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1.
Let u(x,t) be a solution, uA|u| p for xIR 3, t0 where is the d'Alembertian, and A, p are constants with A>0, 1 0–|x–x0|, if the initial data u(x,0), ut(x,0) have their support in the ball |x–x0|t0. In particular global solutions of u=A|u|p with initial data of compact support vanish identically. On the other hand for A>0, p>1+2 global solutions of u=A|u|p exist, if the initial data are of compact support and u is sufficiently small in a suitable norm. For p=2 the time at which u becomes infinite is of order u–2.Dedicated to Hans Lewy and Charles B. Morrey, Jr.The research for this paper was performed at the Courant Institute and supported by the Office of Naval Research under Contract No. N00014-76-C-0301. Reproduction in whole or part is permitted for any purpose of the United States Government. 相似文献
2.
H
( G), f( g) H
( G) , ( , 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim sup p
n=, , , n .. . , 117 234 . . - 相似文献
3.
Let f: XY be a nonlinear differentiable map, X, Y are Hilbert spaces, B( a, r) is a ball in X with a center a and radius r. Suppose f
( x) is Lipschitz in B( a, r) with Lipschitz constant L and f
( a) is a surjection: f
( a) X= Y; this implies the existence of >0 such that f
( a) *
yy, yY. Then, if r,/(2L), the image F=f(B(a,)) of the ball B(a,) is convex. This result has numerous applications in optimization and control. First, duality theory holds for nonconvex mathematical programming problems with extra constraint x–a. Special effective algorithms for such optimization problems can be constructed as well. Second, the reachability set for small power control is convex. This leads to various results in optimal control. 相似文献
4.
B
p,
(r)
( R
n
) l
l
p
. B
p,
(r)
( R
n
) «» . 相似文献
5.
Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice. 相似文献
6.
A necessary and sufficient condition is found for the function to ensure absolute convergence of the Haar—Fourier series of all functions (f) provided that the Haar—Fourier series of f converges absolutely. Absolute convergence means absolute convergence of the series of coefficients, and the condition is that should be in Lip 1.
— 相似文献
7.
We give efficiency estimates for proximal bundle methods for finding f *min Xf, where f and X are convex. We show that, for any accuracy <0, these methods find a point x kX such that f(x k)–f * after at most k=O(1/ 3) objective and subgradient evaluations. 相似文献
8.
Summary Approximations for the function implicitly defined by (u)=(u, (u)) are obtained via the iterative scheme n(u)=(u, n–1(u)). In this paper the uniform convergence of high order derivatives of n to the corresponding derivatives of is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R. 相似文献
9.
We consider boundary value problems associated with the equation T=–A in a Hilbert Space, where T and A are bounded, self adjoint, injective, and A has a bounded inverse. We discuss the stability of the solution when A is perturbed by a self adjoint operator. 相似文献
10.
Ohne Zusammenfassung
Zusatz bei der Korrektur: Ein vollständiger und korrekter Beweis für die Entscheidbarkeit der eingangs angeführten Aanderaaschen Klasse ((0, ), (, , ...)) erscheint demnächst im JSL (S.O. Aanderaa/H.R.Lewis: Prefix classes of Krom formulas). Ebendort wird auch die Reduktionstypeneigenschaft für ((0, ), (0, 0, )) und ((0, )), (0, 0, )) nachgewiesen, während ((0, ), (, )) sich als entscheidbar herausgestellt hat (s. E. Börger: Eine entscheidbare Klasse von Kromformeln. ZMLG 19 (1973), 117–120.) Der Kromsche Reduktionstyp konnte mittlerweile einerseits zu ((0, ), (0, 4)) verschärft werden (s. D. Rödding, E. Börger: The undecidability of (0, 4)-formulae with binary disjunctions, vorgetragen auf dem Logic Coll. Bristol 1973, ein abstract erscheint im JSL), andererseits kündigt H.R.Lewis die Reduktionstypeneigenschaft für ((0, ), (0, 1)) an (s. H.R.Lewis: Krom formulas with one dyadic predicate letter. Notices AMS 20, 5 (1973) A-500, abstr. no. 73T-E78.)Dieser Aufsatz geht aus der Dissertation [2] hervor, die dem Fachbereich Mathematik der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster im Sommersemester 1971 vorgelegt worden ist. Die Ergebnisse stammen aus dem Wintersemester 1970/71. Eine Ankündigung der hauptsächlichen Resultate ist in den Notices of the American Mathematical Society 19, 2 (1972) A-333 unter der abstract no. * 72T-E24 erschienen. 相似文献
11.
Let R(r, m) be the rth order Reed-Muller code of length 2
m
, and let ( r, m) be its covering radius. We prove that if 2 k m - r - 1, then ( r + k, m + k) ( r, m + 2( k - 1). We also prove that if m - r 4, 2 k m - r - 1, and R( r, m) has a coset with minimal weight ( r, m) which does not contain any vector of weight ( r, m) + 2, then ( r + k, m + k) ( r, m) + 2 k(. These inequalities improve repeated use of the known result ( r + 1, m + 1) ( r, m).This work was supported by a grant from the Research Council of Wright State University. 相似文献
12.
The paper is a study of the limiting behaviour of the [ n t]-th iterates of the well-known Post-Widder operators L
n, x used in the real inversion of the Laplace transform. It is shown that the limiting operators constitute a semigroup T
t;t0 of class ( C
0) on a family C
,; , >0 of Banach spaces. Applications of the semigroup structure lead to a pointwise saturation theorem for L
n, x and a characterization of convex functions in C
, through an inequality involving the action of L
n, x. 相似文献
13.
Let M n denote an n-dimensional Riemannian manifold. Its metric is called -strongly spherical if at every point Q M n there exists a -dimensional subspace Q
T QM n such that the curvature operator of the metric of M n satisfies R(X, Y) Z = k(< Y, Z > X < X, Z > Y), where k = const > 0, Y Q
, X, Z #x2208; T QM n. The number is called the index of sphericity and k the exponent of sphericity. The following theorems are proved in the paper. THEOREM 1. Let the Sasakian metric of T 1M n be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if M 2 has constant Gaussian curvature K 1 and k = K 2/4; b) = 3 if and only if M 2 has constant curvature K = 1 and k = 1/4; c) = 0, otherwise. THEOREM 2. Let the Sasakian metric of T 1M n (n M n) be -strongly spherical with exponent of sphericity k. If k > 1/3 and k 1, then = 0. Let us denote by (M n, K) a space of constant curvature K. THEOREM 3. Let the Sasakian metric of T 1(M n, K) (n 3) be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if K = 1/4; b) = 0, otherwise. In dimension n = 3 Theorem 2 is true for k {1/4, 1}.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 150–159, 1992. 相似文献
14.
Summary We define a constraint system
, [0, 0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0, 0), x
m
, y
n
. Finally, we prove a singular perturbation theorem for the system
, [0, 0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
15.
For n2 we consider the Stokes problem in n, -u + p= f, -div u= g, in weighted Soboiev spaces H
6
m,r
, where the weights are proportional to (1+| x|) . We prove the existence of weak solutions for any K, where K is a discrete set of critical values. Furthermore, we characterize the solutions of the homogeneous problem.This research was supported by the DFG research group Equations of Hydrodynamics, Universities of Bayreuth and Paderborn. 相似文献
16.
We study the limiting behavior of the weighted central paths {(x(), s())}
> 0 in linear programming at both = 0 and = . We establish the existence of a partition ( B
, N
) of the index set { 1, , n } such that x
i() and s
j
() as for i B
, and j N
, and x
N (), s
B () converge to weighted analytic centers of certain polytopes. For all k 1, we show that the kth order derivatives x
(k)
() and s
(k)
() converge when 0 and . Consequently, the derivatives of each order are bounded in the interval (0, ). We calculate the limiting derivatives explicitly, and establish the surprising result that all higher order derivatives ( k 2) converge to zero when . 相似文献
17.
It is proved that if D is a bounded open subset of a uniformly convex Banach space X and
is a continuous mapping which is a local pseudo-contraction (e.g., locally nonexpansive) on D, then T has a fixed point in D if there exists xD such that z–Tz相似文献
18.
H={ h
1, I } — , . : , I ¦ (I)¦=¦ I¦, ¦ I¦ — I. H H
={ h
(I), I} . , , . L
p
.
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
19.
. , , –1< <0. .
The present work was written on the basis of two earlier works received by Analysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
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