Kinetic resolution of β-lactams via enantioselective N-acylation

Enantioselective N-acylation of 4-aryl-β-lactams in the presence of acyl transfer catalyst Cl-PIQ provides an effective method for their non-enzymatic kinetic resolution.     

ThermoData Engine (TDE): software implementation of the dynamic data evaluation concept. 5. Experiment planning and product design

ThermoData Engine (TDE) is the first full-scale software implementation of the dynamic data evaluation concept, as reported recently in this journal. In the present paper, we describe development of an algorithmic approach to assist experiment planning through assessment of the existing body of knowledge, including availability of experimental thermophysical property data, variable ranges studied, associated uncertainties, state of prediction methods, and parameters for deployment of prediction methods and how these parameters can be obtained using targeted measurements, etc., and, indeed, how the intended measurement may address the underlying scientific or engineering problem under consideration. A second new feature described here is the application of the software capabilities for aid in the design of chemical products through identification of chemical systems possessing desired values of thermophysical properties within defined ranges of tolerance. The algorithms and their software implementation to achieve this are described. Finally, implementation of a new data validation and weighting system is described for vapor-liquid equilibrium (VLE) data, and directions for future enhancements are outlined.     

ThermoData Engine (TDE): software implementation of the dynamic data evaluation concept. 6. Dynamic web-based data dissemination through the NIST Web Thermo Tables

ThermoData Engine (TDE) is the first full-scale software implementation of the dynamic data evaluation concept, as reported recently in this journal. In the present paper, we describe the development of a World Wide Web-based interface to TDE evaluations of pure compound properties, including critical properties, phase boundary equilibria (vapor pressures, sublimation pressures, and crystal-liquid boundary pressures), densities, energetic properties, and transport properties. This includes development of a system for caching evaluation results to maintain high availability and an advanced window-in-window interface that leverages modern Web-browser technologies. Challenges associated with bringing the principal advantages of the TDE technology to the Web are described, as are compromises to maintain general access and speed of interaction while remaining true to the tenets of dynamic data evaluation. Future extensions of the interface and associated Web-services are outlined.     

A universal planar automaton is determined by its semigroup of input symbols

Universal planar automata are universally attracted objects in the category of automata, for which the set of states and the set of output symbols are equipped with structures of planes. We investigate the problem of determinability of these automata by their semigroups of input symbols.     

Ptolemaic spaces

We show that equilateral pseudolinear quadruples are in a certain sense extremally non-Ptolemaic metric spaces. We find four-point pseudometric spaces that are maximally Ptolemaic.     

Insuring against loss of evidence in game-theoretic probability

Statistical testing can be framed as a repetitive game between two players, Forecaster and Sceptic. In each round, Forecaster sets prices for various gambles, and Sceptic chooses which gambles to make. If Sceptic multiplies by a large factor the capital he puts at risk, he has evidence against Forecaster’s ability. His capital at the end of each round is a measure of his evidence against Forecaster so far. This can go up and then back down. If you report the maximum so far instead of the current value, you are exaggerating the evidence against Forecaster. In this article, we show how to remove the exaggeration. Removing it means systematically reducing the maximum in such a way that a rival to Sceptic can always play so as to obtain current evidence as good as Sceptic’s reduced maximum. We characterize the functions that can achieve such reductions. Because these functions may impose only modest reductions, we think of our result as a method of insuring against loss of evidence. In the context of an actual market, it is a method of insuring against the loss of what an investor has gained so far.     

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

We derive a number of new results on integrals of products of Airy functions, using various integral transform techniques. As an application, we deduce a compact integral representation, suitable for numerical integration, of the one‐loop photon propagator in a magnetic field in 2 + 1 dimensional scalar quantum electrodynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Variations on a theorem of Arhangel’skii and Pytkeev

We identify continuous real-valued functions on a Tychonoff space X with their (closed) graphs thus allowing for C(X) to naturally inherit the lower Vietoris topology from the ambient hyperspace. We then calculate a bitopological version of tightness using the weak Lindelöf numbers of finite powers of X. We also characterize bitopological versions of countable fan and strong fan tightness of the point-open topology with respect to the lower Vietoris topology on C(X) in terms of suitable covering properties of the powers X ⁿ formulated using the language of S ₁ and S _fin selection principles.     

On Zeros of Certain Analytic Functions

Given a function s which is analytic and bounded by one in modulus in the open unit disk \mathbb D{{\mathbb D}} and given a finite Blaschke product J{\vartheta} of degree k, we relate the number of zeros of the function s-J{s-\vartheta} inside \mathbb D{{\mathbb D}} to the number of boundary zeros of special type of the same function.     

Pseudodifferential Operators Approach to Singular Integral Operators in Weighted Variable Exponent Lebesgue Spaces on Carleson Curves

The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential operators on the spaces L^p(·)(\mathbbR ₊,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting on L ^p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential operators on \mathbbR₊{\mathbb{R}_{+}} and local invertibility of singular integral operators on \mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities.