共查询到20条相似文献,搜索用时 31 毫秒
1.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
2.
Clustering of linearly interacting diffusions and universality of their long-time limit distribution
J. M. Swart 《Probability Theory and Related Fields》2000,118(4):574-594
Let K⊂ℝ
d
(d≥ 1) be a compact convex set and Λ a countable Abelian group. We study a stochastic process X in K
Λ, equipped with the product topology, where each coordinate solves a SDE of the form dX
i
(t) = ∑
j
a(j−i) (X
j
(t) −X
i
(t))dt + σ (X
i
(t))dB
i
(t). Here a(·) is the kernel of a continuous-time random walk on Λ and σ is a continuous root of a diffusion matrix w on K. If X(t) converges in distribution to a limit X(∞) and the symmetrized random walk with kernel a
S
(i) = a(i) + a(−i) is recurrent, then each component X
i
(∞) is concentrated on {x∈K : σ(x) = 0 and the coordinates agree, i.e., the system clusters. Both these statements fail if a
S
is transient. Under the assumption that the class of harmonic functions of the diffusion matrix w is preserved under linear transformations of K, we show that the system clusters for all spatially ergodic initial conditions and we determine the limit distribution of
the components. This distribution turns out to be universal in all recurrent kernels a
S
on Abelian groups Λ.
Received: 10 May 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000 相似文献
3.
A. F. Izé 《Annali di Matematica Pura ed Applicata》1973,96(1):21-39
Summary It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) [(d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying
where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.
Entrata in Redazione il 5 gennaio 1972. 相似文献
4.
Let S ⊂ ℜn+1
be the graph of the function ϕ :[−1, 1]
n → ℜ defined by ϕ (x
1
, …, xn) = ∑
j=1
n
|xj|αj, with1<α
1
≤ … ≤ αn, let σ the Euclidean area measure on S. In this article we study the Lp − Lq boundedness of convolution operators with the singular Borel measure on Rn+1
given by μ (E)=σ (E ∩ S) 相似文献
5.
For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. 相似文献
6.
Reinhard Wolf 《Arkiv f?r Matematik》1997,35(2):387-400
One of our main results is the following: LetX be a compact connected subset of the Euclidean spaceR
n
andr(X, d
2) the rendezvous number ofX, whered
2 denotes the Euclidean distance inR
n
. (The rendezvous numberr(X, d
2) is the unique positive real number with the property that for each positive integern and for all (not necessarily distinct)x
1,x
2,...,x
n
inX, there exists somex inX such that
.) Then there exists some regular Borel probability measure μ0 onX such that the value of ∫
X
d
2(x, y)dμ0 (y) is independent of the choicex inX, if and only ifr(X, d
2) = supμ ∫
X
∫
X
d
2(x, y)dμ(x)dμ(y), where the supremum is taken over all regular Borel probability measures μ onX. 相似文献
7.
Zhen Guo 《数学学报(英文版)》2009,25(1):77-84
Let x : Mn^n→ R^n+1 be an n(≥2)-dimensional hypersurface immersed in Euclidean space Rn+1. Let σi(0≤ i≤ n) be the ith mean curvature and Qn = ∑i=0^n(-1)^i+1 (n^i)σ1^n-iσi. Recently, the author showed that Wn(x) = ∫M QndM is a conformal invariant under conformal group of R^n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. 相似文献
8.
Bernstein-Kantorovich quasi-interpolants K^(2r-1)n(f, x) are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ(f, t)p (1 ≤ p ≤+∞) are obtained. 相似文献
9.
LetW be an algebraically closed filed of characteristic zero, letK be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value, and letA(K) (resp. ℳ(K)) be the set of entire (resp. meromorphic) functions inK. For everyn≥7, we show that the setS
n(b) of zeros of the polynomialx
n−b (b≠0) is such that, iff, g ∈W[x] or iff, g ∈A(K), satisfyf
−1(S
n(b))=g
−1(S
n(b)), thenf
n=g
n. For everyn≥14, we show thatS
n(b) is such that iff, g ∈W({tx}) or iff, g ∈ ℳ(K) satisfyf
−1(S
n(b))=g
−1(S
n(b)), then eitherf
n=g
n, orfg is a constant. Analogous properties are true for complex entire and meromorphic functions withn≥8 andn≥15, respectively.
For everyn≥9, we show that the setY
n(c) of zeros of the polynomial
, (withc≠0 and 1) is an ursim ofn points forW[x], and forA(K). For everyn≥16, we show thatY
n(c) is an ursim ofn points forW(x), and for ℳ(K). We follow a method based on thep-adic Nevanlinna Theory and use certain improvement of a lemma obtained by Frank and Reinders. 相似文献
10.
Asymptotic Upper Bounds for Ramsey Functions 总被引:5,自引:0,他引:5
We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf
a
+1(d), where f
a
+1(d)=∫0
1(((1−t)1/(
a
+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(K
k
+
l
,K
n
)≤ (l+o(1))n
k
/(logn)
k
−1. In particular, r(K
k
, K
n
)≤(1+o(1))n
k
−1/(log n)
k
−2.
Received: May 11, 1998 Final version received: March 24, 1999 相似文献
11.
Michael T. Lacey 《Journal d'Analyse Mathématique》1995,67(1):199-206
LetT
1 andT
2 be commuting invertible ergodic measure preserving flows on a probability space (X, A, μ). For t = (u,ν) ∈ ℝ2, letT
t
=T
1
u
T
2
v
. LetS
1 denote the unit circle in ℝ2 and σ the rotation invariant unit measure on it. Then, forf∈Lp(X) withp>2, the averagesA
t
f(x) = ∫
s
1
f(T
ts
x)σ(ds) conver the integral off for a. e.x, ast tends to 0 or infinity. This extends a result of R. Jones [J], who treated the case of three or more dimensions. 相似文献
12.
The purpose of this paper is to study the L
2 boundedness of operators of the form f ↦ ψ(x) ∫ f (γ
t
(x))K(t)dt, where γ
t
(x) is a C
∞ function defined on a neighborhood of the origin in (t, x) ∈ ℝ
N
× ℝ
n
, satisfying γ
0(x) ≡ x, ψ is a C
∞ cut-off function supported on a small neighborhood of 0 ∈ ℝ
n
, and K is a “multi-parameter singular kernel” supported on a small neighborhood of 0 ∈ ℝ
N
. The goal is, given an appropriate class of kernels K, to give conditions on γ such that every operator of the above form is bounded on L
2. The case when K is a Calderón-Zygmund kernel was studied by Christ, Nagel, Stein, and Wainger; we generalize their conditions to the case
when K has a “multi-parameter” structure. For example, when K is given by a “product kernel.” Even when K is a Calderón- Zygmund kernel, our methods yield some new results. This is the first paper in a three part series, the later
two of which are joint with E. M. Stein. The second paper deals with the related question of L
p
boundedness, while the third paper deals with the special case when γ is real analytic. 相似文献
13.
I. J. Schoenberg 《Israel Journal of Mathematics》1971,10(3):261-274
Letx
v
=cos (πν/n) (v=0, 1, …,n). It is shown that theB-splineM(x)=M(x; x
0
,x
1
,…, x
n
) is such thatM
n
(n)
(x) has a constant absolute value (=2
n−2 (n−1)!) in [−1, 1]. Its integralf
0(x)=∫
−1
x
M(t)dt is shown to have an optimal property that allows to solveexplicitly a certain time-optimal control problem. 相似文献
14.
Marin Gutan 《Semigroup Forum》1996,53(1):173-183
Let σ be a nontrivial permutation of ordern. A semigroupS is said to be σ-permutable ifx
1
x
2
...x
n
=x
σ(1)
x
σ(2)
...x
σ(n)
, for every (x
1
,x
2,...,x
n
)∈S
n
. A semigroupS is called(r,t)-commutative, wherer,t are in ℕ*, ifx
1
...x
r
x
r+1
...x
r+t
=x
r+1
...x
r+t
x
1
...x
r
, for every (x
1
,x
2,...,x
r+t
∈S
r+t
. According to a result of M. Putcha and A. Yaqub ([11]), if σ is a fixed-point-free permutation andS is a σ-permutable semigroup then there existsk ∈ ℕ* such thatS is (1,k)-commutative. In [8], S. Lajos raises up the problem to determine the leastk=k(n) ∈ ℕ* such that, for every fixed-point-free permutation σ of ordern, every σ-permutable semigroup is also (1,k)-commutative. In this paper this problem is solved for anyn less than or equal to eight and also whenn is any odd integer. For doing this we establish that if a semigroup satisfies a permutation identity of ordern then inevitably it also satisfies some permutation identities of ordern+1. 相似文献
15.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
16.
Robert S. Strichartz 《Journal of Geometric Analysis》1991,1(3):269-289
Let μ be a measure on ℝn that satisfies the estimate μ(B
r(x))≤cr
α for allx ∈ ℝn and allr ≤ 1 (B
r(x) denotes the ball of radius r centered atx. Let ϕ
j,k
(ɛ)
(x)=2
nj2ϕ(ɛ)(2
j
x-k) be a wavelet basis forj ∈ ℤ, κ ∈ ℤn, and ∈ ∈E, a finite set, and letP
j
(T)=Σɛ,k
<T,ϕ
j,k
(ɛ)
>ϕ
j,k
(ɛ)
denote the associated projection operators at levelj (T is a suitable measure or distribution). Iff ∈Ls
p(dμ) for 1 ≤p ≤ ∞, we show thatP
j(f dμ) ∈ Lp(dx) and ||P
j
(fdμ)||L
p(dx)≤c2
j((n-α)/p′))||f||L
p(dμ) for allj ≥ 0. We also obtain estimates for the limsup and liminf of ||P
j
(fdμ)||L
p(dx) under more restrictive hypotheses.
Communicated by Guido Weiss 相似文献
17.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
18.
Ignacy Kotlarski 《Annali di Matematica Pura ed Applicata》1966,74(1):129-134
Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x1, x2, …, xn be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals fk(t) = E[ei(t,x
k)], (k=1, 2, …, n): let y1=x1 + xn, y2=x2 + xn, …, yn−1=xn−1 + xn.
If the characteristic functional f(t1, t2, …, tn−1) of the random variables (y1, y2, …, yn−1) does not vanish, then the joint distribution of (y1, y2, …, yn−1) determines all the distributions of x1, x2, …, xn up to change of location. 相似文献
19.
We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove some direct
approximation theorems for functions f such that w
σ
f ∈ L
p
(R), where 1 ≤ p ≤ ∞ and w
σ
(x) = exp(−σx
2), σ > 0. 相似文献
20.
Andreas Basse 《Journal of Theoretical Probability》2009,22(4):811-826
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide
necessary and sufficient conditions on the kernel K for X
t
=∫
K
t
(s) dN
s
to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure on a general space S. We study the semimartingale property of X in three different filtrations. First, the ℱ
X
-semimartingale property is considered, and afterwards the ℱ
X,∞-semimartingale property is treated in the case where X is a moving average process and ℱ
t
X,∞=σ(X
s
:s∈(−∞,t]). Finally, we study a generalization of Gaussian Volterra processes. In particular, we provide necessary and sufficient
conditions on K for the Gaussian Volterra process ∫
−∞
t
K
t
(s) dW
s
to be an ℱ
W,∞-semimartingale (W denotes a Wiener process). Hereby we generalize a result of Knight (Foundations of the Prediction Process, 1992) to the nonstationary case. 相似文献