共查询到20条相似文献,搜索用时 31 毫秒
1.
A numerical method for linear quadratic optimal control problems with pure state constraints is analyzed. Using the virtual
control concept introduced by Cherednichenko et al. (Inverse Probl. 24:1–21, 2008) and Krumbiegel and R?sch (Control Cybern. 37(2):369–392, 2008), the state constrained optimal control problem is embedded into a family of optimal control problems with mixed control-state
constraints using a regularization parameter α>0. It is shown that the solutions of the problems with mixed control-state constraints converge to the solution of the state
constrained problem in the L
2 norm as α tends to zero. The regularized problems can be solved by a semi-smooth Newton method for every α>0 and thus the solution of the original state constrained problem can be approximated arbitrarily close as α approaches zero. Two numerical examples with benchmark problems are provided. 相似文献
2.
Abraham Neyman 《International Journal of Game Theory》2012,41(1):195-207
Fix a zero-sum repeated game Γ with incomplete information on both sides. It is known that the value of the infinitely repeated
game Γ∞ need not exist (Aumann and Maschler 1995). It is proved that any number between the minmax and the maxmin of Γ∞ is the value of a long finitely repeated game Γ
n
where players’ information about the uncertain number of repetitions n is asymmetric. 相似文献
3.
Ziyatkhan S. Aliyev 《Central European Journal of Mathematics》2010,8(2):378-388
We consider a fourth order eigenvalue problem containing a spectral parameter both in the equation and in the boundary condition.
The oscillation properties of eigenfunctions are studied and asymptotic formulae for eigenvalues and eigenfunctions are deduced.
The basis properties in L
p
(0; l); p ∈ (1;∞); of the system of eigenfunctions are investigated. 相似文献
4.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
5.
In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation
in a periodic medium. Denoting by ε the period, the diffusion coefficient is scaled as ε2. The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell
spectral equations, three different situations arise when ε goes to zero. First, there is a global homogenized problem as
in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition
on the interface. Third, there is an exponential localization near the interface of the first eigenfunction.
Received: January 10, 2001; in final form: July 9, 2001?Published online: June 11, 2002 相似文献
6.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
7.
The Frankl problem without the spectral parameter was considered by Bitsadze and Smirnov. The present paper gives the eigenvalues and eigenfunctions of the Frankl problem with the odd parity condition. We prove the completeness of eigenfunctions. The Frankl problem with a nonlocal parity condition for the Lavrent’ev-Bitsadze equation is studied. The eigenvalues and eigenfunctions are found, and the basis property of the eigenfunctions in the elliptic part of the domain in the space L 2 is proved. 相似文献
8.
The problem of finding a solution of the Neumann problem for the Laplacian in the form of a simple layer potential Vρ with unknown density ρ is known to be reducible to a boundary integral equation of the second kind to be solved for density.
The Neumann problem is examined in a bounded n-dimensional domain Ω+ (n > 2) with a cusp of an outward isolated peak either on its boundary or in its complement Ω− = R
n
\Ω+. Let Γ be the common boundary of the domains Ω±, Tr(Γ) be the space of traces on Γ of functions with finite Dirichlet integral over R
n
, and Tr(Γ)* be the dual space to Tr(Γ). We show that the solution of the Neumann problem for a domain Ω− with a cusp of an inward peak may be represented as Vρ−, where ρ− ∈ Tr(Γ)* is uniquely determined for all Ψ− ∈ Tr(Γ)*. If Ω+ is a domain with an inward peak and if Ψ+ ∈ Tr(Γ)*, Ψ+ ⊥ 1, then the solution of the Neumann problem for Ω+ has the representation u
+ = Vρ+ for some ρ+ ∈ Tr(Γ)* which is unique up to an additive constant ρ0, ρ0 = V
−1(1). These results do not hold for domains with outward peak. 相似文献
9.
The accuracy of a difference spectral problem for a second-order elliptic equation with mixed derivatives and constant coefficients
is estimated. In so doing, the fact that the eigenfunctions belong to the Sobolyev space W
2
2
in a rectangle is used. Bibliography: 6 titles.
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 59–66. 相似文献
10.
We find the eigenfunctions of a generalized Frankl problem with the use of Bessel functions. We prove that these eigenfunctions
form a Riesz basis in the space L
2(D
+), where D
+ is the elliptic part of the domain. In addition, we prove the Riesz basis property of a trigonometric function system and
the completeness of this system in the space L
2(0, π/2). 相似文献
11.
C. Krattenthaler Thomas W. Müller 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2008,78(1):99-147
Let q be an odd prime, m a positive integer, and let Γ
m
(q) be the group generated by two elements x and y subject to the relations x
2m
=y
qm
=1 and x
2=y
q
; that is, Γ
m
(q) is the free product of two cyclic groups of orders 2m respectively qm, amalgamated along their subgroups of order m. Our main result determines the parity behaviour of the generalized subgroup numbers of Γ
m
(q) which were defined in Müller (Adv. Math. 153:118–154, 2000), and which count all the homomorphisms of index n subgroups of Γ
m
(q) into a given finite group H, in the case when gcd (m,|
H
|)=1. This computation depends upon the solution of three counting problems in the Hecke group ℋ(q)=C
2*C
q
: (i) determination of the parity of the subgroup numbers of ℋ(q); (ii) determination of the parity of the number of index n subgroups of ℋ(q) which are isomorphic to a free product of copies of C
2 and of C
∞; (iii) determination of the parity of the number of index n subgroups in ℋ(q) which are isomorphic to a free product of copies of C
q
. The first problem has already been solved in Müller (Groups: Topological, Combinatorial and Arithmetic Aspects, LMS Lecture
Notes Series, vol. 311, pp. 327–374, Cambridge University Press, Cambridge, 2004). The bulk of our paper deals with the solution of Problems (ii) and (iii).
Research of C. Krattenthaler partially supported by the Austrian Science Foundation FWF, grant S9607-N13, in the framework
of the National Research Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献
12.
T. A. Mel’nyk 《Ukrainian Mathematical Journal》2006,58(2):220-243
A spectral boundary-value problem is considered in a plane thick two-level junction Ωε formed as the union of a domain Ω0 and a large number 2N of thin rods with thickness of order ε = O(N
−1). The thin rods are split into two levels depending on their length. In addition, the thin rods from the indicated levels
are ε-periodically alternating. The Fourier conditions are given on the lateral boundaries of the thin rods. The asymptotic
behavior of the eigenvalues and eigenfunctions is investigated as ε → 0, i.e., when the number of thin rods infinitely increases
and their thickness approaches zero. The Hausdorff convergence of the spectrum is proved as ε → 0, the leading terms of asymptotics
are constructed, and the corresponding asymptotic estimates are justified for the eigenvalues and eigenfunctions.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 195–216, February, 2006. 相似文献
13.
A. M. Nikitin 《Journal of Mathematical Sciences》1996,80(3):1818-1828
We give an estimate for the spectrum of the averaging operator T1(Γ, 1) over the radius 1 for the finite (q+1)-homogeneous quotient graph Γ/X, where X is an infinite (q+1)-homogeneous tree
associated with the free group G over a finite set of generators S={x1 ..., xp} (2p=q+1), and Γ, a subgroup of finite index in G. T1(Γ, 1) is defined on the subspace L2(Γ/G, 1) ⊖ Eex, where Eex is the subspace of eigenfunctions of T1(Γ, 1) with eigenvalue λ such that |λ|=q+1. We present a construction of some finite homogeneous graphs such that the spectrum
of their adjacency matrices can be calculated explicitly. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 92–109.
Translated by A. M. Nikitin. 相似文献
14.
Richard Sharp 《Geometriae Dedicata》2007,125(1):63-74
Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ / Γ0 is amenable.
相似文献
15.
D. A. Gulyaev 《Differential Equations》2012,48(10):1429-1432
We consider a spectral problem with boundary conditions of the third kind one of which contains the spectral parameter occurring linearly. We study the basis property of the system of eigenfunctions of this spectral problem in W 2 m . We obtain conditions under which the system becomes a basis in this space after the deletion of any single eigenfunction. 相似文献
16.
17.
We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of
a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem
includes the covariance selection problem that can be expressed as an ℓ
1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated
as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The
method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a
local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem,
the method can terminate in O(n3/e){O(n^3/\epsilon)} iterations with an e{\epsilon}-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim
19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the
BCGD method can be efficient for large-scale covariance selection problems with constraints. 相似文献
18.
The Hom complex of homomorphisms between two graphs was originally introduced to provide topological lower bounds on the chromatic
number. In this paper we introduce new methods for understanding the topology of Hom complexes, mostly in the context of Γ-actions
on graphs and posets (for some group Γ). We view the Hom(T, ⊙) and Hom(⊙, G) complexes as functors from graphs to posets, and introduce a functor (⊙)1 from posets to graphs obtained by taking atoms as vertices. Our main structural results establish useful interpretations
of the equivariant homotopy type of Hom complexes in terms of spaces of equivariant poset maps and Γ-twisted products of spaces.
When P:= F(X) is the face poset of a simplicial complex X, this provides a useful way to control the topology of Hom complexes. These constructions generalize those of the second
author from [17] as well as the calculation of the homotopy groups of Hom complexes from [8]. 相似文献
19.
Christophe Breuil 《Israel Journal of Mathematics》2011,182(1):349-382
Let ρ be a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/ℚ
p
) over ̅F
p
. The modulo p Langlands correspondence for GL2(ℚ
p
) defined in [5], as realized in [9], can be reformulated as a quite simple recipee giving back the (φ, Γ)-module of the dual of ρ starting from the “Diamond diagram” associated to ρ. Let F be a finite unramified extension of ℚ
p
and ρ a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/F) over ̅F
p
. When one formally extends this recipee to the Diamond diagrams associated to ρ in [6], we show that one essentially finds the (φ, Γ)-module of the tensor induction from F to ℚ
p
of the dual of ρ. 相似文献
20.
Wilhelm Heinrichs 《Numerical Algorithms》2007,44(1):1-10
A least-squares spectral collocation method for the one-dimensional inviscid Burgers equation is proposed. This model problem
shows the stability and high accuracy of these schemes for nonlinear hyperbolic scalar equations. Here we make use of a least-squares
spectral approach which was already used in an earlier paper for discontinuous and singular perturbation problems (Heinrichs,
J. Comput. Appl. Math. 157:329–345, 2003). The domain is decomposed in subintervals where continuity is enforced at the interfaces. Equal order polynomials are used
on all subdomains. For the spectral collocation scheme Chebyshev polynomials are employed which allow the efficient implementation
with Fast Fourier Transforms (FFTs). The collocation conditions and the interface conditions lead to an overdetermined system
which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear
systems. The scheme exhibits exponential convergence where the exact solution is smooth. In parts of the domain where the
solution contains discontinuities (shocks) the spectral solution displays a Gibbs-like behavior. Here this is overcome by
some suitable exponential filtering at each time level. Here we observe that by over-collocation the results remain stable
also for increasing filter parameters and also without filtering. Furthermore by an adaptive grid refinement we were able
to locate the precise position of the discontinuity. Numerical simulations confirm the high accuracy of our spectral least-squares
scheme.
相似文献