Adding activities to the dual instead of cuts to the primal problem

When solving a problem by appending cuts the dimension of the corresponding simplex tableau and the basic inverse oscillates, which makes it difficult to implement a cutting plane algorithm based on a standard LP code. Moreover, it is complicated to express a cut in the original variables. In this paper we show that by formulating the dual to the problem and adding activities, these adverse effects can be circumvented. It is shown that the set of activities which can be added is the same as the set of cuts which can be appended and that it is easy to exhibit an activity in the original primal variables. As a consequence of this a new formulation of a cut in the original primal variables is given.     

An approach to the theory of Lebesgue-Bochner measurable functions and to the theory of measure

Mathematische Annalen -     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

Estimation of production technology when the objective is to maximize return to the outlay

This paper deals with estimation of production technology where endogeneous choice of input and output variables is explicitly recognized. To address this endogeneity issue, we assume that producers maximize return to the outlay. We start from a flexible (translog) transformation function with a single output and multiple inputs and show how the first-order conditions of maximizing return to the outlay can be used to come up with an ‘estimating equation’ that does not suffer from the econometric endogeneity problem although the output and input variables are chosen endogenously. This is because the regressors in this estimating equation are in ratio forms which are uncorrelated with the error term under the assumption that producers maximize return to the outlay. The analysis is then extended to the multiple outputs and multiple inputs case with technical inefficiency. Although the estimating equations in both single and multiple output cases are neither production nor distance functions, they can be estimated in a straightforward manner using the standard stochastic frontier technique without worrying about endogeneity of the regressors. Thus, we provide a rationale for estimating the technology parameters consistently using an econometric model which requires data on only input and output quantities.     

On the stability of the solutions to the compressible Navier-Stokes equations when the Mach number goes to zero

In this paper an asymptotic stability result is estabilished for the compressible navier-Stokes equations. Since the Mach number tends to zero, the incompressible limit solution of compressible Navier-Stokes equations is proved to be stable exponentially. Some results of Stokes' problem are used.     

Regularities of the solutions to the Fokker-Planck-Boltzmann equation

In this paper, we consider the regularities of the solutions to the Fokker-Planck-Boltzmann equation. In particular, we prove that for hard sphere case, the strong solution constructed by Li and Matsumura [H. Li, A. Matsumura, Behavior of the Fokker-Planck-Boltzmann equation near a Maxwellian, Arch. Ration. Mech. Anal. (2008), in press] near Maxwellian becomes immediately smooth with respect to all variables as long as t>0.     

Harmonic mappings of the hexagasket to the circle

Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data.Explicit formulas are also given for the energy of the mapping.We have generalized the results in [10].     

Application of the EAS-concept to a p-version of the finite shell formulation to avoid volumetric locking

A modification of the enhanced assumed strain concept is proposed to avoid volumetric locking phenomena in finite elements using higher-order p-shell element formulations based on Lagrangean polynomials and a linear finite shell kinematics. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The location of public facilities intermediate to the journey to work

Location—allocation models typically locate facilities with respect to points to be served, for example to the homes of potential patrons. Certain types of facility, however, are employed by persons who travel to the facility from their homes and continue their journey to another location. Child care facilities are an example of this pattern of patronage, with parents dropping children off at a centre en route to work. The paper presents a discrete-space location—allocation model minimizing the diversion of patrons' journeys to work. The problem reduces to the structure and combinatorial dimensions of the simple P-median problem. The model is applied to the transit worktrip patterns of single parents in Edmonton, Canada. The facilities generated by the model tend to central locations in the city where workplaces are concentrated and transit connections are efficient. The model provides a compromise between ones minimizing home-facility travel times and facility-workplace travel times.