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1.
LetT(λ) be a bounded linear operator in a Banach spaceX for eachλ in the scalar fieldS. The characteristic value-vector problemT(λ)x = 0 with a normalization conditionφ x = 1, whereφ ε X
*, is formulated as a nonlinear problem inX xS:P(y) ≡ (T(λ)x, φ x - 1) = 0,y= (X, A). Newton's method and the Kantorovič theorem are applied. For this purpose, representations and criteria for existence
ofP′(y)−1 are obtained. The continuous dependence onT of characteristic values and vectors is investigated. A numerical example withT(λ) =A +λB +λ
2
C is presented.
Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462. 相似文献
2.
V. Ya. Yakubov 《Differential Equations》2011,47(3):451-452
We consider three families of equations of the form y″ + (1 + φ(x))y = 0, where the coefficient φ(x) satisfies the condition lim
x→+∞
φ(x) = 0. We obtain solutions of these equations in closed form. We show that the maximum absolute values of solutions grow at
the rate of a logarithmic function, a power-law function, and even an exponential function as x → ∞. 相似文献
3.
For a stochastically continuous stochastic process with independent increments overD[0,T], letN(t,ε) be the number of smaple function jumps that occur in the interval [0,t] of sizes less than −ε or greater than ε, where ε>0. LetM(t,ε)=EN(t,ε), and assumeM(t,0+)=∞ for 0<t≦T. If limε
↓0(M(t,ε)/M(T,ε)) exists and is positive for eacht∈(0,T], then limε
↓0(N(t,ε)/M(T,ε)) for allt∈(0,T] with probability one.
The research of Howard G. Tucker was supported in part by the National Science Foundation, Grant No. MCS76-03591A01. 相似文献
4.
Elbieta Wagner-Bojakowska Wadysaw Wilczyski 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):5-26
We prove that for an arbitrary setA ⊂ ℝ its interior in aψ-density topology equalsA ∩ φβ(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS. 相似文献
5.
The additive subgroup generated by a polynomial 总被引:3,自引:0,他引:3
C. -L. Chuang 《Israel Journal of Mathematics》1987,59(1):98-106
SupposeR is a prime ring with the centerZ and the extended centroidC. Letp(x
1, …,x
n) be a polynomial overC in noncommuting variablesx
1, …,x
n. LetI be a nonzero ideal ofR andA be the additive subgroup ofRC generated by {p(a
1, …,a
n):a
1, …,a
n ∈I}. Then eitherp(x
1, …,x
n) is central valued orA contains a noncentral Lie ideal ofR except in the only one case whereR is the ring of all 2 × 2 matrices over GF(2), the integers mod 2. 相似文献
6.
Let {S
n
} be a random walk on ℤ
d
and let R
n
be the number of different points among 0, S
1,…, S
n
−1. We prove here that if d≥ 2, then ψ(x) := lim
n
→∞(−:1/n) logP{R
n
≥nx} exists for x≥ 0 and establish some convexity and monotonicity properties of ψ(x). The one-dimensional case will be treated in a separate paper.
We also prove a similar result for the Wiener sausage (with drift). Let B(t) be a d-dimensional Brownian motion with constant drift, and for a bounded set A⊂ℝ
d
let Λ
t
= Λ
t
(A) be the d-dimensional Lebesgue measure of the `sausage' ∪0≤
s
≤
t
(B(s) + A). Then φ(x) := lim
t→∞:
(−1/t) log P{Λ
t
≥tx exists for x≥ 0 and has similar properties as ψ.
Received: 20 April 2000 / Revised version: 1 September 2000 / Published online: 26 April 2001 相似文献
7.
Eugene Wesley 《Israel Journal of Mathematics》1973,14(1):104-114
Using the method of forcing of set theory, we prove the following two theorems on the existence of measurable choice functions:
LetT be the closed unit interval [0,1] and letm be the usual Lebesgue measure defined on the Borel subsets ofT. Theorem1. LetS⊂T×T be a Borel set such that for alltεT,S
t
def={x|(t,x)εS} is countable and non-empty. Then there exists a countable series of Lebesgue-measurable functionsf
n: T→T such thatS
t={fn(t)|nεω} for alltε[0,1],W
x={y|(x,y)εW} is uncountable. Then there exists a functionh:[0,1]×[0,1]→W with the following properties: (a) for each xε[0,1], the functionh(x,·) is one-one and ontoW
x and is Borel measurable; (b) for eachy, h(·, y) is Lebesgue measurable; (c) the functionh is Lebesgue measurable. 相似文献
8.
Masahiro Yasumoto 《manuscripta mathematica》1990,66(1):227-235
LetK be an algebraic number field of finite degree andf(X,T) a polynomial overK. For eachφ(X)∈Z[X], we denote byE(φ) the set of all integersa with φ
m
(a) =φ
n
(a) for somem≠n. In this paper, we give a condition for a polynomialφ(X)∈Z[X] to satisfy the following; If forn∈N, there existr∈K anda∈Z−E(φ) such thatf r, φ
m
(a)=0, then there exists a rational functiong(X) overK andk∈N such thatf(g(T)), φ
k
(T))=0 . 相似文献
9.
V. Maiorov 《Advances in Computational Mathematics》2006,25(4):435-450
We consider the manifolds H
n(φ) formed by all possible linear combinations of n functions from the set {φ(A⋅+b)}, where x→Ax+b is arbitrary affine mapping in the space ℝd. For example, neural networks and radial basis functions are the manifolds of type H
n(φ). We obtain estimates for pseudo-dimension of the manifold H
n(φ) for wide collection of the generator function φ. The estimates have the order O(d
2
n) in degree scale, that is the order is proportional to number of parameters of the manifold H
n(φ). Moreover the estimates for ɛ-entropy of the manifold H
n(φ) are obtained.
Mathematics subject classifications (2000) 41A46, 41A50, 42A61, 42C10
V. Maiorov: Supported by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel. 相似文献
10.
Yasushi Taga 《Annals of the Institute of Statistical Mathematics》1971,23(1):355-363
Summary Let {X
n
},n=1,2,..., be a sequence of independent random variables distributed according to a distribution functionF(x) with finite variance,F
n
(x) be the empiric distribution function ofX
1,...,X
n
for eachn, andφ
(n)
*
andφ
* be optimum stratifications corresponding toF
n
(x) andF(x) respectively.
It is shown in this paper thatφ
(a)
*
tends almost surely toφ
* under a suitable criterion.
Institute of Statistical Mathematics 相似文献
11.
Aschbacher’s localC(G; T) theorem asserts that ifG is a finite group withF*(G)=O
2(G), andTεSyl2(G), thenG=C(G; T)K(G), whereC(G; T)=〈N
G
(T
0)|1≠T
0 charT〉 andK(G) is the product of all near components ofG of typeL
2(2
n
) orA
2
n
+1. Near components are also known asχ-blocks or Aschbacher blocks. In this paper we give a proof of Aschbacher’s theorem in the case thatG is aK-group, i.e., in the case that every simple section ofG is isomorphic to one of the known simple groups. Our proof relies on a result of Meierfrankenfeld and Stroth [MS] on quadratic
four-groups and on the Baumann-Glauberman-Niles theorem, for which Stellmacher [St2] has given an amalgam-theoretic proof.
Apart from those results, our proof is essentially self-contained.
For John Thompson
Supported in part by NSF grant #DMS 89-03124, by DIMACS, an NSF Science and Technology Center, funded under contract STC-88-09648,
and by NSA grant #MDA-904-91-H-0043. Prof. Gorenstein died on August 26, 1992. 相似文献
12.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
13.
We study in this paper an M/M/1 queue whose server rate depends upon the state of an independent Ornstein–Uhlenbeck diffusion process (X(t)) so that its value at time t is μ
φ(X(t)), where φ(x) is some bounded function and μ>0. We first establish the differential system for the conditional probability density functions of the couple (L(t),X(t)) in the stationary regime, where L(t) is the number of customers in the system at time t. By assuming that φ(x) is defined by φ(x)=1−ε((x
∧
a/ε)∨(−b/ε)) for some positive real numbers a, b and ε, we show that the above differential system has a unique solution under some condition on a and b. We then show that this solution is close, in some appropriate sense, to the solution to the differential system obtained
when φ is replaced with Φ(x)=1−ε
x for sufficiently small ε. We finally perform a perturbation analysis of this latter solution for small ε. This allows us to check at the first order the validity of the so-called reduced service rate approximation, stating that
everything happens as if the server rate were constant and equal to
.
相似文献
14.
JingMeiGUO 《数学学报(英文版)》2004,20(3):551-556
Let X be a metric space, ε^n(X) be the standard trivial Lip n-bundle over X, and Φ be a Lip automorphism germ of ε^n(X). This paper proves that there is a Lip automorphism Φ‘ of ε^n(X) such that the germ of Φ‘ is Φ. 相似文献
15.
Y. Lacroix 《Israel Journal of Mathematics》2002,132(1):253-263
LetG denote the set of decreasingG: ℝ→ℝ withGэ1 on ]−∞,0], and ƒ
0
∞
G(t)dt⩽1. LetX be a compact metric space, andT: X→X a continuous map. Let μ denone aT-invariant ergodic probability measure onX, and assume (X, T, μ) to be aperiodic. LetU⊂X be such that μ(U)>0. Let τ
U
(x)=inf{k⩾1:T
k
xεU}, and defineG
U
(t)=1/u(U)u({xεU:u(U)τU(x)>t),tεℝ We prove that for μ-a.e.x∈X, there exists a sequence (U
n
)
n≥1
of neighbourhoods ofx such that {x}=∩
n
U
n
, and for anyG ∈G, there exists a subsequence (n
k
)
k≥1
withG
U
n
k
↑U weakly.
We also construct a uniquely ergodic Toeplitz flowO(x
∞,S, μ), the orbit closure of a Toeplitz sequencex
∞, such that the above conclusion still holds, with moreover the requirement that eachU
n
be a cylinder set.
In memory of Anzelm Iwanik 相似文献
16.
W. T. Sulaiman 《Proceedings Mathematical Sciences》2002,112(4):543-550
A general theorem is given which gives the necessary and sufficient conditions satisfied by a sequence (εn) in order to have the series Σa
n
ε
n
summable to |A| whenever Σa
n
is summable to |A| for some summability methodA. 相似文献
17.
V. Yu. Protasov 《Functional Analysis and Its Applications》2011,45(1):46-55
We study continuous subadditive set-valued maps taking points of a linear space X to convex compact subsets of a linear space Y. The subadditivity means that φ(x
1 + x
2) ⊂ φ(x
1) + φ(x
2). We characterize all pairs of locally convex spaces (X, Y) for which any such map has a linear selection, i.e., there exists a linear operator A: X → Y such that Ax ∈ φ(x), x ∈ X. The existence of linear selections for a class of subadditive maps generated by differences of a continuous function is
proved. This result is applied to the Lipschitz stability problem for linear operators in Banach spaces. 相似文献
18.
巫世权 《高校应用数学学报(英文版)》1993,8(2):175-181
Let Cdenote the set of all k-subests of an n-set.Assume Alohtain in Ca,and A lohtain in (A,B) is called a cross-2-intersecting family if |A B≥2 for and A∈A,B∈B.In this paper,the best upper bounds of the cardinalities for non-empty cross-2-intersecting familles of a-and b-subsets are obtained for some a and b,A new proof for a Frankl-Tokushige theorem[6] is also given. 相似文献
19.
Peter Müller 《Israel Journal of Mathematics》1999,109(1):319-337
Letf (X, t)εℚ[X, t] be an irreducible polynomial. Hilbert’s irreducibility theorem asserts that there are infinitely manyt
0εℤ such thatf (X, t
0) is still irreducible. We say thatf (X, t) isgeneral if the Galois group off (X, t) over ℚ(t) is the symmetric group in its natural action. We show that if the degree off with respect toX is a prime ≠ 5 or iff is general of degree ≠ 5, thenf (X, t
0) is irreducible for all but finitely manyt
0εℤ unless the curve given byf (X, t)=0 has infinitely many points (x
0,t
0) withx
0εℚ,t
0εℤ. The proof makes use of Siegel’s theorem about integral points on algebraic curves, and classical results about finite
groups, going back to Burnside, Schur, Wielandt, and others.
Supported by the DFG. 相似文献
20.
Boaz Tsaban 《Israel Journal of Mathematics》2004,140(1):367-374
A topological spaceX has the Fréchet-Urysohn property if for each subsetA ofX and each elementx inĀ, there exists a countable sequence of elements ofA which converges tox. Reznichenko introduced a natural generalization of this property, where the converging sequence of elements is replaced
by a sequence of disjoint finite sets which eventually intersect each neighborhood ofx. In [5], Kočinac and Scheepers conjecture:
The minimal cardinality of a setX of real numbers such thatC
p(X) does not have the weak Fréchet-Urysohn property is equal to b.
(b is the minimal cardinality of an unbounded family in the Baire spaceNℕ.) We prove the Kočinac-Scheepers conjecture by showing that ifC
p(X) has the Reznichenko property, then a continuous image ofX cannot be a subbase for a non-feeble filter on ℕ.
The author is partially supported by the Golda Meir Fund and the Edmund Landau Center for Research in Mathematical Analysis
and Related Areas, sponsored by the Minerva Foundation (Germany). 相似文献