共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we introduce a total step method for solving a system of linear complementarity problems with perturbations and interval data. It is applied to two interval matrices [A] and [B] and two interval vectors [b] and [c]. We prove that the sequence generated by the total step method converges to ([x∗],[y∗]) which includes the solution set for the system of linear complementarity problems defined by any fixed A∈[A],B∈[B],b∈[b] and c∈[c]. We also consider a modification of the method and show that, if we start with two interval vectors containing the limits, then the iterates contain the limits. We close our paper with two examples which illustrate our theoretical results. 相似文献
2.
We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator
to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (Maximum principles and eigenvalue
problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow,
175, pp. 34–48, 1988) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary
value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate
ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006). 相似文献
3.
Summary. We describe an algorithm to approximate the minimizer of an elliptic functional in the form on the set of convex functions u in an appropriate functional space X. Such problems arise for instance in mathematical economics [4]. A special case gives the convex envelope of a given function . Let be any quasiuniform sequence of meshes whose diameter goes to zero, and the corresponding affine interpolation operators. We prove that the minimizer over is the limit of the sequence , where minimizes the functional over . We give an implementable characterization of . Then the finite dimensional problem turns out to be a minimization problem with linear constraints.
Received November 24, 1999 / Published online October 16, 2000 相似文献
4.
J. O. C. Ezeilo 《Annali di Matematica Pura ed Applicata》1963,63(1):387-397
Summary In the peesent paper it is shown that an earlier result [1], and its subsequent generalization [2] concerning the motion of trajectories in the phase space of the differential equation (1 1) can be extended to the more general equation (2.1), and this is done under a considerably weaker condition on h(x). 相似文献
5.
Fernando Quirós Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(2):357-362
We consider the heat equation in the half-line with
Dirichlet boundary data which blow up in finite time. Though the
blow-up set may be any interval [0,a],
depending on the Dirichlet data, we prove that the
effective
blow-up set, that is, the set of points
where the solution behaves like u(0,t), consists always only of the
origin.
As an application of our results we consider a system of two heat
equations with a nontrivial nonlinear flux coupling at the
boundary. We show that by prescribing the non-linearities the two
components may have different blow-up sets. However, the effective
blow-up sets do not depend on the coupling and coincide with the
origin for both components. 相似文献
6.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(2):99-104
According to a theorem first stated by Clifford, Noether [8] and Rosanes [12], which later received a complete proof by Castelnuovo [2], the Cremona group of the plane is generated by de Jonquières transformations. J.F. Ritt [10] asked whether such a result could be generalized to the differential plane. We give a negative answer, relying on a flat system of Rouchon. 相似文献
7.
Vyacheslav N. Pivovarchik 《Integral Equations and Operator Theory》1999,34(2):234-243
It is shown that the potential of the Sturm-Liouville equation on interval [0,a] may be restored by the spectra of three boundary problems generated by the equation on the intervals [0,a], [0, 1/2a] and [1/2a,a], respectively. The algorithm of construction is given as well as the sufficient conditions for three sequences of real numbers to be the spectra of the mentioned boundary problems. The problem on [0,a] describes small vibrations of a smooth string with fixed ends. The problems on the half-intervals describe vibrations of the same string clamped at the point of equilibrium. 相似文献
8.
We develop an obstruction theory for homotopy of homomorphisms between minimal differential graded algebras. We assume that has an obstruction decomposition given by and that f and g are homotopic on . An obstruction is then obtained as a vector space homomorphism . We investigate the relationship between the condition that f and g are homotopic and the condition that the obstruction is zero. The obstruction theory is then applied to study the set of
homotopy classes . This enables us to give a fairly complete answer to a conjecture of Copeland-Shar on the size of the homotopy set [A,B] whenA and B are rational spaces. In addition, we give examples of minimal algebras (and hence of rational spaces) that have few homotopy
classes of self-maps.
Received February 22, 1999; in final form July 7, 1999 / Published online September 14, 2000 相似文献
9.
In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.
14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory
106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem. 相似文献
10.
For systems of second-order nonlinear ordinary differential equations with the Dirichlet boundary conditions, we develop generalized
three-point difference schemes of high-order accuracy on a nonuniform grid. The construction of the suggested schemes requires
solving four auxiliary Cauchy problems (two problems for systems of nonlinear ordinary differential equations and two problems
for matrix linear ordinary differential equations) on the intervals [x
j−1, x
j
] (forward) and [x
j
, x
j+1] (backward) at each grid point; this is done at each step by any single-step method of accuracy order $
\bar m
$
\bar m
= 2[(m+1)/2]. (Here m is a given positive integer, and [·] is the integer part of a number.) We prove that such three-point difference schemes
have the accuracy order $
\bar m
$
\bar m
for the approximation to both the solution u of the boundary value problem and the flux K(x)d
u/dx at the grid points. 相似文献
11.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(8):691-694
Since Serre's work [12], we know that loop spaces play a central role in algebraic topology. In particular, iterated loop spaces pose the tough problem which consists in iterating the Cobar construction (see [2], [10], [11], [14] and [15]). In this Note, to make progress in this topic, we give explanations and complements about Adams ' relation [1] between C*(ΩX) and Cobar C*(X) (Z, Z) when X is the suspension of a reduced (with trivial 0-skeleton) simplicial set, Ω being here the simplicial Kan model [8] of the loop space functor. In particular, our results give a surprising experimental fact: the existence of an “exotic” differential which can replace the classical Adams differential in the Cobar construction. They also permit us to obtain with a new method some previous results of Baues ([2], [3]) about Ω2 X when X is the suspension of a 1-reduced (with trivial 1-skeleton) simplicial set. 相似文献
12.
Consider an interval [H,G] in the lattice of subgroups of a finite soluble groupG. We define a certain set of subgroups in the lattice [H,G], and prove that they are conjugate inG. ForH=1 one gets the prefrattini subgroups ofG. 相似文献
13.
Fernando Quirós Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,50(4):357-362
We consider the heat equation in the half-line with
Dirichlet boundary data which blow up in finite time. Though the
blow-up set may be any interval [0,a],
a ? [0,¥]a\in[0,\infty]
depending on the Dirichlet data, we prove that the
effective
blow-up set, that is, the set of points
x 3 0x\ge0
where the solution behaves like u(0,t), consists always only of the
origin.
As an application of our results we consider a system of two heat
equations with a nontrivial nonlinear flux coupling at the
boundary. We show that by prescribing the non-linearities the two
components may have different blow-up sets. However, the effective
blow-up sets do not depend on the coupling and coincide with the
origin for both components. 相似文献
14.
A. J. Zaslavski 《Applied Mathematics and Optimization》2000,42(3):291-313
In this work we analyze the structure of optimal solutions for a class of infinite-dimensional control systems. We are concerned
with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends
the result of Carlson, Haurie, and Jabrane to a situation where the trajectories are not necessarily bounded. Also, we show
that an optimal trajectory defined on an interval [0,τ] is contained in a small neighborhood of the optimal steady-state in the weak topology for all t ∈ [0,τ] \backslash E , where E \subset [0,τ] is a measurable set such that the Lebesgue measure of E does not exceed a constant which depends only on the neighborhood of the optimal steady-state and does not depend on τ .
Accepted 26 July 2000. Online publication 13 November 2000. 相似文献
15.
Andrés I. Ávila Jianfu Yang 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):459-479
We proved a multiplicity result for a nonlinear elliptic system in RN. The functional related to the system is strongly indefinite. We investigated the relation between the number of solutions
and the topology of the set of the global maxima of the coefficients. 相似文献
16.
For a transcendental meromorphic function f, various propertiesof the set [formula] were obtained in [8] and [9]. Here we establish analogous propertiesfor the smaller sets [formula] introduced in [5], and [formula] We deduce a symmetry result for Julia sets J(f), and also indicatesome techniques for showing that certain invariant curves liein I'(f), Z(f) and J(f). 2000 Mathematics Subject Classification30D05, 37F10, 37F50. 相似文献
17.
Olivier Guibé 《Annali di Matematica Pura ed Applicata》2002,180(4):441-449
We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem -div(a(x,Du))=μ in Ω, u=0 on ∂Ω, where μ is a Radon measure with bounded variation on Ω.
Received: December 27, 2000 Published online: December 19, 2001 相似文献
18.
Narong Punnim 《Graphs and Combinatorics》2002,18(3):597-603
We prove that if G runs over the set of graphs with a fixed degree sequence d, then the values χ(G) of the function chromatic number completely cover a line segment [a,b] of positive integers. Thus for an arbitrary graphical sequence d, two invariants minχ(d):=a and maxχ(d):=b naturally arise. For a regular graphical sequence d=r
n
:=(r,r,…,r) where r is the degree and n is the number of vertices, the exact values of a and b are found in all situations, except the case where n and r are both even and n<2r.
Received: September 16, 2000 Final version received: December 13, 2001
Acknowledgments. We would like to thank Professor Tommy R. Jensen for his useful comment and editing thorough the paper. 相似文献
19.
Paweł Strzelecki Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2006,25(4):431-467
Motivated by previous work on elastic rods with self-contact, involving the concept of the global radius of curvature for
curves (as defined by Gonzalez and Maddocks), we define the global radius of curvature Δ[X] for a wide class of continuous parametric surfaces X for which the tangent plane exists on a dense set of parameters. It turns out that in this class of surfaces a positive lower
bound Δ[X] ≥ θ > 0 provides, naively speaking, the surface with a thickness of magnitude θ; it serves as an excluded volume constraint
for X, prevents self-intersections, and implies that the image of X is an embedded C1-manifold with a Lipschitz continuous normal. We also obtain a convergence and a compactness result for such thick surfaces,
and show one possible application to variational problems for embedded objects: the existence of ideal surfaces of fixed genus
in each isotopy class.
The proofs are based on a mixture of elementary topological, geometric and analytic arguments, combined with a notion of the
reach of a set, introduced by Federer in 1959.
Mathematics Subject Classification (2000) 49Q10, 53A05, 53C45, 57R52, 74K15 相似文献