Fibre cycles of holomorphic maps

This and the second part of the paper are to a great extent parts of my thesis [Si] which also appeared as preprint Mathematica Gottingensis 5/92. This work was partly supported by the S7B170 Geometrie und Analysis in Göttingen     

Ruin Probabilities for Large Claims in Delayed Renewal Risk Model

This paper investigates ruin probabilities (x) in the delayed renewal risk model, where x is the initial capital of an insurance company. Under the assumption that the claim size is heavy-tailed, we aim at a tail equivalence relationship of (x) as x . The result we obtain in this paper is surprisingly the same as the previous classical results.This work was supported by National Science Foundation of China (No. 10071081).     

Packing λ-Fold Complete Multipartite Graphs with 4-Cycles

A maximum packing of any -fold complete multipartite graph (where there are edges between any two vertices in different parts) with edge-disjoint 4-cycles is obtained and the size of each minimum leave is given. Moreover, when =2, maximum 4-cycle packings are found for all possible leaves.This research was supported by Australian Research Council Grant A69701550This research was supported by NSC Grant 88-2115-M-009-013This research was supported by NSF Grant DMS-9531722 and ONR Grant N00014-97-1-1067     

Linear programming with multiple objective functions: Step method (stem)

This paper describes a solution technique for Linear Programming problems with multiple objective functions. In this type of problem it is often necessary to replace the concept of optimum with that of best compromise. In contrast with methods dealing with a priori weighted sums of the objective functions, the method described here involves a sequential exploration of solutions. This exploration is guided to some extent by the decision maker who intervenes by means of defined responses to precise questions posed by the algorithm. Thus, in this man-model symbiosis, phases of computation alternate with phases of decision. The process allows the decision-maker to learn to recognize good solutions and the relative importance of the objectives. The final decision (best compromise) furnished by the man-model system is obtained after a small number of successive phases.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands.     

Composition operators from large weighted Hardy spaces into the Dirichlet space

Given a large weighted Hardy space we show there exists a composition operatorC with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College.     

On the automorphism groups of algebraic bounded domains

This paper is a part of author's doctoral thesis. It was partially supported by Sonderforschungsbereich 237 Unordnung und große Fluktuatuionen of the Deutsche Forschungsgemeinschaft     

A bound for minimal graphs with a normal at infinity

It is shown that a minimal graph with a normal at infinity is in a-priori bounded vertical distance from its approximating halfcatenoid. This is used to show that the exterior contact angle problem is wellposed under natural geometric conditions on the domain, while the exterior Dirichlet problem can be solvable only for data which satisfy an oscillation bound.This paper was written under the support of the Deutsche Forschungsgemeinschaft while the author was visiting the department of mathematics at Stanford University.This article was processed by the author using the LaT_EX style filepljour1 from Springer-Verlag.     

On indefinite superlinear elliptic equations

This paper concerns semilinear elliptic equations of the form – u+m(x)u=a(x)u ^p , wherea changes sign. We discuss the question of existence of positive solutions when the linear part is not coercive.This article was processed by the author using the LATEX style file pljourlm from Springer-Verlag.     

Symmetric hypersurfaces in Riemannian manifolds contracting to Lie-groups by their mean curvature

This paper concerns the deformation by mean curvature of hypersurfaces M in Riemannian spaces Ñ that are invariant under a subgroup of the isometry-group on Ñ. We show that the hypersurfaces contract to this subgroup, if the cross-section satisfies a strong convexity assumption.This forms part of the authors doctoral thesis and was carried out while the author was supported by a scholarship of the Graduiertenkolleg für Geometrie und Mathematische Physik.     

Strongly exposed points and Lyapunov's theorem

This work was supported by the International Foundation A Cultural Initiative.     

Point spectrum of elliptic operators in fibered half-cylinders and the related completeness problem

We consider an elliptic system in a half-cylinder ₊ × with coefficients constant in the direction of the axis and not necessarily smooth. We take different boundary conditions on {0} × and Dirichlet condition on {0}×. This defines a self-adjoint operatorA ^D. The main result in this paper is thatA ^D does not have eigenvalues. This answers conjecture 1.6 raised in [3]. When is bounded, we use this result to prove the completeness of a part of the family of eigenvectors, and associated vectors, of a corresponding operator pencils.This work was supported by INRIA, France, and partially by UCLA.     

Backward perturbation analysis of certain characteristic subspaces

Summary This paper gives optimal backward perturbation bounds and the accuracy of approximate solutions for subspaces associated with certain eigenvalue problems such as the eigenvalue problemAx=x, the generalized eigenvalue problem Ax=Bx, and the singular value decomposition of a matrixA. This paper also gives residual bounds for certain eigenvalues, generalized eigenvalues and singular values.This subject was supported by the Swedish Natural Science Research Council and the Institute of Information Processing of the University of Umeå.     

Growth conditions and regularity,a counterexample

It is shown that the so-called growth conditions are necessary for the local regularity of minimizers.This paper has been written while the author was visiting the Mathematisches Institut der Universität Bonn under the support of the Sonderforschungsberich 256.     

A Kähler structure on the moduli space of isometric maps of a circle into Euclidean space

We study the spaces and and _Lip of smooth (resp. non-degenerate Lipschitz) isometric maps of a circle into Euclidean space modulo orientation preserving Euclidean motions. We prove that and _Lip are infinite dimensional Kähler manifolds. In particular, they are complex Fréchet (resp. Banach) manifolds. This is proved by an infinite dimensional version of the Kirwan, Kempf-Ness Theorem [Kir84], [KN78], [Nes84] relating symplectic quotients to holomorphic quotients, applied to the action ofPSL ₂() on the free loop space ofS ².Oblatum 15-X-1994 & 5-VII-1995This research was supported in part by NSF grant DMS-92-05154.This research was partially supported by AFOSR grant F49620-92-J-0093.     

A remark on the Hardy inequalities

This work was supported by a grant from the Minerva foundation.     

Fluid-dynamic equations for reacting gas mixtures

Starting from the Grad 13-moment equations for a bimolecular chemical reaction, Navier-Stokes-type equations are derived by asymptotic procedure in the limit of small mean paths. Two physical situations of slow and fast reactions, with their different hydrodynamic variables and conservation equations, are considered separately, yielding different limiting results.This work was performed in the frame of the activities sponsored by MIUR (Project Mathematical Problems of Kinetic Theories), by INdAM, by GNFM, by the University of Parma (Italy), and by the European TMR Network Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis.This revised version was published online in April 2005 with a corrected issue number.     

The effect of dimension 4 in Aleksandrov's problem of filling a space by polyhedra

This paper deals with filling the hyperbolic space Hⁿ by non-compact polyhedra. In dimensions n <4 the non-compact case is very different from the compact one, which was investigated by A.D. Aleksandrov. For n 4 the compact and non-compact cases are almost similar. This investigation is closely related to deformations of complete and incomplete hyperbolic orbifolds (in the sense of W. Thurston) for which a strong rigidity result is proved-similar to the one for complete hyperbolic manifolds in dimension exceeding two.     

Variational principles for real eigenvalues of self-adjoint operator pencils

Double variational principles are established for eigenvalues of a (norm) continuous self-adjoint operator valued functionL defined on a real interval [, [.L() is not required to be definite for any . Applications are made to linear, quadratic and rational functionsL.This author acknowledges support from NSERC of Canada and the I.W. Killam Foundation.This author was supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176-MAT.     

Existence of a universal attractor for a fully hyperbolic phase-field system

Here we study a nonlinear hyperbolic integrodifferential system which was proposed by H.G. Rotstein et al. to describe certain peculiar phase transition phenomena. This system governs the evolution of the (relative) temperature and the order parameter (or phase-field) . We first consider an initial and boundary value problem associated with the system and we frame it in a history space setting. This is done by introducing two additional variables accounting for the histories of and . Then we show that the reformulated problem generates a dissipative dynamical system in a suitable infinite-dimensional phase space. Finally, we prove the existence of a universal attractor.     

Quadratic-Residue Codes and Cyclotomic Fields

We present an exposition of quadratic-residue codes through their embedding in codes over the quadratic subfield of the th cyclotomic field, the algebraic number field of th roots of unity. This representation allows the development of effective syndrome decoding algorithms that can fully exploit the code’s error-correcting capability. This is accomplished via Galois automorphisms of cyclotomic fields. For each fixed , the general results hold for all pairs , with a finite number of exceptions that depends on . A complete discussion of the set of quadratic-residue codes of length and dimension illustrates these results. This set includes the Golay code, the only perfect binary three-error-correcting code.A preliminary version of this paper was presented at the International Conference on Statistics, Combinatorics and Related Areas, October 3–5, 2003, University of Southern Maine, Portland, ME, USA.