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1.
We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = − δx(t) + pmax
u∈[t − h, t]
x(u) + f(t) where δ, p ∈ R, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 747–754, June, 1998. 相似文献
2.
Let R be a ring, σ an injective endomorphism of R and δ a σ-derivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ,δ] and both rings have the same left uniform dimension.
Presented by S. Montgomery
Mathematics Subject Classification (2000) 16S90.
Jerzy Matczuk: Supported by the Flemish–Polish bilateral agreement BIL 01/31. 相似文献
3.
Then-th commutator for a,b in a ringR is defined inductively as follows: [a,b]1=[a,b]=ab−ba and[a,b]
n=[[a,b]−1,b]. We characterize the ringsR without non-zero nil right ideals in which[a,b]
nis nilpotent or regular for alla,b∈R. We also examine the case whereR is a semiprime ring with involution in which[t
1, t2]nis nilpotent or regular for all tracest
1,t2∈R. 相似文献
4.
Consider the Cauchy problem ∂u(x, t)/∂t = ℋu(x, t) (x∈ℤd, t≥ 0) with initial condition u(x, 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ. Here Δ is the discrete Laplacian, κ∈ (0, ∞) is a diffusion constant,
and ξ = {ξ(x): x∈ℤ
d
} is an i.i.d.random field taking values in ℝ. G?rtner and Molchanov (1990) have shown that if the law of ξ(0) is nondegenerate,
then the solution u is asymptotically intermittent.
In the present paper we study the structure of the intermittent peaks for the special case where the law of ξ(0) is (in the
vicinity of) the double exponential Prob(ξ(0) > s) = exp[−e
s
/θ] (s∈ℝ). Here θ∈ (0, ∞) is a parameter that can be thought of as measuring the degree of disorder in the ξ-field. Our main result
is that, for fixed x, y∈ℤ
d
and t→∈, the correlation coefficient of u(x, t) and u(y, t) converges to ∥w
ρ∥−2
ℓ2Σz ∈ℤd
w
ρ(x+z)w
ρ(y+z). In this expression, ρ = θ/κ while w
ρ:ℤd→ℝ+ is given by w
ρ = (v
ρ)⊗
d
with v
ρ: ℤ→ℝ+ the unique centered ground state (i.e., the solution in ℓ2(ℤ) with minimal l
2-norm) of the 1-dimensional nonlinear equation Δv + 2ρv log v = 0. The uniqueness of the ground state is actually proved only for large ρ, but is conjectured to hold for any ρ∈ (0, ∞).
empty
It turns out that if the right tail of the law of ξ(0) is thicker (or thinner) than the double exponential, then the correlation
coefficient of u(x, t) and u(y, t) converges to δ
x, y
(resp.the constant function 1). Thus, the double exponential family is the critical class exhibiting a nondegenerate correlation
structure.
Received: 5 March 1997 / Revised version: 21 September 1998 相似文献
5.
Let {ξ(t), t ∈ T} be a differentiable (in the mean-square sense) Gaussian random field with E
ξ(t) ≡ 0, D
ξ(t) ≡ 1, and continuous trajectories defined on the m-dimensional interval
T ì \mathbbRm T \subset {\mathbb{R}^m} . The paper is devoted to the problem of large excursions of the random field ξ. In particular, the asymptotic properties of the probability P = P{−v(t) < ξ(t) < u(t), t ∈ T}, when, for all t ∈ T, u(t), v(t) ⩾ χ, χ → ∞, are investigated. The work is a continuation of Rudzkis research started in [R. Rudzkis, Probabilities of large excursions
of empirical processes and fields, Sov. Math., Dokl., 45(1):226–228, 1992]. It is shown that if the random field ξ satisfies certain smoothness and regularity conditions, then P = e−Q
+ Qo(1), where Q is a certain constructive functional depending on u, v, T, and the matrix function R(t) = cov(ξ′(t), ξ′(t)). 相似文献
6.
Further Results on Finitely Generated Projective Modules 总被引:1,自引:0,他引:1
Tong Suo Wu 《数学学报(英文版)》2002,18(2):225-228
In this paper, the exchange rings R whose primitive factor rings are artinian are studied. The following results are proved: for any exchange ring R and any two-sided ideal I of R, K
0(π) : K
0(R)→K
0(R/I) is a group epimorphism with the kernel {[P]−[Q] |P = PI, Q = QI}; there is an isomorphism of ordered groups from K
0(R) to the gorup of all such functions ƒ
P
: X→Q(P∈p(R)), where X is the set of all primitive ideals of R and Q, the rational integers.
Received February 2, 1999, Accepted December 9, 1999 相似文献
7.
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
8.
9.
This paper gives conditions ensuring the existence for an initial value (x
0,v
0) of a solution to the second order differential inclusionx″(t) ∈F[x(t),x′(t)],x(0)=x
0,x′(0)=v
0 such thatx(t) ∈K for allt whereK is a nonempty given subset ofR
n
.
相似文献
10.
Hidetoshi Marubayashi 《Algebras and Representation Theory》2010,13(5):607-622
It is shown that any Ore extension R = V[x;σ,δ] over a total valuation ring V is always v-Bezout which is a generalization of commutative GCD domains. By using this result, a necessary and sufficient
condition are given for R to be fully left bounded. 相似文献
11.
Gérard Ben Arous Jiří Černý Thomas Mountford 《Probability Theory and Related Fields》2006,134(1):1-43
Let E
x
be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w
xy
= ν exp (−βE
x
) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t
w
+t) = X(t
w
)] and ℙ[X(t') = X(t
w
) ∀ t'∈ [t
w
, t
w
+ t]]. We prove the (sub)aging behaviour of these functions when β > 1. 相似文献
12.
V. D. Ponomarev 《Mathematical Notes》1977,22(3):711-713
It is proved that the following conditions are equivalent: the function ϕ [a, b]→R is absolutely upper semicontinuous (see [1]); ϕ is a function of bounded variation with decreasing singular part; there
exists a summable function g: [a, b] → R such that for anyt′∈[a, b] andt″∈[t′, b], we have ϕ(t″)−ϕ(t′)⩽∫
t′
t″
g (s) ds.
Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 395–399, September, 1977. 相似文献
13.
Wen-Kwei Shiue 《Rendiconti del Circolo Matematico di Palermo》2003,52(3):505-509
LetR a prime ring,L a noncentral Lie ideal ofR anda ∈R. Suppose thatd is a nonzero derivation ofR such thata[d(u),u]
k
=0 for allu ∈L, wherek is a fixed positive integer. Thena=0 except when charR=2 and dim
C
RC=4. 相似文献
14.
Chen-Lian Chuang 《代数通讯》2017,45(7):2837-2847
Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. Our aim (Theorem 1) is to determine any automorphism S of R[t;σ,δ] satisfying S(A)?R for a one-sided ideal A≠0 of R by dropping the assumption t∈R[t;σ,δ]. As an application, if R is a domain, it is shown that any X-inner automorphism of R[t;σ,δ] stabilizes R. 相似文献
15.
Let 𝔄 denote the C*-algebra of bounded operators on L
2 ℝ generated by: (i) all multiplications a(M) by functions a∈C[ − ∞, + ∞], (ii) all multiplications by 2π-periodic continuous functions, and (iii) all operator of the form F
−1
b(M)F, where F denotes the Fourier transform and b∈C[ − ∞, + ∞]. A given A ∈ 𝔄 is a Fredholm operator if and only if σ(A) and γ(A) are invertible, where σ denotes the continuous extension of the usual principal symbol, while γ denotes an operator-valued “boundary principal symbol” (the “boundary” here consists of two copies of the circle, one at
each end of the real line). We give two proofs of the fact that K
0(𝔄) is isomorphic to ℤ and that K
1(𝔄) is isomorphic to ℤ ⊕ ℤ . We do it first by computing the connecting mappings in the six-term exact sequence associated
to σ. For the second proof, we show that the image of γ is isomorphic to the direct sum of two copies of the crossed product
, where α denotes the translation-by-one automorphism. Its K-theory can be computed using the Pimsner–Voiculescu exact sequence,
and that information suffices for the analysis of the standard cyclic exact sequence associated to γ.
Received: February 2006 相似文献
16.
Jumela F. Sarmiento 《Graphs and Combinatorics》2002,18(3):621-632
A t(v,k,λ) design is a set of v points together with a collection of its k-subsets called blocks so that t points are contained in exactly λ blocks. PG(n,q), the n-dimensional projective geometry over GF(q) is a 2(q
n
+q
n−1
+⋯+q+1,q
2+q+1, q
n−2
+ q
n−3
+⋯+q+1) design when we take its points as the points of the design and its planes as the blocks of the design. A 2(v,k,λ) design is said to be resolvable if the blocks can be partitioned as ℱ={R
1,R
2,…,R
s
}, where s=λ(v−1)/(k−1) and each R
i
consists of v/k disjoint blocks. If a resolvable design has an automorphism σ which acts as a cycle of length v on the points and ℱσ=ℱ, then the design is said to be point-cyclically resolvable. The design consisting of points and planes of PG(5,2) is shown to be point-cyclically resolvable by enumerating all inequivalent
resolutions which are invariant under a cyclic automorphism group G=〈σ〉 where σ is a cycle of length v. These resolutions are shown to be the only resolutions which admit point-transitive automorphism group.
Received: November 10, 1999 Final version received: September 18, 2000
Acknowledgments. The author would like to thank A. Munemasa for his assistance in writing computer programs on constructing projective spaces
and searching for partial spreads. Moreover, she's thankful to T. Hishida and M.␣Jimbo for helpful discussions and for verifying
the results of this paper.
Present address: Mathematics Department, Ateneo de Manila University, Loyola Heights, Quezon City 1108, Philippines. e-mail: jumela@mathsci.math.admu.edu.ph 相似文献
17.
18.
For two vertices u and v of a connected graph G, the set I[u,v] consists of all those vertices lying on a u−v shortest path in G, while for a set S of vertices of G, the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S is convex if I[S]=S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. The clique number ω(G) is the maximum cardinality of a clique in G. If G is a connected graph of order n that is not complete, then n≥3 and 2≤ω(G)≤con(G)≤n−1. It is shown that for every triple l,k,n of integers with n≥3 and 2≤l≤k≤n−1, there exists a noncomplete connected graph G of order n with ω(G)=l and con(G)=k. Other results on convex numbers are also presented.
Received: August 19, 1998 Final version received: May 17, 2000 相似文献
19.
Mark L. Agranovsky 《Journal d'Analyse Mathématique》2011,113(1):305-329
Let C
t
= {z ∈ ℂ: |z − c(t)| = r(t), t ∈ (0, 1)} be a C
1-family of circles in the plane such that lim
t→0+
C
t
= {a}, lim
t→1−
C
t
= {b}, a ≠ b, and |c′(t)|2 + |r′(t)|2 ≠ 0. The discriminant set S of the family is defined as the closure of the set {c(t) + r(t)w(t), t ∈ [0, 1]}, where w = w(t) is the root of the quadratic equation ̅c′(t)w
2 + 2r′(t)w + c′(t) = 0 with |w| < 1, if such a root exists. 相似文献
20.
Ido Shemer 《Israel Journal of Mathematics》1984,49(4):331-342
Acyclic d-polytope is ad-polytope that is combinatorially equivalent to a polytope whose vertices lie on the moment curve {(t, t
2, …,t
d):t∈R}. Every subpolytope of an even-dimensional cyclic polytope is again cyclic. We show that a polytope [or neighborly polytope]
withv vertices that is not cyclic has at mostd+1 [respectivelyd]d-dimensional cyclic subpolytopes withv−1 vertices, providedd is even andv≧d+5. 相似文献