Invariant Euler–Lagrange Equations and the Invariant Variational Bicomplex

In this paper, we derive an explicit group-invariant formula for the Euler–Lagrange equations associated with an invariant variational problem. The method relies on a group-invariant version of the variational bicomplex induced by a general equivariant moving frame construction, and is of independent interest.     

Decomposability in queues with background states

A symmetric queue is known to have a nice property, the so-called insensitivity. In this paper, we generalize this for a single node queue with Poisson arrivals and background state, which changes at completion instants of lifetimes as well as at the arrival and departure instants. We study this problem by using the decomposability property of the joint stationary distribution of the queue length and supplementary variables, which implies the insensitivity. We formulate a Markov process representing the state of the queue as an RGSMP (reallocatable generalized semi-Markov process), and give necessary and sufficient conditions for the decomposability. We then establish general criteria to be sufficient for the queue to possess the property. Various symmetric-like queues with background states, including continuous time versions of moving server queues, are shown to have the decomposability.This author is partially supported by NEC C&C Laboratories.     

Transference numbers for anhydrous methanol solutions at 10 and 25°C

Transference numbers are reported for LiCl and NaCl in methanol at 25°C and for NaCl, KCl, and Bu₄NBr in methanol at 10°C. The potentiometric moving-boundary method as developed by Kay and Fratiello was employed to give a precision of about 0.05% and an accuracy of at least 0.1% as indicated by two independent determinations of the conductances of the Cl^– and Br^– ions. The data are extrapolated by the Fuoss-Onsager theory, and the magnitude of the electrophoretic effect is calculated as described by Kay and Dye. The agreement with this theory is quite good at both temperatures, although the å value required in the case of Bu₄NBr is considerably larger than that obtained from conductance data. This agreement contrasts with that obtained for ethanol and acetone solutions where the measured electrophoretic effect is considerably larger than the corresponding calculated values. The importance of this fact in the determination of ion-pair association constants is discussed.     

Quantum calculations in a unique rest frame

The distribution of astronomical redshifts and the cosmic background radiation define a unique inertial reference frame. This paper contains an investigation of questions concerning quantum theory which arise with the introduction of a unique rest frame into spacetime. The Mössbauer effect, photon pair production, and photoelectric effect are treated together with photon scattering by a moving reflector and the Compton effect. Dirac's 1928 quantum theory of electrons is shown to yield its well-known energy spectrum for the hydrogen atom independently of the velocity of the atom relative to the rest frame.1. Address for the academic year 1990–91: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602, USA.     

The Flow Patterns and Wall Stresses in a Louvered‐Wall Moving Granular Filter Bed of Quartz Sand

The flow patterns and wall stresses in a two‐dimensional louvered moving granular filter bed of quartz sand were investigated. The flow pattern histories of granular solids in the filter bed were recorded using a digital camcorder and a pressure gauge for simultaneously measuring the normal stresses as well as shear stresses of the granular solids. The static wall stress distributions produced by the granular solids were measured, and agreed with a theoretical prediction formed using the differential slice and Runge‐Kutta (order four) methods. The variations in the dynamic wall stresses with time in a moving granular filter bed were obtained and the effect of the louver angle upon the flow patterns and wall stresses was also investigated. Employing the results obtained by stress measurements and image processing, the wall pressure pulsation phenomena in a moving granular filter bed may be further understood. The results reported here provide fundamental information for the design of moving granular filter beds to act as high‐temperature flue gas cleanup filters.     

Density,conductance, transference numbers,and diffusion measurements in concentrated solutions of nickel chloride at 25°C

The Hittorf technique for measuring transference numbers has been modified to produce precise data in concentrated aqueous electrolyte solutions. Density, molar conductance, transference number, tracer-diffusion, and mutual diffusion data are reported for aqueous NiCl₂ solutions up to 4M concentration at 25°C.Visiting Fellow at the Australian National University on leave from the School of Chemical Sciences, Universiti Sains Malaysia, Penang, Malaysia.     

Less common applications of simulated moving bed chromatography in the pharmaceutical industry

Simulated moving bed (SMB) chromatography is often perceived in the pharmaceutical industry as chromatographic method for separating binary mixtures, like racemates. However, SMB can also be used for unbalanced separations, i.e. binary mixtures of varying compositions and multi-component mixtures. These less common application modes of isocratic SMB chromatography are exemplified for four different compounds (racemates and diastereomers) and discussed in view of the so-called 'triangle theory' from an industrial perspective.     

A note on a generalization of Diliberto’s Theorem for certain differential equations of higher dimension

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.This research was supported by Grant No. 201/99/0295 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected missing date string.     

Equidistributing principles in moving finite element methods

Recently Miller and his co-workers proposed a moving finite element method based on a least squares principle. This was followed by a similar method by the present authors using a Petrov—Galerkin approach. In this paper the two methods are compared. In particular, it is shown that both methods move their nodes according to an approximate equidistributing principle. This observation leads to a criterion for the placement of the nodes. It is also shown that the penalty function designed by Miller may also be used with the Petrov—Galerkin method. Finally, numerical examples are given, illustrating the performance of the two methods.