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1.
S. V. Petras 《Journal of Mathematical Sciences》1984,24(3):380-386
The behavior of the poles zn(), n=1,2,... of the scattering matrix of the operatorl
u=–u(x), x , (u/n)+(x)u|=0 as 0 is considered. It is proved that |zn()–zn|=0((1/2)qn), where qn is the order of the pole of the scattering matrix for the operator 0u=–u, u/=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981. 相似文献
2.
Reiterated homogenization is studied for divergence structure parabolic problems of the form u
/t–div (a(x,x/,x/2,t,t/ k)u
)=f. It is shown that under standard assumptions on the function a(x, y
1,y
2,t,) the sequence {u
} of solutions converges weakly in L
2 (0,T; H
0
1
()) to the solution u of the homogenized problem u/t– div(b(x,t)u)=f.This revised version was published online in April 2005 with a corrected missing date string. 相似文献
3.
Summary For solving the nonlinear systemG(x, t)=0,G|
n
× 1
n
, which is assumed to have a smooth curve of solutions a continuation method with self-choosing stepsize is proposed. It is based on a PC-principle using an Euler-Cauchy-predictor and Newton's iteration as corrector. Under the assumption thatG is sufficiently smooth and the total derivative (1
G(x, t)2
G(x, t)) has full rankn along the method is proven to terminate with a solution (x
N
, 1) of the system fort=1. It works succesfully, too, if the Jacobians 1
G(x, t) become singular at some points of , e.g., if has turning points. The method is especially able to give a point-wise approximation of the curve implicitly defined as solution of the system mentioned above. 相似文献
4.
Fausto Segala 《Annali di Matematica Pura ed Applicata》1985,140(1):285-299
Sunto Si costruisce una parametrice per il problema di Dirichlet relativo ad operatori P del tipo (1/i(/t))2 + tx, nella regione t0. Tenuto conto che per tali operatori è nota la parametrice del problema di Cauchy nella regione t 0, ciò consente di costruire una soluzione (modO
) dell'equazione Pu=f , t (–T, T), T>0. 相似文献
5.
J. C. Liu 《Journal of Optimization Theory and Applications》1991,69(1):153-167
Necessary Kuhn-Tucker conditions up to precision without constraint qualification for -Pareto optimality of multiobjective programming are derived. This article suggests the establishment of a Wolfe-type -duality theorem for nondifferentiable, nonconvex, multiobjective minimization problems. The -vector Lagrangian and the generalized -saddle point for Pareto optimality are studied. 相似文献
6.
Otto Röschel 《Journal of Geometry》1993,47(1-2):131-140
In part I we have studied a map of osculating elements of an affine Cayley-Klein (CK-) plane into the Lie algebra A4(2) of the aequiform transformations A4(2) of the given plane A2(, 2). If we use the real projective space P3() over A4(2) each osculating element defines a straight line in P3(). We now give a one parameter motion in A4(2) and study second order properties and their analogon in the Lie algebra and P3(), respectively. We show that the wellknown relationship between the points of the moving frame and the osculating circles of the point paths in the fixed frame may be interpreted as part of a quadratic map of certain straight Lines of P3(). An analogous result holds for the curvature of pairs of envelopes; the mapV induced in P3() than is contained in a cubic relationship of straight lines.
Herrn Professor Oswal Giering zum 60. Geburtstag gewidmet 相似文献
Herrn Professor Oswal Giering zum 60. Geburtstag gewidmet 相似文献
7.
Ethan D. Bloch 《Discrete and Computational Geometry》1989,4(1):365-374
LetK
n
n
be a triangulatedn-ball. Examples are given to show that unlike in the two-dimensional case, the following hold for alln3: (1) there are nonconvexK
n
with no convex simplexwise linear embeddingsK
n
n
, even though there are strictly convex simplexwise linear embeddings K
n
n
; (2) there are convexK
n
, with no spanning simplices, such that not every simplexwise linear embeddingf: K
n
n
with convex image can be extended to a simplexwise linear embedding ofK
n
; (3) there are convexK
n
such that the space of simplexwise linear homeomorphisms ofK
n
, fixed on K
n
, is not path connected.Partially supported by NSF Contract DMS-8503388. 相似文献
8.
V. G. Sushko 《Mathematical Notes》1970,8(3):646-652
The proximity is investigated of the solution of Cauchy's problem for the equation u
t
+((u))x= u
xx
((u) > 0) to the solution of Cauchy's problem for the equation ut+ ((u))x= 0, when the solution of the latter problem has a finite number of lines of discontinuity in the strip 0 t T. It is proved that, everywhere outside a fixed neighborhood of the lines of discontinuity, we have |u–u| C, where the constant C is independent of. Similar inequalities are derived for the first derivatives of u–u.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 309–320, September, 1970.In conclusion we express our gratitude to L. A. Chudov for his valuable advice concerning this work. 相似文献
9.
Morten E. Harris 《Algebra Colloquium》2000,7(3):291-294
Let A be a p-group acting on a finite Abelian p-group P. We give a necessary and sufficient condition on an A-irreducible decomposition of 1(P) = i1Ui for the existence of an A-indecomposable decomposition of P = i1Ri such that 1(Ri) = Ui for all i I. This readily implies a main result of [1].2000 Mathematics Subject Classification: 20D15 相似文献
10.
Rod Gow 《Geometriae Dedicata》1997,64(3):283-295
Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers
k
V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies 2 = 0 and (
k
V)
k–1
V We prove that (
k
V)= ker
k–1
V except when k=m+2. In the exceptional case, (
m+2
V) has codimension 2m in ker
m
V and we show that the quotient module ker
m
V/
m+2
V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in
m
V and multiplicity 0 in all other components of V. 相似文献
11.
V. G. Maz'ya 《Journal of Mathematical Sciences》1984,27(1):2500-2514
Let be a domain in n, n >2, the boundary of which has a cusp point, pointing inside or outside the domain. The purpose of the paper is to characterize the traces on of the elements of the space H1() of functions with a finite Dirichlet integral. As a consequence one establishes the existence of a linear continuous extension operator H1 () H1(n) under the presence of an interior cusp point on . Theorems on domains with cusps are proved with the aid of results on cylindrical domains. In the space of functions with a finite Dirichlet integral in the exterior or the interior of the cylinder one introduces the norm, depending on a small parameter and generating a norm of the trace on as an element of the quotient space. The latter is placed in correspondence with an explicitly described norm of functions on the boundary, uniformly equivalent relative to . One constructs an operator of extension of functions from the exterior of the cylinder to Rn, preserving H1, whose norm is uniformly bounded relative to . For the optimal operator of extension from the inside of the cylinder one finds the asymptotic behavior of the norm as 0. From these results there follow similar theorems on functions with a finite Dirichlet integral inside and outside a thin closed tube (of width ).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 117–137, 1983. 相似文献
12.
Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L
2() with generalized Robin boundary conditions where is an arbitrary open subset of R
n
and is a Borel measure on the boundary of . This operator generates a sub-Markovian C
0-semigroup on L
2(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L
p
() is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture. 相似文献
13.
Rafael López 《Annals of Global Analysis and Geometry》2001,20(1):59-75
We study the problem of finding constant mean curvature graphsover a domain of a totally geodesic hyperplane andan equidistant hypersurface Q of hyperbolic space. We findthe existence of graphs of constant mean curvature H overmean convex domains Q and with boundary for –H
< H |h|, where H
> 0 is the mean curvature of the boundary . Here h is the mean curvature respectively of the geodesic hyperplane (h= 0) and of the equidistant hypersurface (0 < |h|< 1). The lower bound on H is optimal. 相似文献
14.
E. P. Fadeeva 《Journal of Mathematical Sciences》1991,53(1):87-94
We present an explicit solution of the problem of optimal linear filtering: the recovery of the useful signal(s) at the instantt+, (>0,<0, or=0) from known values of the received signal(s)=(s)+(s) in the past, i.e., at the instantt–s, s0. In doing so we assume the random processes(s) and /gr(s) are stationary and jointly stationary, while the stationary process of noise (s) with zero mean is assumed to be mutually correlated and jointly stationary with the process(s) under the assumption that there exists a common spectral densityf() for these processes.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 83–91, 1986. 相似文献
15.
Albrecht Küster 《manuscripta mathematica》1985,53(3):255-259
This paper contains a sharp version of the well-known linear isoperimetric inequality for minimal surfacesX area(X)1/2oscillation(X)length(X).Supported by Sonderforschungsbereich 72 der Deutschen Forschungsgemeinschaft at Bonn University. 相似文献
16.
Alexander Ženíšek 《Applications of Mathematics》2003,48(5):367-404
A modification of the Nikolskij extension theorem for functions from Sobolev spaces H
k() is presented. This modification requires the boundary to be only Lipschitz continuous for an arbitrary k however, it is restricted to the case of two-dimensional bounded domains. 相似文献
17.
Fausto Segala 《Annali di Matematica Pura ed Applicata》1986,146(1):311-336
Summary In this paper we give the construction of a parametrix for a class of differential operators of the type 2/t2–t2k+1 + tq(/xi), k N, q N, qk. 相似文献
18.
Shiqi Song 《应用数学学报(英文版)》1993,9(2):115-124
LetX be the solution of the SDE:dX
t = (X
t)dB
t +b(X
t)dt, with andb C
b
(R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form:
k
(u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if
k
is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of
k
, must be a constant function. 相似文献
19.
We consider the controlled parabolic obstacle problem with the controlu appearing through the Neumann condition y/v=u on the boundary of an open domain ofR
N
. Given a smooth open subsetQ
0 of ×(0,T) we prove that the problemQ
0 {(x, t) Q, y
u
(x, t)=0} is approximately solvable. Numerical tests are given.This work was done while Viorel Barbu was the Otto Szasz Visiting Professor at the University of Cincinnati. 相似文献
20.
On a variational problem with lack of compactness: the topological effect of the critical points at infinity 总被引:5,自引:0,他引:5
Abbas Bahri Yanyan Li Olivier Rey 《Calculus of Variations and Partial Differential Equations》1995,3(1):67-93
We study the subcritical problemsP
:–u=u
p–,u>0 on;u=0 on , being a smooth and bounded domain in N,N–3,p+1=2N/N–2 the critical Sobolev exponent and >0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P0).
Résumé Nous étudions les problèmes sous-critiquesP :–u=u p–,u > 0 sur;u=0 sur –où est un domaine borné et régulier de N,N–3,p + 1=2N/N –2 est l'exposant critique de Sobolev, et >0 tend vers zéro, afin de calculer la différence de toplogie induite par les points critiques à l'infini entre les ensembles de niveau de la fonctionnelle correspondant au cas limite (P0).相似文献