Experimental mathematics. I. Computational study on the limit cycle behavior of a two-dimensional chemical oscillator

A computational procedure, developed from the power series method, is used to investigate oscillating systems. In addition to its great accuracy and reduced computer time, the method is very easily programmable since the algorithm is provided by the reaction mechanism itself.     

Entropy of transfer of n-nitroalkanes from n-octane to water at 25°C

Entropy of transfer of nitromethane, nitroethane, 1-nitrobutane, 1-nitropentane, and 1-nitrohexane from n-octane to water at 25°C is calculated using an electrostatic model. The calculations indicate that the electrostatic transfer entropy depends primarily on the dipole moment and the size of the-C–NO₂ group, showing a trend which is similar to that previously found for the transfer free energy of the same process.     

A control-theoretic approach to the plasma confinement problem

The problem of confining a collisionless plasma by means of external electromagnetic fields is formulated as an optimal control or variational problem. The paper begins with a formal development of the equations governing the plasma motion. Then, various mathematical formulations of the confinement problem are discussed. Specific results are obtained for the simplified case where confinement is achieved by means of a spatially uniform, time-varying magnetic field. Physical interpretations of these results are also given.This work was supported by the Office of Scientific Research of the United States Air Force under Grant No. AFOSR-68-1547.     

Notiz zur Synthese des Nonactins

With (?)-nonactic acid and the 8-epitosylate of benzyl (+)-nonactate usingWalden inversion (?)-nonactyl-(+)-nonactic acid is constructed. The latter forms by way of its imidazolide or its α-mercaptopyridyl ester the macrotetrolide nonactine in poor yield.     

Transmission measurements of soft X-ray absorption fine structure in solids by a new scintillation technique

Transmission measurements of the extended X-ray absorption fine structure above the oxygen K-edge have been made by using a new scintillation detection technique. The absorption spectrum is in close resemblance with the total electron yield spectrum recorded at the same time. This new technique is of interest for studies of soft X-ray absorption spectroscopy for thin films of solid materials.     

Improved hydrogen release from LiB0.33N0.67H2.67 with noble metal additions

The hydrogen release behavior of the quaternary hydride LiB(0.33)N(0.67)H(2.67) has been successfully improved through the incorporation of small quantities of noble metal. Adding 5 wt % Pd either as Pd metal particles or as PdCl(2) reduced the temperature T(1/2) corresponding to the midpoint of the hydrogen release reaction by DeltaT(1/2) = -43 degrees C and -76 degrees C, respectively. PtCl(2) and Pt nanoparticles supported on a Vulcan carbon substrate proved to be even more effective, with DeltaT(1/2) = -90 degrees C. The amount of NH(3) released during dehydrogenation is reduced compared to that from additive-free material, and, more importantly, at temperatures below 210 degrees C hydrogen is released with no detectable NH(3). In contrast to additive-free LiB(0.33)N(0.67)H(2.67), which melts completely above 190 degrees C and releases hydrogen from the liquid state only above approximately 250 degrees C, hydrogen release from LiB(0.33)N(0.67)H(2.67) + 5 wt % Pt/Vulcan carbon is accompanied by partial melting plus a cascade through a series of solid intermediate phases. Calorimetric measurements indicate that both additive-free and Pt-added LiB(0.33)N(0.67)H(2.67) release hydrogen exothermically, and hence the reverse reaction is thermodynamically unfavorable. By exposing partially dehydrogenated samples to high H(2) pressures at modest temperatures, fractional hydrogen uptake (roughly 15% of the released hydrogen) has been achieved. The mechanism by which noble metals promote hydrogen release is not known, but the behavior is consistent with that expected for a catalyst, including a large effect with small additions and saturation of the effect at low concentration.     

Hereditary properties of partitions, ordered graphs and ordered hypergraphs

In this paper we use the Klazar–Marcus–Tardos method (see [A. Marcus, G. Tardos, Excluded permutation matrices and the Stanley–Wilf conjecture. J. Combin. Theory Ser. A 107 (2004) 153–160]) to prove that, if a hereditary property of partitions has super-exponential speed, then, for every k-permutation π, contains the partition of [2k] with parts {{i,π(i)+k}:i[k]}. We also prove a similar jump, from exponential to factorial, in the possible speeds of monotone properties of ordered graphs, and of hereditary properties of ordered graphs not containing large complete, or complete bipartite ordered graphs.Our results generalize the Stanley–Wilf conjecture on the number of n-permutations avoiding a fixed permutation, which was recently proved by the combined results of Klazar [M. Klazar, The Füredi–Hajnal conjecture implies the Stanley–Wilf conjecture, in: D. Krob, A.A. Mikhalev, A.V. Mikhalev (Eds.), Formal Power Series and Algebraic Combinatorics, Springer, Berlin, 2000, pp. 250–255] and Marcus and Tardos [A. Marcus, G. Tardos, Excluded permutation matrices and the Stanley–Wilf conjecture, J. Combin. Theory Ser. A 107 (2004) 153–160]. Our main results follow from a generalization to ordered hypergraphs of the theorem of Marcus and Tardos.     

Inventory control with fixed cost and price optimization in continuous time

We continue to study the problem of inventory control, with simultaneous pricing optimization in continuous time. In our previous paper [8], we considered the case without set up cost, and established the optimality of the base stock-list price (BSLP) policy. In this paper we consider the situation of fixed price. We prove that the discrete time optimal strategy (see [11]), i.e., the (s, S, p) policy can be extended to the continuous time case using the framework of quasi-variational inequalities (QVIs) involving the value function. In the process we show that an associated second order, nonlinear two-point boundary value problem for the value function has a unique solution yielding the triplet (s, S, p). For application purposes the explicit knowledge of this solution is needed to specify the optimal inventory and pricing strategy. Se- lecting a particular demand function we are able to formulate and implement a numerical algorithm to obtain good approximations for the optimal strategy.