Quantitative isotope enrichment in a thermal diffusion arrangement

The problem of enrichment of a gas sample by a definite factor is considered. It occurs, for example, when the radiocarbon dating method is to be extended to higher ages. The case of a thermal diffusion column with finite reservoirs at both ends is investigated and the decisive benefit of a high separation factor for the sufficient knowledge and reproducibility of the enrichment factor is pointed out. The relation between the factors as well as their temporal behaviour is developed in two ways: Simple formulae with physical evidence are adapted to make allowance for the content of the column itself, and then verified by deriving the exact isotope distribution from the partial differential equation.     

Lamellarity of artificial phospholipid-membranes determined by photometric phase-contrast microscopy

A method is presented to discern phospholipid vesicles larger than 30 μm surrounded by a single bilayer from those whose membrane is multilamellar. It is based on the photometric observation of the contrast of the membrane contours in a second image-plane of a phase-contrast microscope.     

Mechanical resonance dispersion in polytetrafluorethylene rods in transverse vibration

Summary Polytetrafluorethylene rods in transverse vibration exhibit sharp non-harmonic resonances when subjected to a static tensile stress during vibration. The extent and location of the resonances are critically dependent on the exact static stress state and history of the rods. Rods under no external tension have no anomalous behavior in the range 100 to 2000 cps, but under static tension varying from 1.5×10⁵ to 3.0×10⁶ dynes/cm² (2.2 to 44 psi) sharp resonances appear in the vicinity of 400 cps. The mechanical resonance dispersions in complex shear compliance previously reported byFitzgerald are thus substantiated by the present work. The failure of certain other investigators to observe the dispersion in polytetrafluorethylene is attributed to the fact that insufficient attention was paid to the static stress conditions in their tests.

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Zusammenfassung Polytetrafluor?thylen-Streifen zeigen bei transversaler Schwingung scharfe nicht-harmonische Resonanzen, wenn sie w?hrend der Vibration einem statischen Zug unterworfen sind. Intensit?t und Lage der Resonanzen h?ngen kritisch vom statischen Spannungszustand und der Geschichte der Proben ab. Proben unter keiner ?u?eren Spannung zeigen im Bereich von 100–200 Hz kein anomales Benehmen, doch erscheinen bei statischer Belastung zwischen 1,5×10⁵ zu 3,0×10⁶ dyn/cm² scharfe Resonanzen in der N?he von 400 Hz. Die mechanische Resonanzdispersion der komplexen Scherungsnachgiebigkeit, früher vonFitzgerald mitgeteilt, werden mit der vorliegenden Arbeit best?tigt. Da? anderen Bearbeitern die Beobachtung der Dispersion bei Polytetrafluor?thylen mi?lungen ist, ist der Tatsache zuzuschreiben, da? den statischen Spannungszust?nden in ihren Proben ungenügende Rechnung zuteil wurde.

     

Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces

We introduce a new method for proving the estimate

where solves the equation . The method can be applied to the Laplacian on . It also allows us to obtain similar estimates when we replace the Laplacian by an infinite-dimensional Ornstein-Uhlenbeck operator or other elliptic operators. These operators arise naturally in martingale problems arising from measure-valued branching diffusions and from stochastic partial differential equations.

     

Generalized oscillator strengths for two transitions in CO2 at incident electron energies of 300, 400 and 500 eV

Generalized oscillator strengths have been obtained for two transitions in CO₂ from inelastic electron scattering determinations as a function of angle. Excitation energies for the two transitions are 11.04 and 11.38 eV, respectively. This spectral region was studied previously by Lassettre and Shiloff¹ but at a resolution too low to resolve the two transitions. In the present experiments the two are clearly resolved. Results are compared with the previous experiments of Foo et al.². Since substantial discrepancies are found both with the previous results of Lassettre and Shiloff and that of Foo et al., the accuracy of angular trends has been checked by comparing elastic scattering with the accurate determinations of Bromberg.⁶ Agreement is good. Multiple scattering is shown to be absent by varying the pressure. Generalized oscillator strengths are compared with the theoretical calculations of McKoy and collaborators. The change in the shape of the CO₂ spectrum in the region of 7–10 eV excitation energy is also studied.     

An improved computer program for calculating formation constants of ligand complexes from pH data

Several improvements are made to available computer programs for calculating formation constants from pH data. The most important features are wide portability of program among computers, ability to optimize any parameter in the model equations and to fix any parameters (including stepwise formation constants) to a constant, and options to allow for variations in thermodynamic activity of ions and to fit pH after fitting the volume of added reagent. The latter feature was used with synthetic data to explore the effects of random errors in either reagent volume or pH or both. Whereas fits to reagent volume will usually be more accurate for systems with pK_a values near 7, this is not the case for systems with pK_a values which differ by > 2.0 from 7.     

Simulated annealing for constrained global optimization

Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generateany point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by anadaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.This material is based on work supported by a NATO Collaborative Research Grant, no. 0119/89.