Thermal stability of organic monolayers chemically grafted to minerals

The thermal degradation of monolayers of alkylsilicon hydrides (RSiH(3)), alkylphosphonic acids (RP(O)(OH)(2)), and alkyldimethylchlorosilanes (R(CH(3))(2)SiCl) supported on silica, alumina, titania, zirconia, and calcium hydroxyapatite particles was investigated using thermal gravimetric analysis (TGA). The common feature in the TGA was a dramatic weight loss between approximately 200 and approximately 600 degrees C (N(2) atmosphere), which was not present for bare minerals, and, thus, was assigned to the degradation of the surface grafted organic species. The onset of weight loss and the temperature of maximal weight loss rate (T(MAX)) showed no dependence on the mineral and were determined by the nature of the chemical group directly attached to the surface. The T(MAX) values were approximately 400-450 degrees C (monolayers of RSiH(3) and RP(O)(OH)(2)) and approximately 250 degrees C (monolayers of RSi(CH(3))(2)Cl). The activation energies (E(A)) of the degradation processes were determined using TGA at multiple heating rates. Surprisingly, the substrate material did not show a significant effect on E(A). For example, all the monolayers of octadecyl groups (R=C(18)H(37)) supported on silica, alumina, titania, and zirconia showed closed E(A) values approximately 265+/-15 kJ/mol. The weight loss, IR, MS, and chemical analysis data suggested that monolayer degradation occurred through pyrolysis of the hydrocarbon moieties (R groups) via cleavage of the CC and SiC (monolayers of silanes) or CC and PC bonds (monolayers of phosphonic acids). The inorganic portion of the molecule remained attached to the surface of the mineral (presumably as silicates or phosphates).     

The numerical index of the space

We give a partial answer to the problem of computing the numerical index of for .

     

Annealed Lower Tails for the Energy of a Charged Polymer

We consider a randomly charged polymer. Each monomer carries a random charge, and only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we obtain the correct temperature-scale for the Gibbs measure.     

Antidirected Hamiltonian paths and directed cycles in tournaments

We prove that in a tournament of odd order $n\ge 5$, the number of antidirected Hamiltonian paths starting with a forward arc and the number of Hamiltonian circuits have the same parity.     

A regularized stiffened-gas equation of state

An alternative to the stiffened-gas equation of state is proposed that corrects for unphysical behavior, namely the returning of negative pressure values for densities lower than the reference density. The question of generalizing a given isentropic equation of state is first addressed. Then, a regularized stiffened-gas equation of state is derived, which is the main goal of this work. Finally, the use of the new equation of state is briefly illustrated for a classical computational fluid dynamics benchmark concerning the evaluation of liquid impact on a wall.     

Exclusionary population dynamics in size-structured,discrete competitive systems

A discrete multi-species size-structured competition model is considered. By using decreasing growth functions, we achieve the self-regulation of species. We develop various biologically significant conditions for global convergence to the extinction state of the dominated species in the competitive system. With an example we illustrate coexistence in a chaotic supr transient. The chaotic attractor has an unusual pulsating nature.     

The Lie theory of certain modular form and arithmetic identities

Modular form identities lying in the framework of Shimura’s theory of nearly holomorphic modular forms are obtained by Lie theoretic means as consequences of identities relating the Maass–Shimura operator and the Rankin–Cohen brackets, which in turn follow from change-of-basis formulae in the theory of Verma modules. The Lie theoretic origin of known van der Pol and Lahiri-type arithmetic identities is thus unveiled, and similar new ones are derived in a systematic way. These identities relate divisor functions, Ramanujan’s τ-function and functions defined by the Fourier coefficients of other cusp forms and involve hybrid coefficients, drawn from Lie theory and number theory, given explicitly by formulae combining the arithmetic Clebsch–Gordan coefficients and the Bernoulli numbers. A few side results, interesting in their own right, such as Leibniz-type rules satisfied by the Rankin–Cohen brackets, are also obtained.     

Discrete-time Metapopulation Dynamics and Unidirectional Dispersal

The effects of unidirectional dispersal on single pioneer species discrete-time metapopulations where the pre-dispersal local patch dynamics are of the same (compensatory or overcompensatory) or mixed (compensatory and overcompensatory) types are studied. Single-species unidirectional metapopulation models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and the dispersal rate is low. The pioneer species goes extinct in at least one patch when the dispersal rate is high, while it persists when the rate is low. Unidirectional dispersal can generate multiple attractors with fractal basin boundaries whenever the pre-dispersal local patch dynamics are overcompensatory, and is capable of altering the local patch dynamics in mixed systems from compensatory to overcompensatory dynamics and vice versa.     

Allee effects in a discrete-time SIS epidemic model with infected newborns

We extend the framework of Rios-Soto et al. (Contemporary Mathematics, 2006, 410, 297) to include both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number ?₀, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This is in contrast to the recent observations of Franke and Yakubu, that the demographic dynamics can be chaotic while the infective dynamics are oscillatory and non-chaotic in periodically-forced SIS epidemic models (Mathematical Biosciences, 2006, 204, 68).