The potential of pyrolysis/gas chromatography/mass spectrometry for determining the progress of lignification: An investigation of maturing asparagus sclerenchyma tissue

Sclerenchyma tissues from semi-mature and mature asparagus spears were analysed by pyrolysis/gas chromatography/mass spectrometry and by conventional chemical methods in order to determine the degree of lignification and compare analytical techniques. The pyrolysis data are similar to those obtained by a chemical method involving alkaline extraction at 70°C followed by spectrophotometric determination of phenolic content. The pyrolysis method was more rapid, sensitive and informative than the chemical technique and shows considerable potential for studying the chemical basis of the textural development of plant foods.     

One-Dimensional Poisson Growth Models With Random and Asymmetric Growth

Suppose there is a Poisson process of points X _i on the line. Starting at time zero, a grain begins to grow from each point X _i , growing at rate A _i to the left and rate B _i to the right, with the pairs (A _i , B _i ) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A _i +B _i , and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A _i , B _i ) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A _i =B _i =1. Simulation results are given to illustrate the various theorems.     

Protonated ethanol and its neutral counterparts

Collisionally activated dissociation and neutralization-reionization experiments reveal that protonation of ethanol leads to two distinct isomers, the classical ion CH₃CH₂OH⁺₂ and the proton-bound complex C₂H₄…H⁺…OH₂. The neutral counterpart of the latter is unstable, whereas that of the former can be produced in a bound state if the CH₃CH₂OH⁺₂ precursor ion is formed under low ion source pressure conditions and, thus, with higher internal energies. This suggests that there are substantial differences in the geometries of CH₃CH₂OH⁺₂ and the hypervalent CH₃CH₂OH₂ ·. This provides only a partial explanation for unusual isotope effects; C₂H₅OD₂ ·, CH₃CD₂OD₂ ·, and CD₃CH₂OD₂ · are substantially more stable than C₂D₅OD₂ · and C₂H₅OH₂ ·.     

Backward bifurcations in simple vaccination models

We describe and analyze by elementary means some simple models for disease transmission with vaccination. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. We extend the results to include models in which the parameters may depend on the level of infection.     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.     

An effective modeling and solution approach for the generalized independent set problem

The generalized independent set (GIS) problem was first introduced by Hochbaum and Pathria (Forest Sci 43(4), 544–554, 1997) and independently explored in greater detail by Hochbaum (Manage Sci 50(6), 709–123, 2004). This problem, with applications in forest management and a variety of related areas, is a generalization of the classical maximum independent set problem. In this paper we highlight a natural, nonlinear formulation for the problem that is an attractive alternative to the linear model found in the literature. The effectiveness of this alternative formulation is demonstrated by computational experience on test problems of varying size and density, disclosing a dramatic reduction in the time to obtain optimal and near optimal solutions and an ability to solve much larger problems.     

The phase diagram of the lyotropic nematic mesophase in the TTAB/NaBr/water system

The phase diagram of the nematic mesophase present in the tetradecyltrimethylammonium bromide/sodium bromide/water ternary system was determined. A calamitic nematic mesophase (N_C) was observed which extends to very high concentrations of electrolyte. The order parameters of the surfactant head group in the mesophases were studied by the NMR quadrupolar splitting of the deuterated surfactant. On increasing the temperature of nematic mesophases with low electrolyte concentrations, a phase separation occurs with the formation of a more highly ordered hexagonal phase and an isotropic phase. Diffusion measurements of the isotropic micellar solution by the NMR PFG method were used to estimate hydrodynamic radii at low surfactant concentrations and to study micelle diffusion as the concentration of the surfactant was increased to the liquid crystalline region. At higher surfactant concentrations, the diffusion coefficient reached a limiting value. The calamitic nematic mesophase in this surfactant/electrolyte/water system appears to be formed by long wormlike micelles.