Concerning the validity of the stochastic approach to chemical kinetics

A simple argument advanced recently in support of the legitimacy of the stochastic formulation of chemical kinetics has been criticized because it seems to require the imminent collision of widely separated molecules. It is argued here that this criticism is unwarranted because it is based on an incorrect use of probabilities. To illustrate the various probabilistic considerations involved, a detailed analysis is presented of a closely related but mathematically simpler problem: the calculation of the collision probability per unit time for a thermally equilibrized one-dimensional gas of point particles.     

A line intensity transfer model for the rotational raman spectrum of ethylene

A new model for the spectrum of ethylene, utilizing the line-mixing concept for overlapping lines, is presented here. The Lorentzian line shape is assigned to all the lines, with the single transitions having the usual directly pressure-dependent widths, and with overlapping lines considered as a single composite feature having an inversely pressure-dependent width. This model is compared with two sets of data: interferometric data over a range of pressures, and an ad hoc model that matches experimental line spectrum data at a single pressure. Inversely pressuredependent widths are obtained for the two comparisons, and the discrepancy between the results is explained.     

Simplified ohmic and Schottky contact formation for field effecttransistors using the single layer integrated metal field effecttransistor (SLIMFET) process

A new III-V semiconductor device fabrication process for GaAs-based field effect transistors (FET) is presented which uses a single lithographic process and metal deposition step to form both the ohmic drain/source contacts and the Schottky gate contact concurrently. This single layer integrated metal FET (SLIMFET) process simplifies the fabrication process by eliminating an additional lithographic step for gate definition, a separate gate metallization step, and thermal annealing for ohmic contact formation. The SLIMFET process requires a FET structure which incorporates a compositionally graded In_xGa_1-xAs cap layer to form low resistance, nonalloyed ohmic contacts using standard Schottky metals. The SLIMFET process also uses a Si₃N₄ mask to provide selective removal of the InGaAs ohmic layers from the gate region prior to metallization without requiring an additional lithographic step. GaAs MESFET devices were fabricated using this new SLIMFET process which achieved DC and RF performance comparable to GaAs MESFET's fabricated by conventional methods     

A novel thermal rearrangement of the 2-thiabicyclo[3,1,0]hex-3-ene system. The crystal and molecular structure of ethyl-2,4-dichloro-5-hydroxy-6-methylbenzoate

Thermal rearrangement of 1,3-dichloro-6-ethoxycarbonyl-2-thiabicyclo[3, 1, 0]hex-3-ene does not follow the anticipated course, but leads instead to ethyl-2,4-dichloro-5-hydroxy-6-methylbenzoate, whose structure has been confirmed by an X-ray crystal structure determination.     

Fourier series criteria for operator decomposability

Let U be an invertible operator on a Banach space Y. U is said to betrigonometrically well-bounded provided the sequence {Uⁿ} _n =– is the Fourier-Stieltjes transform of a suitable projection-valued function E(·): [0, 2](Y). This class of operators is known to apply naturally to a variety of classical phenomena which exclude the presence of spectral measures. In the case Y reflexive we use the Cesáro means _n(U, t) of the trigonometric series _k0 k^–e^iktU^k, whichformally transfers the discrete Hilbert transform to Y, in order to give three separate necessary and sufficient conditions for U to be trigonometrically well-bounded. One of these conditions is sup {_n(U,t): n 1, t [0,2]} <      

The numerical stability of leaping methods for stochastic simulation of chemically reacting systems

Tau-leaping methods have recently been proposed for the acceleration of discrete stochastic simulation of chemically reacting systems. This paper considers the numerical stability of these methods. The concept of stochastic absolute stability is defined, discussed, and applied to the following leaping methods: the explicit tau, implicit tau, and trapezoidal tau.     

Models of molecular geometry

Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.