A Process for Determining Priorities and Weights for Large-Scale Linear Goal Programmes

Many planning models can be formulated as large-scale linear goal-programming problems in which the analyst and user must establish thousands of objective-function weights that reflect the priorities of the many goals. How to select such weights so as to have the resulting optimal solution be a suitable compromise solution is the main focus of this paper. We first describe the problem setting that gave rise to the need, here military personnel planning, and then a process by which a set of goal priorities and objective-function weights can be developed using Saaty's analytic hierarchy process.     

An order topologyfor finitely generated free monoids

In this article a method is given for embedding a finitely generated free monoid as a dense subset of the unit interval. This gives an order topology for the monoid such that the submonoids generated by an important class of maximal codes occur as “thick” subsets. As an ordered topological space, the notion of thickness in a frec monoid can be interpreted in a number of ways. One such notion is that of density. In particular, subsets of a free monoid that fail to meet all two sided ideals (the thin sets, of which recognizable codes are an example) are shown (corollary 4.2) to be nowhere dense. Furthermore, it is shown (corollary 5.1) that a thin code is maximal if and only if the submonoid that it generates is dense on some interval. Thus thin codes that are maximal are precisely those that generate thick submonoids. Another notion of thickness is that of category. The embedding allows the free monoid to be viewed as a subspace of the unit interval. In theorem 5.6 it is shown that a thin code is maximal just in case the closure of the submonoid that it generates is second category in the unit interval. A mild connection with Lebesque measure is then made. In what follows, all free monoids are assumed to be generated by a finite set of at least two elements. IfA is such a set, thenA ^* denotes the free monoid generated byA. The setA is called an alphabet, the elements ofA ^* are called words, ande denotes the empty word inA ^*. Topological terminology and notation follows that of Kelley [2].     

Encounters with degeneracy: A personal view

We give a brief history of degeneracy and cycling and discuss aspects of these topics that have been of interest to the author.     

An analytical model for close combat dynamics

A coherent dynamic combat model is developed from basic principles. The governing set of equations has a striking resemblance to the continuity equation in fluid dynamics with an additional term for the losses of combat units. The salient features of the model are a moving battle front, the replenishment of losses, and the withdrawal of combat units while others are still engaged. A basic example shows that the often used force ratio of three can produce a frontline movement up to 90% of the speed of the attacker. Another example simulates a well documented battle from the American Civil War. It is shown that terrain influences and the absence of reconnaissance had a large adverse effect on the outcome of the battle for the Confederate forces.     

Conflict Analysis in the Politico-Military Environment of a New World Order

A methodology is developed to analyse present and future crisis and conflict potentials of small or large geopolitical regions. A set of criteria is used to describe the present economic, social, political and military conditions of a country and the future criteria trends. A multi-criteria decision analysis model is invoked to compute the crisis and conflict potentials under simultaneous consideration of all other countries in that region. The methodology is demonstrated in the crisis and conflict potentials analysis of the former Soviet republics including bordering countries.     

The groups of the semigroup of compact subsets of a topological group

The compact subsets of a topological groupG form a semigroup,S(G), when multiplication is defined by set product. This semigroup is a topological semigroup when given the Vietoris topology. It would be expected that the subgroups ofS(G) should in some way be related to the groupG. This is the case. It is shown that the subgroups ofS(G) are both algebraically and topologically exactly the groups obtained as quotients of certain subgroups ofG. One consequence of this is that every subgroup ofS(G) is a topological group. Conditions are also given for these subgroups to be open or closed. Green's relations inS(G) have a particularly nice formulation. As a result, the relationsD andJ are equal inS(G). Moreover, the Schützenberger group of aD-class is a topological group that is topologically isomorphic to a quotient of certain subgroups ofG.     

Rational design of combination enzyme therapy for celiac sprue

Celiac sprue (also known as celiac disease) is an inheritable, gluten-induced enteropathy of the upper small intestine with an estimated prevalence of 0.5%-1% in most parts of the world. The ubiquitous nature of food gluten, coupled with inadequate labeling regulations in most countries, constantly poses a threat of disease exacerbation and relapse for patients. Here, we demonstrate that a two-enzyme cocktail comprised of a glutamine-specific cysteine protease (EP-B2) that functions under gastric conditions and a PEP, which acts in concert with pancreatic proteases under duodenal conditions, is a particularly potent candidate for celiac sprue therapy. At a gluten:EP-B2:PEP weight ratio of 75:3:1, grocery store gluten is fully detoxified within 10 min of simulated duodenal conditions, as judged by chromatographic analysis, biopsy-derived T cell proliferation assays, and a commercial antigluten antibody test.     

A cube in a tetrahedron: microwave-assisted synthesis of an octametallic Fe(III) cluster

The microwave-assisted reaction of Fe(O2CMe)2 with salicylaldoxime (saoH2) in pyridine produces an octametallic cluster in crystalline form in 2 min. The core describes a cube encapsulated in a tetrahedron, while sao2- exhibits a novel coordination mode.     

Planar tetranuclear lanthanide clusters with the Dy4 analogue displaying slow magnetic relaxation

Two isostructural tetranuclear lanthanide clusters of general formula [Ln(III)(4)(μ(3)-OH)(2)(o-van)(4)(O(2)CC(CH(3))(3))(4)(NO(3))(2)]·CH(2)Cl(2)·1.5H(2)O (Ln = Gd (1) and Dy (2)) (o-van = 3-methoxysalicylaldehydato anion) are reported. The metallic cores of both complexes display a planar 'butterfly' arrangement. Magnetic studies show that both are weakly coupled, with 2 displaying probable SMM behaviour.