Homogeneous decatungstate-catalyzed photooxygenation of tetrasubstituted alkenes: a deuterium kinetic isotope effect study

The decatungstate W10O32(4-) homogeneous photocatalyzed oxygenation of tetrasubstituted alkenes has been mechanistically studied. In all cases, allylic hydroperoxides are the major products. The primary inter- and intramolecular as well as the remote delta-secondary deuterium kinetic isotope effects for the photooxidation of the 2,3-dimethyl-2-butene and 1,1,1-trideuterio-7-methyl-2-(trideuteriomethyl)octa-2,6-diene along with product analysis suggest a hydrogen abstraction in the rate-determining step. For comparison, singlet oxygen photosensitized oxidations of the above substrates were also studied.     

Finitary-Algebraic ‘Resolution’ of the Inner Schwarzschild Singularity

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Differential Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed. As in previous works [Mallios, A. and Raptis, I. (2001). Finitary spacetime sheaves of quantum causal sets: Curving quantum causality. International Journal of Theoretical Physics, 40, 1885 [gr-qc/0102097]; Mallios, A. and Raptis, I. (2002). Finitary Čech-de Rham cohomology. International Journal of Theoretical Physics, 41, 1857 [gr-qc/0110033]; Mallios, A. and Raptis, I. (2003). Finitary, causal and quantal vacuum Einstein gravity. International Journal of Theoretical Physics 42, 1479 [gr-qc/0209048]], which this paper continues, the starting point for the present application of ADG is Sorkin's finitary (:locally finite) poset (:partially ordered set) substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of ‘discrete events,’ but also at a suitable ‘classical spacetime continuum limit’ of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. The upshot of this is two-fold: On the one hand, the field equations are seen to hold when only finitely many events or ‘degrees of freedom’ of the gravitational field are involved, so that no infinity or uncontrollable divergence of the latter arises at all in our inherently finitistic-algebraic scenario. On the other hand, the law of gravity—still modelled in ADG by a differential equation proper—does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as it is traditionally maintained in the usual manifold-based analysis of spacetime singularities in General Relativity (GR). At the end, some brief remarks are made on the potential import of ADG-theoretic ideas in developing a genuinely background-independent Quantum Gravity (QG). A brief comparison between the ‘resolution’ proposed here and a recent resolution of the inner Schwarzschild singularity by Loop QG means concludes the paper. PACS numbers: 04.60.−m, 04.20.Gz, 04.20.−q     

Temperature-induced crystallization in concentrated suspensions of multiarm star polymers: a molecular dynamics study

In this work, we study temperature-induced crystallization in dense suspensions of multiarm star polymers. This is a continuation of a previous study, which identified and studied the emergence of "glassy" amorphous states, in accordance with experimental observations. We performed molecular dynamics simulations on two types of star polymers: 128-arm stars and 64-arm stars dissolved in n-decane in the temperature range of 20-60 degrees C. These supramolecules are modeled as "soft spheres" interacting via a theoretically developed potential of mean field. Both systems attain a crystalline structure with the characteristics of a face-centered-cubic (fcc) crystal beyond a certain temperature. Kinetics is sensitive on initial configuration. Interestingly, kinetic trapping in "temporary" energy wells leads to highly crystalline structures, yet less ordered than their genuine equilibrium fcc structure. This complication illustrates the difficulty in reaching the equilibrium state, which is crystalline at high temperatures. A structural analysis of the final conformations is presented. The effect of size dispersity and star functionality of soft spheres on microstructure is also examined. Both factors influence crystallization and their effect is quantified by our study.     

Chromatographic analysis of penicillins in pharmaceutical formulations and biological fluids

Natural penicillin (benzylpenicillin) is the oldest antibiotic observed by Alexander Fleming in 1928. To broaden its spectrum of activity, natural penicillin was modified, giving rise to a group of antibiotics under the name 'penicillins'. Although an increasing number of bacteria appear to be resistant to them, penicillins are used to treat a variety of bacterial infections including Gram-positive, Gram-negative aerobic and anaerobic bacteria. Consequently, they are widely used in human and veterinary medicine to prevent and treat diseases. This review covers the analytical methodologies, mainly chromatographic, employed to the penicillins determination in pharmaceutical formulations, biological fluids and in production-scale fermentations reported in the literature. Results of published assays are comparatively presented focusing on sample preparation regarding isolation and purification, chromatographic conditions and method validation. Information on chemical structure, spectrum of activity and action mechanism of common penicillins has also been given.     

Martingale Approach to Stochastic Control with Discretionary Stopping

We develop a martingale approach for continuous-time stochastic control with discretionary stopping. The relevant Dynamic Programming Equation and Maximum Principle are presented. Necessary and sufficient conditions are provided for the optimality of a control strategy; these are analogues of the "equalization" and "thriftiness" conditions introduced by Dubins and Savage (1976) in a related, discrete-time context. The existence of a thrifty control strategy is established.     

General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.     

Improved local convergence of Newton’s method under weak majorant condition

We provide a local convergence analysis for Newton’s method under a weak majorant condition in a Banach space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than before [14]. Special cases and numerical examples are also provided in this study.     

Perturbation and robust stability of autonomous singular linear matrix difference equations

In the perturbation theory of linear matrix difference equations, it is well known that the theory of finite and infinite elementary divisors of regular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. By using matrix pencil theory and the Weierstrass canonical form of the pencil we obtain bounds for the finite elementary divisors of a perturbed pencil. Moreover we study robust stability of a class of linear matrix difference equations (of first and higher order) whose coefficients are square constant matrices.