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.     

Metabolic profiling of normal and hypertensive rat kidney tissues by hrMAS-NMR spectroscopy

Intact kidney tissue samples of normal and spontaneously hypertensive rats (SHRs) were analyzed by hrMAS-NMR spectroscopy and principal component analysis (PCA). Radial components (cortex, outer stripe of the outer medulla, inner stripe of the outer medulla, and papilla) were sampled from various regions across the kidney from multiple animals in order to establish inter- and intra-animal variability. The effects of temperature were also measured. Papilla was differentiated from the other tissue types, and this variation by tissue type was greater than the effect of temperature on the samples (spectra were compared from samples at 2 and 30 °C). This study also revealed long term stability issues of tissue storage at -80 °C. The PCA showed that the greatest differentiation between normal rats and SHRs was found in the cortex and the regions in the NMR spectra that were correlated with this variation were identified.Abbreviations hrMAS High-resolution magic angle spinning - NMR Nuclear magnetic resonance - PCA Principal component analysis - CSA Chemical shift anisotropy - DD Dipolar coupling - SHR Spontaneously hypertensive rat     

Characteristics of positive reciprocal matrices in the analytic hierarchy process

Positive reciprocal matrices (PRMs) are the basic elements used by the Analytic Hierarchy Process (AHP) for resolving an important class of multi-criteria decision problems. A PRM, A=(a _ij ), is square with all a _ij >0 and a _ji =1/a _ij . We discuss characteristics of such matrices based on an analysis of both real-world and randomly generated sets.     

Das Größenspektrum des natürlichen atmosphärischen Aerosols

The size distribution of natural occuring aerosol particles with a radius between 10^?5 and 10^?6cm was measured simultaneously by two different methods: Firstly the measurement of the current, caused by the natural distribution of electric charges on the particles, which move along the axis of a cylindrical condenser; secondly the distribution of thoron decay products on the size spectrum of the aerosol. The both methods have their maximum sensitivity in different regions of the size spectrum. The distributions obtained with the two methods are in rather good agreement. The small deviation of the two spectra is ascribed to systematic differences of the measuring methods.     

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].     

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.     

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.     

Anion dependent redox changes in iron bis-terdentate nitroxide {NNO} chelates

The reaction of [Fe(II)(BF(4))(2)]·6H(2)O with the nitroxide radical, 4,4-dimethyl-2,2-di(2-pyridyl) oxazolidine-N-oxide (L(?)), produces the mononuclear transition metal complex [Fe(II)(L(?))(2)](BF(4))(2) (1) which has been investigated using temperature dependent susceptibility, Mo?ssbauer spectroscopy, electrochemistry, density functional theory (DFT) calculations, and X-ray structure analysis. Single crystal X-ray diffraction analysis and Mo?ssbauer measurements reveal an octahedral low spin Fe(2+) environment where the pyridyl donors from L(?) coordinate equatorially while the oxygen containing the radical from L(?) coordinates axially forming a linear O(?)··Fe(II)··O(?) arrangement. Magnetic susceptibility measurements show a strong radical-radical intramolecular antiferromagnetic interaction mediated by the diamagnetic Fe(2+) center. This is supported by DFT calculations which show a mutual spatial overlap of 0.24 and a spin density population analysis which highlights the antiparallel spin alignment between the two ligands. Similarly the monocationic complex [Fe(III)(L(-))(2)](BPh(4))·0.5H(2)O (2) has been fully characterized with Fe-ligand and N-O bond length changes in the X-ray structure analysis, magnetic measurements revealing a Curie-like S = 1/2 ground state, electron paramagnetic resonance (EPR) spectra, DFT calculations, and electrochemistry measurements all consistent with assignment of Fe in the (III) state and both ligands in the L(-) form. 2 is formed by a rare, reductively induced oxidation of the Fe center, and all physical data are self-consistent. The electrochemical studies were undertaken for both 1 and 2, thus allowing common Fe-ligand redox intermediates to be identified and the results interpreted in terms of square reaction schemes.