Some concepts of positive dependence for bivariate interchangeable distributions

In this work we consider some familiar and some new concepts of positive dependence for interchangeable bivariate distributions. By characterizing distributions which are positively dependent according to some of these concepts, we indicate real situations in which these concepts arise naturally. For the various families of positively dependent distributions we prove some closure properties and demonstrate all the possible logical relations. Some inequalities are shown and applied to determine whether under- (or over-) estimates, of various probabilistic quantities, occur when a positively dependent distribution is assumed (falsely) to be the product of its marginals (that is, when two positively dependent random variables are assumed, falsely, to be independent). Specific applications in reliability theory, statistical mechanics and reversible Markov processes are discussed. This work was partially supported by National Science Foundation GP-30707X1. It is part of the author's Ph.D. dissertation prepared at the University of Rochester and supervised by A. W. Marshall. Now at Indiana University.     

Cross sections at “asymptotic” energies in thep¯p collider

As a whole new range of energies will be soon experimentally studied, we present predictions for hadronic cross sections at future very high energy accelerators. All calculations are based on results accumulated in reggeon field theory, where methods of field theory (in the continuum and on the lattice) and statistical mechanics have been used. We have employed these results and translated them into a manageable phenomenological analysis of existing FERMILAB-ISR data. The size of the non-leading terms is determined and enables us to predict cross sections at energies in the range of the near futurep¯p collider. Parameter-free scaling functions and critical exponents which are exactly calculable in RFT are thus brought to an experimental test.     

Structure of mercaptobiphenyl monolayers on mercury

The molecular-scale structure and phase behavior of single-component Langmuir films of 4'-methyl-4-mercaptobiphenyl (MMB) and 4'-perfluoromethyl-4-mercaptobiphenyl (FMMB) on mercury were studied using surface tensiometry, grazing incidence X-ray diffraction, and X-ray reflectivity. At low coverages, a condensed but in-plane disordered single layer of surface-parallel molecules is found for both compounds. At high coverages, both compounds exhibit in-plane-ordered phases of standing-up molecules. For MMB, the biphenyl core dominates the structure, yielding a centered-rectangular unit cell with an area A(x) of 21.8 A(2)/molecule, with molecules tilted by approximately 14 degrees from the surface normal in the nearest-neighbor direction, and a coherence length xi of >1000 A for the crystalline domains. For FMMB, the perfluoromethyl group dominates the structure, yielding a hexagonal unit cell with untilted molecules, an area A(x) of 24.2 A(2)/molecule, and a much smaller xi of approximately 110 A. The structure is discussed in comparison with self-assembled monolayers of MMB on crystalline Au(111) and similar-length alkanethiolate SAMs on Au(111) and on mercury. The differences in the structure are discussed and traced to the differences in the substrate's surface structure, and in the molecular cross section and rigidity.     

Formation of inclusion organoactinide complexes with boron-containing macrocycles

Reaction of the organoactinide complexes (C5Me5)2AnMe2 (An = Th, U) with catecholborane yields an inclusion complex where the actinide is encapsulated inside a 15-membered, hexaoxo, trianionic macrocycle built from alternating catechol and catecholborate fragments. In the presence of LiOH, a dimer of two encapsulated actinide macrocycles is formed. The X-ray molecular structure for all the complexes is presented.     

Formation of hexacoordinate complexes of PhCCSiF3 with 2,2'-bipyridine and with 1,10-phenanthroline through intermolecular silicon...nitrogen interactions

Bidentate intermolecular Si...N interactions were utilized to form new hypervalent complexes of trifluoro-phenylethynyl-silane with 2,2'-bipyridine and with 1,10-phenanthroline. X-ray structures obtained for these complexes display a somewhat distorted octahedral geometry about the silicon atom. Binding constants ranging from 170 to 1600 M(-1) at 25 degrees C in CDCl3 were measured for the formation of these complexes, suggesting that such hypervalent complexes of silicon could be used as new motifs in supramolecular chemistry.     

Design of Stacked Self-Healing Rings Using a Genetic Algorithm

Ring structures in telecommunications are taking on increasing importance because of their self-healing properties. We consider a ring design problem in which several stacked self-healing rings (SHRs) follow the same route, and, thus, pass through the same set of nodes. Traffic can be exchanged among these stacked rings at a designated hub node. Each non-hub node may be connected to multiple rings. It is necessary to determine to which rings each node should be connected, and how traffic should be routed on the rings. The objective is to optimize the tradeoff between the costs for connecting nodes to rings and the costs for routing demand on multiple rings. We describe a genetic algorithm that finds heuristic solutions for this problem. The initial generation of solutions includes randomly-generated solutions, complemented by seed solutions obtained by applying a greedy randomized adaptive search procedure (GRASP) to two related problems. Subsequent generations are created by recombining pairs of parent solutions. Computational experiments compare the genetic algorithm with a commercial integer programming package.     

Cosmological Relativity: A New Theory ofCosmology1

A new general-relativistic theory of cosmology, the dynamical variables of whichare those of Hubble's, namely distances and redshifts, is presented. The theorydescribes the universe as having a three-phase evolution with a deceleratingexpansion followed by a constant and an accelerating expansion, and it predictsthat the universe is now in the latter phase. The theory is actually a generalizationof Hubble's law taking gravity into account by means of Einstein's theory ofgeneral relativity. The equations obtained for the universe expansion are elegantand very simple. It is shown, assuming ₀ = 0.24, that the time at which theuniverse goes over from a decelerating to an accelerating expansion, i.e., theconstant expansion phase, occurs at 0.03 from the big bang, where is theHubble time in vacuum. Also, at that time the cosmic radiation temperature was11 K. Recent observations of distant supernovae imply, in defiance of expectations,that the universe's growth is accelerating, contrary to what has always beenassumed, that the expansion is slowing down due to gravity. Our theory confirmsthese recent experimental results by showing that the universe now is definitelyin a stage of accelerating expansion.