Age of the universe and the density parameter

An exact formula for the age of the universe in terms of the density parameter is found that may be used instead of the approximate one in current use, among other purposes, for the estimate of an upper bound of relic particles in the present universe.     

A class of laplace transforms arising in a diffusion problem

It is shown that the function [α + (1 + 2s)^1/2]^?1, s ≥ 0, with fixed α ≥ ?1, is the Laplace transform of an explicitly given non-negative function g(x;α), × ≥ 0. This class of functions has easily computable convolutions. This property is used to identify the distribution of a sojourn time integral for the diffusion defined as Brownian motion on the real line with constant drift to the origin. © 1994 John Wiley & Sons, Inc.     

Efficient solution approaches for a discrete multi-facility competitive interaction model

In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments show that the approximate approach (with small α) performs extremely well solving large scale problems while the exact approach performs very well for small to medium-sized problems.     

Long-lived charge carrier generation in ordered films of a covalent perylenediimide–diketopyrrolopyrrole–perylenediimide molecule

The photophysics of a covalently linked perylenediimide–diketopyrrolopyrrole–perylenediimide acceptor–donor–acceptor molecule (PDI–DPP–PDI, 1) were investigated and found to be markedly different in solution versus in unannealed and solvent annealed films. Photoexcitation of 1 in toluene results in quantitative charge separation in τ = 3.1 ± 0.2 ps, with charge recombination in τ = 340 ± 10 ps, while in unannealed/disordered films of 1, charge separation occurs in τ < 250 fs, while charge recombination displays a multiexponential decay in ∼6 ns. The absence of long-lived, charge separation in the disordered film suggests that few free charge carriers are generated. In contrast, upon CH₂Cl₂ vapor annealing films of 1, grazing-incidence X-ray scattering shows that the molecules form a more ordered structure. Photoexcitation of the ordered films results in initial formation of a spin-correlated radical ion pair (electron–hole pair) as indicated by magnetic field effects on the formation of free charge carriers which live for ∼4 μs. This result has significant implications for the design of organic solar cells based on covalent donor–acceptor systems and shows that long-lived, charge-separated states can be achieved by controlling intramolecular charge separation dynamics in well-ordered systems.     

Stability of vibrations of finite amplitude in an electron-ion ring

The article discusses transverse vibrations of finite amplitude in an electron-ion ring. Far from the region of linear resonances, an equation is obtained for slowly varying amplitudes, and the conditions are found for the excitation of instability of the negative pressure type. Near the lower boundary of the region of linear instability, the conditions are found under which nonlinearity breaks down the stability of the vibrations with finite amplitudes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 170–172, May–June, 1974.The author is indebted to B. V. Chirikov for his evaluation of the results of the work.     

Cyclization of protected N-acylhydroxyguanidine to 3-amino-1,2,4-oxadiazole

The acid mediated cyclization of a protected N-acylhydroxyguanidine into the corresponding 3-amino-1,2,4-oxadiazole and confirmation of its structure by single crystal X-ray crystallography is reported herein. The yield of the cyclization is comparable to literature reports utilizing alternative procedures. Importantly, these new conditions provide complementary chemoselectivity to current synthetic procedures which may be useful for the synthesis of 3-amino-1,2,4-oxadiazoles in general.     

Microwave assisted synthesis of bridgehead alkenes

A new, concise method to synthesize triene precursors for the type 2 intramolecular Diels-Alder reaction has been developed. Microwave irradiation of the trienes provides a convenient method for the synthesis of bridgehead alkenes. Higher yields, shorter reaction times, and lower reaction temperatures provide a general and efficient route to this interesting class of molecules.     

Discrete cooperative covering problems

A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p facilities from a given set of potential sites. Two other problems that can be solved by the max-cover approach are the equivalents to set covering and p-centre problems. The problems are formulated, analysed and solved on networks. Optimal and heuristic algorithms are proposed and extensive computational experiments reported.     

The minmax regret gradual covering location problem on a network with incomplete information of demand weights

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only information on the range of these random variables, this study is aimed at finding the “minmax regret” location that minimizes the worst-case coverage loss. We show that under some conditions, the problem is equivalent to known location problems (e.g. the minmax regret median problem). Polynomial time algorithms are developed for the problem on a general network with linear coverage decay functions.