On the uniqueness of pre-image measures

A necessary and sufficient condition for the uniqueness of the pre-image measure in the situation studied by Yershov [8] and other authors [4, 5] is given. This very natural condition, different from that in [8], has been discovered by Eisele [2] under more restrictive assumptions. Our main theorem extends this result to the situation considered by Yershov.The authors wish to express their cordial thanks to Prof. D. Kölzow for his many suggestions given during the elaboration of this common version of their papers.     

A refined theorem concerning the conditioning of semidefinite programs

Using a weaker version of the Newton-Kantorovich theorem [6] given by us in [3], we show how to refine the results given in [8] dealing with the analyzing of the effect of small perturbations in problem data on the solution. The new results are obtained under weaker hypotheses and the same computational cost as in [8].     

Locally testable semigroups

The locally testable semigroups were discovered in the study of finite automata (see [8], [12] for history and motivation). In this paper, we study the locally testable semigroups from a purely algebraic viewpoint, as a simultaneous generalization of both the normal bands and the nilpotent semigroups. We generalize the results of [8] and [12] to the infinite case and, under mild restrictions on the semigroups, obtain subdirect product decompositions which sharpen these results. This research was supported in part by the Advanced Research Projects Agency of the Office of the Secretary of Defense (F44620-70-C-0107) and is monitored by the Air Force Office of Scientific Research. A preliminary version of this paper appeared as a technical report, Department of Computer Science, Carnegie-Mellon University, March 1971.     

An alternating method for an inverse Cauchy problem

In this paper, an iterative boundary element method based on our relaxed algorithm introduced in [8] is used to solve numerically a class of inverse boundary problems. A dynamical choice of the relaxation parameter is presented and a stopping criterion based on our theoretical results is used. The numerical results show that the algorithm produces a reasonably approximate solution and improves the rate of convergence of Kozlov's scheme [10]. This revised version was published online in June 2006 with corrections to the Cover Date.     

A parallel projection method for solving generalized linear least-squares problems

Summary A parallel projection algorithm is proposed to solve the generalized linear least-squares problem: find a vector to minimize the 2-norm distance from its image under an affine mapping to a closed convex cone. In each iteration of the algorithm the problem is decomposed into several independent small problems of finding projections onto subspaces, which are simple and can be tackled parallelly. The algorithm can be viewed as a dual version of the algorithm proposed by Han and Lou [8]. For the special problem under consideration, stronger convergence results are established. The algorithm is also related to the block iterative methods of Elfving [6], Dennis and Steihaug [5], and the primal-dual method of Springarn [14].This material is based on work supported in part by the National Science foundation under Grant DMS-8602416 and by the Center for Supercomputing Research and Development, University of Illinois at Urbana-Champaign     

Some Properties of Hadamard Matrices Coming from Dihedral Groups

 In [4], one of the authors introduced a method to construct Hadamard matrices of degree 8n+4 from the dihedral group of order 2n. Here we study some properties of this construction. Received: May 7, 1999 Final version received: February 28, 2000     

First and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditions

An extension and unification is presented, of the recent results of Shapiro [16] and Gatjvin & Janin [8] about second order differentiability of the optimal value function and directional differentiability of optimal solutions of perturbed mathematical programs, under a relaxed directional version of the Managasarian-Fromowitz constraint qualification condition introduced by Gollan [9]     

A generalized conjugate gradient,least square method

Summary A generalizeds-term truncated conjugate gradient method of least square type, proposed in [1a, b], is extended to a form more suitable for proving when the truncated version is identical to the full-term version. Advantages with keeping a control term in the truncated version is pointed out. A computationally efficient new algorithm, based on a special inner product with a small demand of storage is also presented.We also give simplified and slightly extended proofs of termination of the iterative sequence and of existence of ans-term recursion, identical to the full-term version. Important earlier results on this latter topic are found in [15, 16, 8 and 11].The research reported in this paper was partly supported by NATO Grant No. 648/83     

Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

Notes on trimodal singularities

Singularities of functions of modality 1 or 2 were classified by Arnold [3]. Types of those of modality 3 were listed in [14]. Here we show that these are all Newton non-degenerate in the extended sense introduced in [17], and use this fact to obtain explicit regular bases and precise normal forms for right and for contact equivalence. This requires care since the only existing method for non-semiquasihomogeneous germs (using Arnold's “Condition A”) does not apply to all our cases. Received: 8 February 1999 / Revised version: 28 May 1999     

A temperature-based GENERIC approach for the thermodynamically consistent integration of thermoelastic solids

This work deals with the thermodynamically consistent (TC) time integration of thermoelastic systems with polyconvex density functions using the notion of the tensor-cross-product. While energy-momentum preserving integrators are well-known for conservative (isothermal) mechanical systems, Romero introduced in [7, 8] the new class of TC integrators. While [8] dealt with the sample application of thermo-elastodynamics, the scope of application was extended in [2] to coupled thermo-viscoelastodynamics in temperature form. A first step towards the systematic design of a TC integrator is to cast the evolution equations into the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework [6] which reveals additional underlying physical structures of the system. Relying on a polyconvex density function and using the notion of the tensor-cross-product [1] we arrive at a polyconvex version of the GENERIC framework. Further applying the notion of a discrete gradient leads to a TC integrator. Using the entropy as the thermodynamical state variable as in [5, 8] the GENERIC framework possesses an easy structure. However, this choice of thermodynamical state variable only allows to prescribe entropy Dirichlet boundary conditions directly. This drawback can be compensated by using Lagrange-multipliers to be able to handle temperature Dirichlet boundary conditions leading to an extended system of algebraic equations to be solved, see [5]. Alternatively, the present work uses the temperature as the thermodynamical state variable, see also [2, 3] and the use of an energy-based Newton-Raphson termination criterion. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new version of the ergodic method of Yu. V. Linnik in number theory

A new version of a known method of analytic number theory is developed. This version is demonstrated with a very simple model example — the problem on the asymptotically uniform distribution of integer points of a sphere with respect to a given modulus.This paper is a reworking of §5 of survey [6].Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 50, pp. 179–186, 1975.     

A robin-neumann problem in bounded domains with splitting boundary

We consider a mixed boundary-value problem for the homogeneous Laplace equation in a bounded domain which boundary splits up into two disjoint smooth components. On the one boundary component we pose a homogeneous Robin condition and an inhomogeneous Neumann condition on the other. We give a weak formulation, interpret this problem as a generalized spectral (eigenvalue) problem in the sense of F.Stummel (cf.[12]) and investigate existence, uniqueness and regularity of weak solutions. This problem is a cut-off version of a basic problem in water-wave theory (cf.Ramm [8], pp.394-395, Simon/Ursell [10] Stoker [11])     

The Kähler cone of a compact hyperkähler manifold

 This paper is a sequel to [11]. We study a number of questions only touched upon in [11] in more detail. In particular: What is the relation between two birational compact hyperk?hler manifolds? What is the shape of the cone of all K?hler classes on such a manifold? How can the birational K?hler cone be described? Most of the results are motivated by either the well-established two-dimensional theory, i.e. the theory of K3 surfaces, or the theory of Calabi-Yau threefolds and string theory. Received: 6 June 2001 / Revised version: 13 January 2003 / Published online: 8 April 2003     

Mean field bounds on Lyapunov exponents in Z d at the critical energy

We further develop the supersymmetric formalism initiated in [W1] (see also [SjW]). We obtain the optimal mean field bounds at the critical energy for Lyapunov exponents of random walks in random potentials in Z ^d at weak disorder. This extends some of the results in [W1]. Received: 9 December 1999 / Revised version: 8 May 2000 /?Published online: 15 February 2001     

A Relaxation of a Min-Cut Problem in an Anisotropic Continuous Network

Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized the problems and called the generalized problems max-flow and min-cut problems of Strang's type. In this paper we formulate a relaxed version of the min-cut problem of Strang's type and prove the existence of optimal solutions under some suitable conditions. The conditions are essential. In fact, there is an example of the relaxed version which has no optimal solutions if the conditions are not fulfilled. We give such an example in the final section. Accepted 8 October 1998     

Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

An integral characterization of random permutations. A point process approach

We consider random finite permutations and prove the following version of Thoma’s theorem in [8]: Random finite permutations which are class functions satisfy a new integration by parts formula if and only if they are given by a certain Ewens-Sütö process. The main source of inspiration for the results in this note is the fundamental work of Andras Sütö [7], from which some results are reestablished here again in the present point process approach.     

A limit theorem for sequences generated by Weyl transformation: Disappearance of dependence

 We prove a limit theorem for certain pseudo-random sequences generated by Weyl transformations, thereby extending a result of Sugita in [3]. Received: 8 June 2001 / Revised version: 4 March 2002 / Published online: 22 August 2002