William A. Johnson

IN this paper experiments are described which show that ketonic acids can react in animal tissues according to the general scheme R. CO.COOH + R'. CO. COOH + H20-R. COOH + C02 + R'. CH(OH). COOH ...... (1) oa-ketonic a-ketonic carboxylic a-hydroxy-acid acid I acid II acid or R. CO. COOH + R'. CO . CH2. COOH + H20-R. COOH + CO2 + R'. CH(OH) .C0. COOH ....(2). ae-ketonic fl-ketonic acid carboxylic ,-hydroxy-acid acid acid

Abstract During the last decade much progress has been made in the analysis of the anaerobic fermentation of carbohydrate, but very little is so far known about the intermediate stages of the oxidative breakdown of carbohydrate. A number of reactions are known in which derivatives of carbohydrate take part and which are probably steps in the breakdown of carbohydrate; we know furthermore, from the work of S zent -G yorgyi 20) that succinic acid, fumaric acid and oxaloacetic acid play some role in the oxidation of carbohydrate, but the details of this role are still obscure. In the present paper experiments are reported which throw new light on the problem of the intermediate stages of oxidation of carbohydrate; in conjunction with the work of S zent -G yorgyi 20), S tare and B aumann 19) and M artius and K noop 13,14) the new experiments allow us to outline the principal steps of the oxidation of sugar in animal tissues.

In the present paper experiments are reported which throw new light on the problem of the intermediate stages of oxidation of carbohydrate; in conjunction with the work of S zent ‐G yörgyi 20 ), S tare and B aumann 19 ) and M artius and K noop 13 , 14 ) the new experiments allow us to outline the principal steps of the oxidation of sugar in animal tissues.

A simple approximate theory is developed for the electrostatic forces operating in a micromechanical comb actuator. The comb drive is considered both without (for simplicity) and with an underlying ground plane. The forces are partitioned into local forces (electric fields confined to the cross-sections of the individual comb fingers) and global force corrections (electric fields resulting from effective equipotential sheets representing the engaged and unengaged comb finger regions). The local forces are obtained by applying the principle of virtual work (both engaged and unengaged regions are involved when a ground plane is present beneath the comb fingers). The global forces are obtained from the force between magnetic current filaments introduced to model the electric-potential discontinuities in the effective equipotential sheets of the engaged and unengaged finger regions. Conformal mapping, in addition to a static mode decay approximation, is used to obtain simple and accurate formulas for the local charge per unit length (local forces) and, when a ground plane is present, for the effective sheet potentials (magnetic currents and global forces). The forces in the separated case (which are also global in nature) are also obtained by the principle of virtual work. The results of the paper show that the attractive local forces are independent of engagement distance and the smaller repulsive global forces are inversely proportional to engagement distance. The attractive separated forces are inversely proportional to the separation distance without the ground plane and inversely proportional to the square of the separation distance with the ground plane.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Ewald method is applied to accelerate the evaluation of the Green's function of an infinite periodic phased array of line sources. The Ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave, and a systematic general procedure is applied to extend previous results. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. Singularities and convergence rates are analyzed, and a recipe for selecting the Ewald splitting parameter /spl epsiv/ is given to handle both low and high frequency ranges. Indeed, it is shown analytically that the choice of the standard optimal splitting parameter /spl epsiv//sub 0/ will cause overflow errors at high frequencies. Numerical examples illustrate the results and the sensitivity of the Ewald representation to the splitting parameter /spl epsiv/.