomials of degree
≤n and algebraic polynomials of degree ≤n with the coefficients of xk (k≤n) being zero. In this paper, in cases of r<k and r≥k while [a, b]=[−1,1] (or r<k,k≤r<2k and r>2k while [a,b]=[0, 1]),
we separately discuss the condtions for r-times continuously differentiable function f which enables
. 相似文献