Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Influence of cytotoxic agents on thermogenesis in streptococcus faecalis

Changes in the thermogenesis of S. faecalis cells resulting from the addition of cyanide, fluoride, penicillin, tetracycline, or human serum have been observed using isothermal calorimetry. The character and extent of the decrease in the thermogenesis rate is reproducible and different for each cytotoxic agent studied. The changes in thermogenesis on addition of tetracycline are quantitatively related to the concentration of antibiotic added to the bacterial culture.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Maximum entropy approach to statistical inference for an ocean acoustic waveguide

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations.     

A nonlocal effective operator for coupling forward and backward propagating modes in inhomogeneous media

In an acoustic waveguide spatial inhomogeneities couple the forward and backward propagating modal amplitudes. To address the nature of such coupling the integral equation for the range-dependent modal amplitudes is decomposed into components that satisfy the asymptotic boundary conditions of the free Green's function operator. An equivalent set of equations is obtained by eliminating the components that become the asymptotically backward propagating channels to leave a set of integral equations that describe only the components that become asymptotically the forward propagating channels. The elimination of the components that become asymptotically the backward propagating channels is done at the expense of introducing a nonlocal effective coupling operator. The nonlocal operator contains all the effects of the asymptotically backward propagating field on the asymptotically forward propagating field. An expansion of the effective coupling operator allows an investigation of the importance of the coupling and provides a systematic approach to add correction terms to the forward only equation. Idealistic underwater waveguides with various degrees of inhomogeneities are used to illustrate the main features of the convergence characteristics for the expansion.     

Active sound transmission control of a double-panel module using decoupled analog feedback control: experimental results

Low-frequency sound transmission through passive lightweight partitions often renders them ineffective as means of sound isolation. As a result, researchers have investigated actively controlled lightweight partitions in an effort to remedy this problem. One promising approach involves active segmented partitions (ASPs), in which partitions are segmented into several distinctly controlled modules. This paper provides an experimental analysis of a double-panel ASP module wherein the source- and transmitting-side panels are independently controlled by an analog feedback controller. Experimental results, including plant frequency response functions, acoustic coupling strengths, frequency response functions, and transmission losses (TLs) of single- and double-panel modules, are presented and compared to numerical predictions. Over the bandwidth of 20 Hz to 1 kHz, the average measured TL for an actively controlled single-panel module was 29 dB, compared to 14 dB for the passive case. The average measured TL over the same bandwidth for the actively controlled double-panel module was 57 dB, compared to 31 dB for the passive case.