Massive gauge theories and the photon

A model containing the massless photon as well as other massive vector mesons is constructed from a gauge-invariant theory of massless vector mesons with scalars transforming under a mixed linear-non-linear group realization, so that one massive scalar also remains finally. A Georgi-Glashow-type Lagrangian in the unitary gauge can be induced by appropriate choice of non-minimal gauge-invariant interactions in the ancestor Lagrangian. It is thus likely that this ancestor Lagrangian, which is non-polynomial, is also renormalizable.     

Electron-transfer reactions of amines with α-ferrocenylcarbonium ions

The production observed in the reactions of α-ferrocenylcarbonium ions with tertiary amines do not originate from ferrocenylcarbene intermediates. Evidence is presented in support of an electron-transfer mechanism leading to α-ferrocenylcarbinyl radicals as reaction intermediates.     

Infinite number of conservation laws in two-dimensional superconformal models

Superconformal theories in two-dimensional space-time are considered. Noether's theorem and the Belinfante improvement procedure are extended to superspace where they are used to construct the supercurrent. With its aid, an infinite number of classical conservation laws are derived. These laws are shown to survive quantization in the supersymmetric, non-linear, O(N) sigma model.     

Soft acoustic mode in thallium arsenic Sulphide Tl3AsS42

Ultrasonic measurements of the slow shear mode velocity in Tl₃AsS₄ have been made as a function of hydrostatic pressure up to 2.6 GPa at room temperature. The velocity is a decreasing function of pressure over the entire pressure range. Two pressure-induced phase transitions are observed, one (at 2.1 GPa) characterized by a discontinuous drop in velocity, and the other (at 2.6 GPa) by a continuous softening of the velocity to zero. The results are discussed in terms of the Miller-Axe theory of internal-strain coupling to a soft optic mode. Comparison is made with results on Tl₃PSe₄, where only one transition is observed.     

Vapor-liquid equilibrium of aqueous crown ether solutions

The activity of water in crown ether solutions has been obtained at 298,313 and 333 K over a wide range of concentrations. A minimum in the activity coefficient of water is observed. The minimum becomes more pronounced with decreasing temperature.     

A convenient preparation of mixed allylic and allenic thiosulfinates

The first successful preparation of propargylic and allylic chloroalkoxy disulfides in high yields is reported. Facile 1,4-electrophilic addition of these to 2,3-dimethyl-1,3-butadiene, followed by [2,3]-sigmatropic rearrangements affords mixed allyl allenic and bis-allylic thiosulfinates, respectively. Due to their similarity to allicin, the latter are of potential biological interest.     

Peierls transition in helical structures

Summary In long molecules with helical structure it is shown that the electron’s response functionF(q,T) is singular for various wave vectors. Then deformed phases associated with different periodicites can occur as a function of external pressure. The calculation was done as a function of temperature and for small number of atoms per turn.

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Riassunto Si mostra in lunghe molecole con struttura elicoidale che la funzione di risposta dell’elettroneF(q, T) è singolare per vari vettori d’onda. Allora possono verificarsi fasi deformate associate a diverse periodicità in funzione della pressione esterna. Si effettua il calcolo in funzione della temperatura e per un numero ridotto di atomi per spira.

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Резюме В длинных молекулах с геликоидальной структурой показывается, что функция электронного откликаF(q, T) является сингулярной для различных волновых векторов. В связи с этим могут возникать деформированные фазы, связанные с различными периодичностями, в зависимости от внешнего давления. Проводятся вычисления в зависимости от температуры и для малого числа атомов на виток.

     

Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

On Time Discretizations for Spectral Methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.     

Time-optimal control for a model of bacterial growth

A time-optimal control problem is solved for Monod's model of bacterial growth in continuous culture. The solution is obtained using Green's theorem and has a simple feedback form.