The Dual of a Logical Linear Programme

A Linear Programme (LP) involves a conjunction of linear constraints and has a well defined dual. It is shown that if we allow the full set of Boolean connectives {, , } applied to a set of linear constraints we get a model which we define as a Logical Linear Programme (LLP). This also has a well defined dual preserving most of the properties of LP duality. Generalisations of the connectives are also considered together with the relationship with Integer Programming formulation.     

Lineare Programme

Ohne Zusammenfassung     

Cost-Benefit Study of a Proposed Daylight Running Lights Safety Programme

This article reports a model developed for the U.S. Department of Transportation (D.O.T.) to evaluate the costs and safety benefits of a proposed safety regulation on daylight running lights. Three alternative policies are considered: (A) not to issue the regulation and not to engage in any further investigation; (B) to issue the regulation as soon as possible; (C) to undertake further research and field testing before making a decision. The model does not require the assignment of a specific societal value per highway fatality prevented; rather, it determines for what range of values each of the alternatives (A)-(C) is most preferred. Based on the model, a recommendation was made within D.O.T. to pursue alternative (C).     

2001 Publication Programme

Publishers Note

2001 Publication Programme     

A multi-criteria model for auditing a Predictive Maintenance Programme

Auditing tools can play a key role in the continuous improvement of maintenance policies, in particular to enhance predictive maintenance (PM). This paper proposes a multi-criteria model for auditing a Predictive Maintenance Programme (PMP) developed and implemented in the General Hospital of Ciudad Real (GHCR) in Spain. The model has a two-level structure, with top level auditing areas specified by second level auditing criteria on which the performance of the PMP should be appraised. This structure resulted from the analysis and discussion of an internal questionnaire to the management, technical and consulting staff of GHCR. This also guided the association of a performance scale with each criterion, describing several reference levels of accomplishment. Using the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) approach, a hierarchical additive value model was constructed, with criteria weights and value scales derived from staff judgments of comparison of different reference levels and profiles of performance. This model enables managers to measure the performance of the PMP and its added value for the hospital, not only against each audit criterion individually, but also on each area and in overall terms. Integrated in a management “tableau de bord”, the model outputs permit the identification of PMP deficiencies requiring urgent intervention and corrective measures for its continuous improvement.     

Solution of a Busemann problem

We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature).     

SOLUTION OF A RESEARCH PROBLEM

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Lineare Programme und allgemeine Vertretersysteme

Ohne Zusammenfassung     

Solution of a problem of Ulam

In this paper we solve the following Ulam problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist” and establish results involving a product of powers of norms [[5.]; [5.]; [5.]]. There has been much activity on a similar “ -isometry” problem of Ulam [ [1.], 633–636; [2.], 263–277; [4.]]. This work represents an improvement and generalization of the work of [3.], 222–224].     

Solution of a question of Knarr

The Moufang condition is one of the central group theoretical conditions in Incidence Geometry, and was introduced by Jacques Tits in his famous lecture notes (1974).

About ten years ago, Norbert Knarr studied generalized quadrangles (buildings of Type ) which satisfy one of the Moufang conditions locally at one point. He then posed the fundamental question whether the group generated by the root-elations with its root containing that point is always a sharply transitive group on the points opposite this point, that is, whether this group is an elation group.

In this paper, we solve the question and a more general version affirmatively for finite generalized quadrangles.

Moreover, we show that this group is necessarily nilpotent (which was only known up till now when both Moufang conditions are satisfied for all points and lines).

In fact, as a corollary, we will prove that these groups always have to be -groups for some prime .

     

Solution of a problem of Skolem

T. Skolem shows that there are at most six integer solutions to the Diophantine equation x⁵ + 2y⁵ + 4z⁵ ? 10xy³z + 10x²yz² = 1. The author shows here that there are precisely three integer solutions.     

Solution to a problem of FitzGerald

Semigroup Forum - FitzGerald identified four conditions (RI), (UR), (RI*) and (UR*) that are necessarily satisfied by an algebra if its monoid of endomorphisms has commuting idempotents. We show...     

Existence of a Nonstationary Poiseuille Solution

The nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution of the inverse problem for the heat equation. The existence and uniqueness of such nonstationary Poiseuille solution with the prescribed flux F(t) of the velocity field is studied. It is proved that under some compatibility conditions on the initial data and flux F(t) the corresponding inverse problem has a unique solution in Holder spaces.Original Russian Text Copyright © 2005 Pileckas K. and Keblikas V.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 649–662, May–June, 2005.     

Solution of a tridiagonal operator equation

Let H be a separable Hilbert space with an orthonormal basis {e_n/n∈N}, T be a bounded tridiagonal operator on H and T_n be its truncation on span ({e₁, e₂, … , e_n}). We study the operator equation Tx = y through its finite dimensional truncations T_nxⁿ = y_n. It is shown that if and are bounded, then T is invertible and the solution of Tx = y can be obtained as a limit in the norm topology of the solutions of its finite dimensional truncations. This leads to uniform boundedness of the sequence . We also give sufficient conditions for the boundedness of and in terms of the entries of the matrix of T.     

Solution of a resource allocation game

Translated from Vychislitel'nye Sistemy i Voprosy Prinyatiya Reshenii, pp. 180–183, 1991.     

一道习题的几何解法

从几何角度分析一道高等数学习题,指出所求的点的几何特征,给出了基于几何思想的解法.