On the periodic points of a two-parameter family of maps of the plane

We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation.     

A radiometric investigation of the precipitation of calcium fluoride

Errors arising from solubility losses and co-precipitation in the gravimetric determination of fluoride by precipitation of calcium fluoride by classical and homogeneous methods have been investigated by radiometric techniques. It is shown that co-precipitation of chloride is the larger source of error and least in the homogeneous method. Distribution of chloride in the calcium fluoride precipitate is shown to follow the Doerner-Hoskins distribution law.     

Characterisation of the first authenticated organomercury hydroxide, 4-Me2NC6H4HgOH

4-Me₂NC₆H₄HgOH was prepared from 4-Me₂NC₆H₄HgOAc. Full characterisation showed that it crystallises as discrete molecules, the first example of a true organomercury hydroxide in the solid state. The structures of 4-Me₂NC₆H₄HgOAc and (4-Me₂NC₆H₄)₂Hg are also discussed.     

Testing an alternative search algorithm for compound identification with the ‘Wiley Registry of Tandem Mass Spectral Data,MSforID’

A tandem mass spectral database system consists of a library of reference spectra and a search program. State‐of‐the‐art search programs show a high tolerance for variability in compound‐specific fragmentation patterns produced by collision‐induced decomposition and enable sensitive and specific ‘identity search’. In this communication, performance characteristics of two search algorithms combined with the ‘Wiley Registry of Tandem Mass Spectral Data, MSforID’ (Wiley Registry MSMS, John Wiley and Sons, Hoboken, NJ, USA) were evaluated. The search algorithms tested were the MSMS search algorithm implemented in the NIST MS Search program 2.0g (NIST, Gaithersburg, MD, USA) and the MSforID algorithm (John Wiley and Sons, Hoboken, NJ, USA). Sample spectra were acquired on different instruments and, thus, covered a broad range of possible experimental conditions or were generated in silico. For each algorithm, more than 30 000 matches were performed. Statistical evaluation of the library search results revealed that principally both search algorithms can be combined with the Wiley Registry MSMS to create a reliable identification tool. It appears, however, that a higher degree of spectral similarity is necessary to obtain a correct match with the NIST MS Search program. This characteristic of the NIST MS Search program has a positive effect on specificity as it helps to avoid false positive matches (type I errors), but reduces sensitivity. Thus, particularly with sample spectra acquired on instruments differing in their setup from tandem‐in‐space type fragmentation, a comparably higher number of false negative matches (type II errors) were observed by searching the Wiley Registry MSMS. Copyright © 2013 John Wiley & Sons, Ltd.     

The existence of approximate solutions for two-dimensional potential flow problems

A proof is given of the existence of an approximate Complex Variable Boundary Element Method solution for a Birichlet problem. This constructive proof can be used as a basis for numerical calculations. © 1996 John Wiley & Sons, Inc.     

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

The equation of state of binary ionic mixtures of similar ions, such as nitrogen, oxygen and carbon, has been extensively studied. The study of dense asymmetric mixtures, where Z₂ >> Z₁, has primarily focused on mixtures of hydrogen and iron at solar conditions. Using molecular dynamics simulations, we examine the behavior of highly asymmetric binary ionic mixtures, where the coupling of the high‐Z species may be orders of magnitude higher than the coupling of the low‐Z species. For the conditions we have studied, we find that strong correlations and signatures of solidification occur in the high‐Z species, while the low‐Z species exists as a freely flowing fluid within the high‐Z solid matrix. Solidification of the low‐Z species is correlated with the coupling between the two components. Using the Widom expansion method, we compute the plasma screening enhancement of the nuclear reaction rates for Z = 1 in a high‐Z matrix. We also provide some estimates of the coefficient of binary diffusion in the mixture. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical analysis of the anomalous spectral splitting of tetracene in 4He droplets

We present a theoretical analysis of the electronic absorption spectra of tetracene in (4)He droplets based on many-body quantum simulations. Using the path integral ground state approach, we calculate one- and two-body reduced density matrices of the most strongly localized He atoms near the molecule surface and use these to investigate the helium ground-state quantum coherence and correlations when tetracene is in its electronic ground and excited states. We identify a trio of quasi-one-dimensional, strongly localized atoms adsorbed along the long axis of the molecule that show some quantum coherence among themselves but far less with the remaining solvating helium. We evaluate the single-particle natural orbitals of the localized He atoms by diagonalization of the one-body density matrix and use these to construct single- and many-particle solvating helium basis states with which the zero-phonon spectral features of the tetracene-(4)He(N) absorption spectrum are then calculated. The absorption spectrum resulting from the three-body density matrix for the strongly bound trio of helium atoms is in very good agreement with the experimental data, accounting quantitatively for the anomalous splitting of the zero-phonon line [Hartmann, M.; Lindinger, A.; Toennies, J. P.; Vilesov, A. F. Chem. Phys. 1998, 239, 139; Krasnokutski, S.; Rouillé, G.; Huisken, F. Chem. Phys. Lett. 2005, 406, 386]. Our results indicate that the combination of strong localization and the quasi-one-dimensional nature of trios of helium atoms adsorbed along the long axis of tetracene leads to a quantum coherent, yet highly correlated ground state for the helium density closest to the molecule. The spectroscopic analysis shows that this feature accounts quantitatively for the anomalous splittings and hitherto unexplained fine structure observed in the absorption spectra of tetracene and suggests that it may be responsible for the corresponding zero-phonon splittings in other quasi-one-dimensional planar aromatic molecules.     

Relative partial photoionization cross-section of methylacetylene to the X2E ion state over the photon energy range 11–26 eV

Relative partial cross-sections for photoionization to the X²E ground state of the methylacetylene ion over the photon energy range 11–26 e V have been determined using synchrotron radiation. The observed cross-sections show a broad resonance feature similar to the results for photoionization to the X²II_u ground state of the acetylene ion. An explanation involving autoionization from a π^* (e) excited state is proposed.     

Test driving three 1995 genetic algorithms: New test functions and geometric matching

Genetic algorithms have attracted a good deal of interest in the heuristic search community. Yet there are several different types of genetic algorithms with varying performance and search characteristics. In this article we look at three genetic algorithms: an elitist simple genetic algorithm, the CHC algorithm and Genitor. One problem in comparing algorithms is that most test problems in the genetic algorithm literature can be solved using simple local search methods. In this article, the three algorithms are compared using new test problems that are not readily solved using simple local search methods. We then compare a local search method to genetic algorithms for geometric matching and examine a hybrid algorithm that combines local and genetic search. The geometric matching problem matches a model (e.g., a line drawing) to a subset of lines contained in a field of line fragments. Local search is currently the best known method for solving general geometric matching problems.