共查询到20条相似文献,搜索用时 35 毫秒
1.
I. T. Kiguradse 《Annali di Matematica Pura ed Applicata》1969,81(1):169-191
Summary The sufficient conditions for the existence and uniqueness of solution u(t) of the differential equation u″=f(t, u, u′), are
established, satisfying the condition
u(t)= =u0, u(t)≥0 and u′(t)≥0 for t ε (0,+∞).
Entrata in Redazione il 26 aprile 1968. 相似文献
2.
Massimo Cicognani 《Annali dell'Universita di Ferrara》1987,33(1):259-292
Riassunto Si studia il problema di Cauchy per operatori differenziali lineari del secondoordine strettamente iperbolici con coefficienti
lipschitziani rispetto al tempo. Si trovano risultati di buona positura del problema negli spazi
gli ordinari spazi di Sobolev, e risultati di propagazione della regolaritàC
∞ della soluzione.
Summary We study the Cauchy problem for linear second order strictly hyperbolic differential operators whose coefficients are assumed to be Lipschitz-continuous with respect to time. We prove results ofH ∞ andH −∞ well-posedness, the usual Sobolev spaces, and results on the propagation ofC ∞-regularity of the solution.相似文献
3.
We prove that if is the error of a simple quadrature formula and ω(ε, δ)1 is the integral modulus of continuity, then, for any δ ≥/π andn,r = 1, 2, …, the following equality is true: whereD
r
is the Bernoulli kernel. 相似文献
4.
Achiya Dax 《BIT Numerical Mathematics》1997,37(3):600-622
This paper presents a proximal point algorithm for solving discretel
∞ approximation problems of the form minimize ∥Ax−b∥∞. Let ε∞ be a preassigned positive constant and let ε
l
,l = 0,1,2,... be a sequence of positive real numbers such that 0 < ε
l
< ε∞. Then, starting from an arbitrary pointz
0, the proposed method generates a sequence of points z
l
,l= 0,1,2,..., via the rule
. One feature that characterizes this algorithm is its finite termination property. That is, a solution is reached within
a finite number of iterations. The smaller are the numbers ε
l
the smaller is the number of iterations. In fact, if ε
0
is sufficiently small then z1 solves the original minimax problem.
The practical value of the proposed iteration depends on the availability of an efficient code for solving a regularized minimax
problem of the form minimize
where ∈ is a given positive constant. It is shown that the dual of this problem has the form maximize
, and ify solves the dual thenx=A
T
y solves the primal. The simple structure of the dual enables us to apply a wide range of methods. In this paper we design
and analyze a row relaxation method which is suitable for solving large sparse problems. Numerical experiments illustrate
the feasibility of our ideas. 相似文献
5.
Deh-phone Kung Hsing 《Annali di Matematica Pura ed Applicata》1976,109(1):235-245
Summary We consider the system(L):
, t ⩾ p, y(t)=f(t), t⩽0, where y is an n-vector and each Ai, B(t) are n × n matrices. System(L) generates a semigroup by means of Ttf(s)=y (t+s, f), f(s) ∈ BCl(− ∞, 0]. Under some hypotheses concerning the roots ofdet
where
is the Laplace transform of B(t), the asymptotic behavior of y(t) is discussed. Two typical results are: Theorem 3.1: suppose
∥B(t)∥ ɛ L1[0, ∞),
thendet
forRe λ>0 iff for every ɛ>0 there is an Mɛ>0 such that ∥Ttf∥l ⩽ ⩽ Mɛ
exp [ɛt]∥f∥l for t ⩾ 0. Corollary 3.1.1: suppose
exp [at]B(t) ∈ ∈ L1[0, ∞) for some a>0 anddet
forRe λ>−a. Then the solution of(L) is exponentially asymptotically stable.
Entrata in Redazione il 21 marzo 1975.
The author is grateful to ProfessorC. Corduneanu for suggesting this problem and for many helpful discussions during the preparation of the paper. 相似文献
6.
In this paper we consider
, in one case that fx
0 (t) is a ΛBMV function on [0, ∞], and in another case thatfεL
1
m-1(Rn) and
when |k|=m−1 and f(x)=0 when |x−x0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]). 相似文献
7.
The main result of this paper is that if a sequence of complex numbers (a
n)n≥0 satisfies
and % MathType!MTEF!2!1!+-
for some integerr≥0, thena
n=0 for alln>r. As an application, we deduce a localized form of a theorem of Allan about nilpotent elements in Banach algebras, and this
in turn leads to an invariant-subspace theorem. As a further application, we prove a variant of Carleman's theorem on the
unique determination of probability distributions by their moments. The paper concludes with a quantitative form of the main
result.
Research supported by grants from the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR of Québec,
and the Ministry of Education of Québec (co-opération Québec-France). 相似文献
8.
Let A be a Noetherian local ring and I an ideal of A. In this paper we use a slightly generalized notion of a symbolic power
I(n) of I and considerR =
. First we characterize the property of R to be Noetherian by an equimultiplicity condition of some symbolic power I(k). The main purpose of this note is to explore the problem whenR,R′ =
and
are Cohen-Macaulay or Gorenstein algebras in the case that A is a normal domain and ht I=1.
Partially supported by the Max-Planck-Institute of Mathematics Bonn.
Supported by a grant of the Heinrich Hertz-Stiftung.
Supported by a grant of the Alexander von Humboldt-Stiftung. 相似文献
9.
For positive integersn, m and realp≥1, let
Upper and lower bounds for this quantity are derived, extending results of Brown and Spencer forB
1(n,n), corresponding to the Gale-Berlekamp switching problem. For a Minkowski spaceM of dimensionm, define
a quantity investigated by Dvoretzky and Rogers. 相似文献
10.
1. IntroductionLet f: Re -- R be a differelltiable fUnction. f reaChes its extremes on the setJ = {x E R"lfx(x) = 0}, (1.1)where,x(X) = (V,..., V)". (1.2)If jx can be observed exactly at any x e R", then there are various numerical methods toconstruct {xh}, xk E Re such that the distance d(xk, J) between uk and J tends to zero ask -- co. However, in many application problems jx can only be observed with noise, i.e.,the observation at time k 1 isYk 1 = fi(~k) (k 1, (1'3)where xk is … 相似文献
11.
12.
V. V. Andrievskii 《Journal d'Analyse Mathématique》2005,96(1):283-295
LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp
n be a non-constant complex polynomial of degree at mostn. We establish the inequality
whereα
n < 0 depends onn, K,
and the geometrical structure of ϖG. 相似文献
13.
Frank Blume 《Israel Journal of Mathematics》1998,108(1):1-12
If (X,T) is a completely ergodic system, then there exists a positive monotone increasing sequence {a
n
}
n
1/∞
with lim
n
→∞a
n
=∞ and a positive concave functiong defined on [1, ∞) for whichg(x)/x
2 isnot integrable such that
for all nontrivial partitions α ofX into two sets. 相似文献
14.
Jürgen Weyer 《manuscripta mathematica》1979,28(4):305-316
In a Hilbert space H, we consider operators of type A=L*ϕ·L, where L is a closed, linear operator and ϕ is a maximal cyclically monotone, coercive operator. The operators ϕ, L, L* and their inverses are not necessarily everywhere defined. Our principle result is a nonlinear extension of an earlier theorem
of v. Neumann for A=L*L.Theorem: Suppose that either (L*)−1 is bounded or that both L−1 is bounded and, D(ϕ) υ N (L*). The L*ϕ·L, is maximal cyclically monotone. Maximality of sums
is also considered, and the theory is applied to concrete differential operators of the form
, with monotone functions f1 and various boundary conditions.
相似文献
15.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):135-140
Summary LetF be a distribution function over the real line. DefineR
p(y)=∫|x−y|pdF(x) forp≧1. Forp>1 there is a unique minimizer ofR
p(·), sayγ
p. Under mild conditions onF it is shown that
exists and that the limit is a median. Thus, one could use this limit as a definition of a unique median. Also it is shown
that
whereR is the right extremity ofF andL is the left extremity ofF provided that −∞<L≦R<∞. A similar result is available ifL=−∞,R=∞, yetF has symmetric tails. 相似文献
16.
Let {X
k
,k=1,2,…} be a sequence of independent binomial variables, with
the Fourier transform of the distribution ofY. Finally denote lim [P
k
− 1/2] byδ. We haveTheorem.
Research supported by N.S.F. Grant GP-25736.
Research supported by N.S.F. Grant GP-12365. 相似文献
17.
Zheng Zukang 《数学学报(英文版)》1994,10(4):337-347
LetX
1,X
2, ...,X
n
be a sequence of nonnegative independent random variables with a common continuous distribution functionF. LetY
1,Y
2, ...,Y
n
be another sequence of nonnegative independent random variables with a common continuous distribution functionG, also independent of {X
i
}. We can only observeZ
i
=min(X
i
,Y
i
), and
. LetH=1−(1−F)(1−G) be the distribution function ofZ. In this paper, the limit theorems for the ratio of the Kaplan-Meier estimator
or the Altshuler estimator
to the true survival functionS(t) are given. It is shown that (1)P(δ(n)=1 i.o.)=0 ifF(τ
H
) < 1 andP(δ
n
=0 i.o. )=0 ifG(τH) > 1 where δ(n) is the corresponding indicator function of
and
have the same order
a.s., where {T
n
} is a sequence of constants such that 1−H(T
n
)=n
−α(logn)β(log logn)γ. 相似文献
18.
Zhang Lixin 《数学学报(英文版)》1998,14(1):113-124
Let {X, X
n
;n>-1} be a sequence of i.i.d.r.v.s withEX=0 andEX
2=σ2(0 < σ < ∞).
we obtain some sufficient and necessary conditions for
to hold, get the widest range ofk’s and answer a question of Hanson and Russo (1983).
Supported by National Natural Science Foundation of China and China Postdoctoral Science Foundation 相似文献
19.
O. P. Filatov 《Mathematical Notes》1999,66(3):348-354
For a continuous almost periodic function
, we show that the function
where the supremum is taken over all solutions of the system of differential inclusion
,
, has the following limit (as μ→+0):
, Thus if the parameter μ is small, then
and the limit of the maximal mean can approximately be determined by solving problems of smaller dimensionality. Moreover,
if the compact sets
and
are nondegenerate, then Ψ
f
is independent of initial data.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 431–438, September, 1999. 相似文献
20.
E. Amar 《Journal of Geometric Analysis》1991,1(4):291-305
We show that if f1, f2 are bounded holomorphic functions in the unit ball
of ℂn such that
, |f1(z)|2 + |f2(z)2|2 ≥ δ2 >; 0, then any functionh in the Hardy space
,p < +∞ can be decomposed ash = f1h1
+ f2h2 with
. The Corona theorem in
would be the same result withp = +∞ and this question is still open forn ≳-2, but the preceding result goes in this direction. 相似文献