On asymmetry of some convex bodies

We determine Minkowski's measure of asymmetry for convex hulls of a point and some sets for which the asymmetry is known. Some properties of the asymmetry measure are found which may indicate some interesting properties of convex bodies. Received March 1, 2001, and in revised form June 29, 2001. Online publication December 17, 2001.     

A Riemannian version of Korn's inequality

We prove a Korn type inequality for vector fields on a Riemann manifold. This inequality includes the special cases proved in the literature for domains in . If the domain is convex, we can considerably weaken the needed assumption on the boundary values. Received: 26 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001     

A polynomial case of unconstrained zero-one quadratic optimization

Unconstrained zero-one quadratic maximization problems can be solved in polynomial time when the symmetric matrix describing the objective function is positive semidefinite of fixed rank with known spectral decomposition. Received: August 2000 / Accepted: March 2001?Published online May 18, 2001     

Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices

It is shown that a function is completely determined by the samples of on sets where and is irrational if and of If then the samples of on and only the first k derivatives of at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions and are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero and satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials that are not Riesz bases for A signal processing application in which such sampling sets arise naturally is described in detail.     

A Survey on Contractible Edges in Graphs of a Prescribed Vertex Connectivity

 The aim of the present paper is to survey old and recent results on contractible edges in graphs of a given vertex connectivity. Received: June 5, 2001 Final version received: August 23, 2001     

Stability of the Lipschitz extension property under metric transforms

We show that the linear and nonlinear Lipschitz extension properties of a metric space are not changed when the original metric is replaced by a new metric obtained by composition with an arbitrary concave function. Submitted: January 2001, Revised: February 2001.     

On Risk-Sensitive Ergodic Impulsive Control of Markov Processes

Impulsive control of continuous-time Markov processes with risk- sensitive long-run average cost is considered. The most general impulsive control problem is studied under the restriction that impulses are in dyadic moments only. In a particular case of additive cost for impulses, the impulsive control problem is solved without restrictions on the moments of impulses. Accepted 30 April 2001. Online publication 29 August 2001.     

Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses

It is proved that families of solutions of the complex Monge-Ampère equation with fixed boundary values and certain bounds on the right hand side are equicontinuous. Received: 24 April 2001; in final form: 10 August 2001 / Published online: 28 February 2002     

Hodge equations with change of type

A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces to the equations for harmonic 1-forms on the projective disc is studied in detail. A boundary-value problem for this example is formulated and shown to possess weak solutions. Received: May 16, 2001; in final form: September 24, 2001?Published online: October 30, 2002