A Note on an Input Control Model of a Predictive Regression Interval

A well-known problem of prediction in linear regression models is to find a confidence interval for the random value of the dependent variable when the values of the independent variables are given. Such a situation may arise in economic quality control models when the independent variables are costly inputs and the dependent variable is some measure of quality or production. In such a circumstance, an important control objective may be to find values for the inputs that will maximize the lower limit of the prediction confidence interval for a fixed budget, or alternatively, to minimize the cost of the inputs for a fixed lower limit of the confidence interval. In this paper, we shall show that global optima can be found using known algorithms. The special case of simple linear regression is discussed and an illustrative example is provided.     

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates. The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions of Non-linear Evolution Equations”.     

A characterization of certain irreducible symplectic 4-folds

 We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface. Received: 26 June 2002 / Revised version: 9 September 2002 Published online: 14 February 2003 Mathematics Subject Classification (2000): Primary 14J32, Secondary 32Q20     

General Information

In this paper, we propose and analyze an SQP-type method for solving linearly constrained convex minimization problems where the objective functions are too complex to be evaluated exactly. Some basic results for global convergence and local superlinear convergence are obtained according to the properties of the approximation sequence. We illustrate the applicability of our approach by proposing a new method for solving two-stage stochastic programs with fixed recourse.     

A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards

We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.      

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations

The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via coupling methods.     

Differential effects of synchronous and asynchronous multifinger coactivation on human tactile performance

Background  

Repeated execution of a tactile task enhances task performance. In the present study we sought to improve tactile performance with unattended activation-based learning processes (i.e., focused stimulation of dermal receptors evoking neural coactivation (CA)). Previous studies show that the application of CA to a single finger reduced the stationary two-point discrimination threshold and significantly increased tactile acuity. These changes were accompanied by an expansion of the cortical finger representation in primary somatosensory cortex (SI). Here we investigated the effect of different types of multifinger CA on the tactile performance of each finger of the right hand.