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1.
A joining characterization of ergodic isometric extensions is given. We also give a simple joining proof of a relative version
of the Halmos-von Neumann theorem.
Research partly supported by KBN grant 2 P03A 002 14 (1998).
Received June 5, 2001; in revised form March 4, 2002 相似文献
2.
On the convergence of a new trust region algorithm 总被引:12,自引:0,他引:12
Ya-xiang Yuan 《Numerische Mathematik》1995,70(4):515-539
Summary.
In this paper we
present a new trust region algorithm for general nonlinear constrained
optimization problems. The algorithm is based on the
exact penalty
function. Under very mild conditions, global convergence results
for the algorithm are given.
Local convergence properties are also studied.
It is shown that
the penalty parameter generated by the algorithm will be eventually
not less than the norm of the Lagrange multipliers at
the accumulation point. It is proved that the method is
equivalent to the sequential quadratic programming method for all
large , hence superlinearly convergent results of the
SQP method can be applied.
Numerical results are also reported.
Received March 21, 1993 相似文献
3.
Krzysztof Fraączek 《Monatshefte für Mathematik》2000,131(4):279-307
In this paper we introduce the notion of degree for C
1-cocycles over irrational rotations on the circle with values in the group SU(2). It is shown that if a C
1-cocycle over an irrational rotation by α has nonzero degree, then the skew product
is not ergodic and the group of essential values of ϕ is equal to the maximal Abelian subgroup of SU(2). Moreover, if ϕ is of class C
2 (with some additional assumptions) the Lebesgue component in the spectrum of the skew product has countable multiplicity.
Possible values of degree are discussed, too.
(Received 8 February 2000; in revised form 26 September 2000) 相似文献
4.
In [7], Nogueira and Rudolph proved that for irreducible permutations not of rotation class almost every (a.e.) interval
exchange transformation (i.e.t.) is topological weak mixing. It is conjectured that the claim holds if topological weak mixing
is replaced by weak mixing. Here we study the behaviour of eigenfunctions of i.e.t. Our analysis gives alternative proofs
of results due to Katok and Stepin [4] and Veech [10]: for certain permutations a.e. i.e.t. is weak mixing and for irreducible
permutations a.e. i.e.t. is totally ergodic.
(Received 1 February 2001) 相似文献
5.
In this paper, we build up a modification of the Midpoint method, reducing its operational cost without losing its cubical
convergence. Then we obtain a semilocal convergence result for this new iterative process and by means of several examples
we compare it with other iterative processes.
(Received 11 April 2000; in final form 27 March 2001) 相似文献
6.
《Optimization》2012,61(3):287-300
This article presents an optimization problem involving a system governed by a non-linear parabolic equation (dy/dt) + Ay = u where A is a radially continuous, monotone and coercive Volterra operator with the cost functional weakly lower semi-continuous and radially unbounded (coercive). In a first preparatory part of the article we prove two existence theorems. In the second part we present the Galerkin approximation and we prove existence of the weak and strong condensation points of a set of solution of the approximate optimization problems. Each of this points is a solution of the initial optimization problem. Finally we shall give examples using the obtained results. 相似文献
7.
It is known that for any finite group G given by a finite group presentation there exists a finite semigroup presentation for G of the same deficiency, i.e. satisfying . It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and
sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.
(Received 17 April 2001; in revised form 15 September 2001) 相似文献
8.
The title of this paper states precisely what the subject is. The first part of the paper concerns the radially-symmetric
problem in the exterior of the unit ball. It is shown that in time the solution of the problem converges to one of two specific
self-similar solutions of the porous media equation, dependent upon the dimensionality of the problem. Moreover, the free
boundary of the solution converges to that of the self-similar solution. The critical space dimension is two, for which there
is no distinction between the self-similar solutions, and the form of the convergence is exceptional. The technique used is
a comparison principle involving a variable that is a weighted integral of the solution. The second part of the paper is devoted
to the problem in an arbitrary spatial domain with no conditions of symmetry. A special invariance principle and the results
obtained for the radially-symmetric case are used to determine the large-time behaviour of solutions and their free boundaries.
This behaviour is decidedly different from when the boundary data are fixed and not homogeneous. 相似文献
9.
New properties of a nonlinear conjugate gradient method 总被引:6,自引:0,他引:6
Yu-Hong Dai 《Numerische Mathematik》2001,89(1):83-98
Summary. This paper provides several new properties of the nonlinear conjugate gradient method in [5]. Firstly, the method is proved
to have a certain self-adjusting property that is independent of the line search and the function convexity. Secondly, under
mild assumptions on the objective function, the method is shown to be globally convergent with a variety of line searches.
Thirdly, we find that instead of the negative gradient direction, the search direction defined by the nonlinear conjugate
gradient method in [5] can be used to restart any optimization method while guaranteeing the global convergence of the method.
Some numerical results are also presented.
Received March 12, 1999 / Revised version received April 25, 2000 / Published online February 5, 2001 相似文献
10.
In this paper, we consider the mean value of the product of multiplicative arithmetic functions with shifted argument. The
investigated functions have to satisfy the following conditions: their moduli do not exceed 1; the values on the set of primes
are close to 1 for one of the functions and close to a fixed complex number for the other function. Some consequences for
the classical functions are given. 相似文献
11.
Xianghong Gong 《Mathematische Annalen》2002,323(2):227-257
We show that reversible holomorphic mappings of have periodic points accumulating at an elliptic fixed point of general type. On the contrary, we also show the existence
of holomorphic symplectic mappings that have no periodic points of certain periods in a sequence of deleted balls about an
elliptic fixed point of general type. The radii of the balls are carefully chosen in terms of the periods, which allows us
to show the existence of holomorphic mappi
ngs of that are not reversible with respect to any involution with a holomorphic linear part, and that admit no invariant totally real and real surfaces.
Received: 5 December 2000 / Published online: 4 April 2002 相似文献
12.
Yuk-Kam Lau 《Monatshefte für Mathematik》2002,136(1):35-45
We study the asymptotic formula of for some arithmetical functions f and g. This generalizes the case investigated by Balakrishnan and Pétermann.
Received 15 January 2001; in revised form 7 July 2001 相似文献
13.
We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.Supported partly by the Wittgenstein 2000 Award of Peter Markowich, funded by the Austrian Science Foundation (FWF), research grants of DFG (436 RUS 113/615/0-1(R)) and RFBR (01-01-04002).On leave Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia. Supported partly by Max Planck Institute for the Mathematics in Sciences (Leipzig) and the Austrian Science Foundation (FWF) START Project (Y-137-TEC) of Norbert Mauser. 相似文献
14.
Summary. We describe a new iterative method for the solution of large, very ill-conditioned linear systems of equations that arise
when discretizing linear ill-posed problems. The right-hand side vector represents the given data and is assumed to be contaminated
by measurement errors. Our method applies a filter function of the form with the purpose of reducing the influence of the errors in the right-hand side vector on the computed approximate solution
of the linear system. Here is a regularization parameter. The iterative method is derived by expanding in terms of Chebyshev polynomials. The method requires only little computer memory and is well suited for the solution of
large-scale problems. We also show how a value of and an associated approximate solution that satisfies the Morozov discrepancy principle can be computed efficiently. An application
to image restoration illustrates the performance of the method.
Received January 25, 1997 / Revised version received February 9, 1998 / Published online July 28, 1999 相似文献
15.
Variant fountain theorems and their applications 总被引:5,自引:0,他引:5
Wenming Zou 《manuscripta mathematica》2001,104(3):343-358
In this paper we establish some variant fountain theorems without (P.S.)-type assumption. The abstract results will be used to study the symmetric nonlinear Schr?dinger equations and Dirichlet boundary value problems. Under no Ambrosetti–Rabinowitz's superquadraticity condition, we obtain infinitely many large energy and small negative energy solutions respectively. Received: 12 September 2000 相似文献
16.
We prove asymptotic stability results for nonlinear bipolar drift-diffusion-Poisson Systems arising in semiconductor device
modeling and plasma physics in one space dimension. In particular, we prove that, under certain structural assumptions on
the external potentials and on the doping profile, all solutions match for large times with respect to all q-Wasserstein distances. We also prove exponential convergence to stationary solutions in relative entropy via the so called
entropy dissipation (or Bakry-émery) method.
Authors’ addresses: Marco Di Francesco, Sezione di Matematica per L’Ingegneria, Dipartimento di Matematica Pura ed Applicata,
Università di L'Aquila, Piazzale E. Pontieri, 2, Monteluco di Roio, 67040 L’Aquila, Italy; Marcus Wunsch, Fakult?t für Mathematik,
Universit?t Wien, Nordbergstra?e 15, A-1090 Wien, Austria 相似文献
17.
Janina Kotus 《Monatshefte für Mathematik》2006,149(2):103-117
We consider the class of elliptic functions whose critical points in the Julia set are eventually mapped onto ∞. This paper
is a continuation of our previous papers, namely [11] and [12]. We study the geometry and ergodic properties of this class
of elliptic functions. In particular, we obtain a lower bound on the Hausdorff dimension of the Julia set that is bigger than
the estimate proved in [11]. Let h be the Hausdorff dimension of the Julia set of f. We construct an atomless h-conformal measure m and prove the existence of a (unique up to a multiplicative constant) σ-finite f-invariant measure μ equivalent to m. The measure μ is ergodic and conservative. 相似文献
18.
Zhang Wenpeng 《Monatshefte für Mathematik》2003,139(3):247-257
Let q3 be an odd number, a be any fixed positive integer with (a, q)=1. For each integer b with 1b<q and (b, q)=1, it is clear that there exists one and only one c with 0<c<q such that bca (mod q). Let N(a, q) denote the number of all solutions of the congruent equation bca (mod q) for 1b, c<q in which b and c are of opposite parity, and let
. The main purpose of this paper is to study the distribution properties of E(a, q), and to give a sharper hybrid mean value formula involving E(a, q) and Kloosterman sums.Received January 24, 2002; in revised form August 12, 2002
Published online February 28, 2003 相似文献
19.
We deal with all the maps from the exponential family f
ε(z) = (e
−1 + ε)exp(z), with ε ≥ 0. Let h
ε = HD(J
r,ε) be the Hausdorff dimension of the radial Julia sets J
r,ε. Observing the phenomenon of parabolic implosion, it is shown that the function ε ↦ h
ε is not continuous from the right.
The research of the first author was supported in part by the NSF Grant DMS 0100078. 相似文献
20.
Alessandro Zinani 《Monatshefte für Mathematik》2003,139(4):341-348
We calculate E[V
4(C)], the expected volume of a tetrahedron whose vertices are chosen randomly (i.e. independently and uniformly) in the interior of C, a cube of unit volume. We find
The result is in convincing agreement with a simulation of 3000·106 trials.Received February 12, 2002; in revised form August 13, 2002
Published online February 28, 2003 相似文献