How to Turn All Lights Out

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How to Turn All Lights Out

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Confined modified realizability

We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with (a weak version of) our interpretation in the case when least elements exist (e.g. natural numbers). The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well‐founded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thiazolidine-based organocatalysts for a highly enantioselective direct aldol reaction

A set of enantiopure thiazolidine-based organocatalysts have been synthesized from l-cysteine, in a straightforward manner allowing numerous structural variations. In particular, organocatalyst 3a exhibits the highest catalytic performance working in an aqueous medium. It catalyzed the direct catalytic asymmetric intermolecular aldol reaction between unmodified ketones and an aldehyde with excellent stereocontrol and furnished the corresponding aldol products in up to 99% ee. Compound 3a also showed excellent asymmetric catalytic activity in the asymmetric Michael reaction (up to 99% ee).     

Red, green, and blue lanthanum phosphate phosphors obtained via surfactant-controlled hydrothermal synthesis

A new solution route for the obtainment of highly pure luminescent rare-earth orthophosphates in hydrothermal conditions was developed. By starting from soluble precursors (lanthanide tripolyphosphato complexes, i.e. with P₃O₁₀⁵⁻ as a complexing agent and as an orthophosphate source) and by applying surfactants in a water/toluene medium, the precipitations are confined to reverse micelle structures, thus yielding nanosized and homogeneous orthophosphates. The method was employed to obtain lanthanide-activated lanthanum phosphates, which can be applied as red (LaPO₄:Eu³⁺), green (LaPO₄:Ce³⁺,Tb³⁺) and blue (LaPO₄:Tm³⁺) phosphors. The produced materials were analyzed by powder X-ray diffractometry, scanning electron microscopy, infrared spectroscopy and luminescence spectroscopy (emission, excitation, lifetimes and chromaticity coordinates).     

Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

Topology change and θ-vacua in 2D Yang-Mills theory

We discuss the existence of θ-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of π₁(G) if M is orientable, and with the IUR's of π₁(G)/2π₁(G) if M is non-orientable.     

Spin-glass energy landscape

We consider a nearest-neighbor-interaction ±J Ising spin glass in a square lattice. Inspired by natural evolution, we design a dynamic rule that includesselection, randomness, andmultibranch exploration. Following this rule, we succeed in walking along the space of states between local energy maxima and minima alternately. During the walk, we store various information about the spin states corresponding to these minima and maxima for later statistical analysis. In particular, we plot a histogram displaying how many times each minimum (or maximum) energy is visited as a function of the corresponding density value. Through finite-size scaling analysis, we conclude that a nonvanishing fraction of bonds remains unsatisfied (satisfied) at these energy minimum (maximum) states in the thermodynamic limit. This fraction measures the degree of unavoidable frustration of the system. Also in this limit, the width of these histograms vanishes, meaning that almost all metastable states occur at the same energy density value, with no dispersion.