Anisotropies in the cosmic microwave background: Theoretical foundations

The analysis of anisotropies in the cosmic microwave background (CMB) has become an extremely valuable tool for cosmology. There is even hope that planned CMB anisotropy experiments may revolutionize cosmology. Together with determinations of the CMB spectrum, they represent the first precise cosmological measurements. The value of CMB anisotropies lies in large part in the simplicity of the theoretical analysis. Fluctuations in the CMB can be determined almost fully within linear cosmological perturbation theory and are not severely influenced by complicated nonlinear physics. In this contribution the different physical processes causing or influencing anisotropies in the CMB are discussed: the geometry perturbations at and after last scattering, the acoustic oscillations in the baryon-photon plasma prior to recombination, and the diffusion damping during the process of recombination. The perturbations due to the fluctuating gravitational field, the so-called Sachs-Wolfe contribution, is described in a very general form using the Weyl tensor of the perturbed geometry.     

Velocity measurement by the laser speckle method using optical fibres

An optical device for in-plane velocity measurement is described. Laser light is focused by the use of an optical fibre onto the object, and the device utilizes the dynamic sparkle effect for velocity determination. The influence of different optical fibres on the speckle formation is investigated with special respect to fibre movement, and as the diameter of the aperture used for speckle detection also affects the measuring signal, an optimum value is found. A simple electronic circuit processes the measuring value proportional to the object velocity.     

ULTRAVIOLET-INDUCED LETHALITY AND REVERSION TO PROTOTROPHY IN ESCHERICHIA COLI STRAINS WITH NORMAL AND REDUCED DARK REPAIR ABILITY

Abstract— Two derivatives of E. coli B/r having the same auxotrophic marker but differing in their ability to dark repair u.v.-induced dimers in DNA were compared for their sensitivity to u.v.-induced lethality and reversion to prototrophy. Ability to dark repair influenced both biological endpoints to the same extent. Thus, dimers may be primary photochemical lesions for both effects. A possible model for the system was proposed. According to this model, organisms which have more than a critical number of dimers are inactivated and organisms with the critical number or slightly fewer, survive as revertants. Post-irradiation influences which enhance or reduce repair of dimers, in effect shift the population distribution of dimers. The result is either a net increase or decrease in the number of revertants depending upon the U.V. dose and upon whether repair is enhanced or reduced.     

Approximate solution of singularly perturbed nonlinear pursuit-evasion games

A methodology to obtain an approximate solution of a singularly perturbed nonlinear differential game is presented. The outcome of the game with approximate strategies, defined as extended value, is related to the saddle-point value of the game. In an example of a simple pursuit-evasion game, it is shown that the proposed methodology leads to an easily implementable feedback form solution with fairly accurate results. This approach seems to be attractive for analyzing realistic air-combat models without solving a two-point boundary-value problem.This research was partially supported by AFSC Contract No. F-49620-79-6-0135. The authors are grateful to Prof. J. V. Breakwell for encouraging the approach taken in this research. Thanks are also due to Dr. S. Gutman and Dr. J. Lewin for their useful comments.     

Struktur-Reaktivitäts-Beziehungen bei koordinativ ungesättigten Chelatkomplexen. I. Spektrophotometrische Gleichgewichtsuntersuchungen zum Einfluß der äquatorialen Ligandsubstitutuenten auf die Adduktbildung planarer Bis (3-oxo-1-enaminato)-nickel(II)-chelate mit Pyridin

Structure Reactivity Correlations in Coordinatively Unsaturated Chelate Complexes. I. Spectrophotometric Equilibrium Investigations on the Effect of the Equatorial Ligand Substituents on the Adduct Formation of Planar Bis(3-oxo-l-enaminato)nickel(II) Chelates with Pyridine . The effect of the equatorial ligand substituents R, R¹, and R² on the ability of the diamagnetic planar nickel(II) chelates I, II , and III to form paramagnetic, octahedral bis(adducts) with pyridine is examined by determination of equilibrium constants (and thermodynamic data) for the equilibrium (1) using spectrophotometric and (in part) magnetic methods. Several new compounds of the types I and II are synthesized and characterized by visible and ¹HNMR spectra. Some different methods for computing the photometric measurements of simple equilibria are compared. The K values vary from <10^?4 to > 10⁵ l² mol^?2 in dependence on the ligand substituents. The distinct influence of the peripherhal substituents R¹/R² correlates with their inductive effect. The N-substituents R act mainly on the field strength of the equatorial ligands.     

Detection of partially resolved carbon-13–proton couplings with selective population inversion (SPI)

In a heteronuclear ¹³C? {¹H} selective population inversion ¹³C NMR spectrum a splitting, resulting from a (CH) coupling over more than one bond, can be detected even when no splitting is observed in the single-frequency ¹³C NMR spectrum. The relationship between the observed splitting, coupling constant and line width is discussed. A method is proposed from which the value of the coupling constant can be estimated, and its application illustrated by the splittings observed in the ¹³C NMR spectra of the mycotoxin, ochratoxin A.     

Stability of stochastic partial differential equation

Stochastic partial differential equations such as occur in vibration problems for mechanical structures subjected to random loading are modelled as infinite dimensional stochastic Itô differential equations using a semigroup approach. Sufficient conditions for exponential stability of the expected energy of the system, as well as for the exponential decay of the sample paths of the displacement and velocity, are given. Under these same conditions it is shown that the zero solution is pathwise asymptotically stable relative to finite dimensional initial conditions. Illustrative examples are included.