Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Photocatalyzed degradation of polymers in aqueous semiconductor suspensions. I. Photooxidation of solid particles of polyvinylchloride

The photocatalyzed oxidative decompositions of solid particles of polyvinylchloride (PVC; size about 100 to 200 μm), of the polyvinylidene chloride copolymer (95% PVC/5% PVLC; size ∼ 400–600 μm), and a PVC film have been examined in suspensions of titania and zinc oxide illuminated by UV light and/or by natural sunlight. Dechlorination and evolution of carbon dioxide were monitored, the latter occurring by the intermediacy of acetic and formic acids. The photodegradation of polymer specimens was enhanced in TiO₂/water media by such added oxidants as hydrogen peroxide and potassium persulfate. Photocorrosion of these particulates was also examined by scanning electron microscopy. © 1996 John Wiley & Sons, Inc.     

Thiocarbonylthio end group removal from RAFT‐synthesized polymers by a radical‐induced process

The removal of thiocarbonylthio end groups by radical‐addition‐fragmentation‐ coupling from polymers synthesized by RAFT polymerization has been studied. We found that a method, which involves heating the polymer with a large excess (20 molar equivalents) of azobis(isobutyronitrile) (AIBN), while successful with methacrylic polymers, is less effective with styrenic or acrylic polymers and provides only partial end group removal. This is attributed to the propagating radicals generated from the latter polymers being poor radical leaving groups relative to the cyanoisopropyl radical. Similar use of lauroyl peroxide (LPO) completely removes the thiocarbonylthio groups from styrenic or acrylic polymers but, even with LPO in large excess, produces a polymer with a bimodal molecular weight distribution. The formation of a peak of double molecular weight is indicative of the occurrence of self‐termination and ineffective radical trapping. We now report that by use of a combination of LPO (2 molar equivalents) and AIBN (20 molar equivalents) we are able to completely remove thiocarbonylthio end groups of styrenic or acrylic polymers and minimize the occurrence of self termination. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6704–6714, 2009     

An ecogenetic model

A model for the effects of a predator on a genetically distinguished prey population is formulated and investigated. The predator-free system settles at an equilibrium which can be destabilized by the predators if a suitably defined parameter, the predator invasion number, exceeds a threshold. The system can then coexist at a stable equilibrium or via persistent oscillations.     

A lacunary interpolation algorithm on arbitrary points

Here, the following lacunary interpolation problem is considered: to find the polynomial which together with its second and third derivatives agrees on arbitrary points with the corresponding values of a given function. The representation of the polynomial depends on the solution of a linear algebraic system. The method is constructed on this observation. The error analysis shows that it behaves like the corresponding Lagrange interpolation problem with an equivalent number of conditions. Some applications are shown.     

Numerical Burniat and Irregular Surfaces

In this paper, we construct three numerical Burniat surfaces as desingularizations of double planes of degree >10. Two are surfaces having the bigenus P ₂=4 and the third is a surface having the bigenus P ₂=5. In addition, another surface of general type is constructed as a desingularization of a double plane of degree 12 having the birational invariants: q=p _g =1, P ₂=4. One of the numerical Burniat surfaces with P ₂=4 is obtained as a desingularization of a double plane of degree 22 with an irreducible branch locus, so it is a good candidate for having torsion zero. Moreover, its bicanonical transformation seems to be birational.     

Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals

Summary. Starting with some results of Lyness concerning the Euler-Maclaurin expansion of Cauchy principal value integrals over it is shown how, by the use of sigmoidal transformations, good approximations can be found for the Hadamard finite-part integral where The analysis is illustrated by some numerical examples. Received March 13, 1996     

Metallation reactions XXVII.: Metallation of (methylthio)anilines

The metallation reactions of (methylthio)anilines with organolithium reagents and with the butyllithium–potassium tert-butoxide superbasic mixture are here described. The results show that the para isomer when treated with butyllithium gave a mixture of products with no selectivity. Using tert-butyllithium or superbases we obtained the substitution of the thiomethyl hydrogen. Moreover, superbase allowed to prepare the disubstituted product with the new groups in the thiomethyl and in ortho to this group. On the other side, both ortho and meta isomers were lithiated at the thiomethyl carbon by butyllithium and the other reagents. Starting from the unalkylated amine we prepared through three successive one-pot monometallations N,N-disubstituted amines with equal or different groups and bearing an alkylthio chain as long as wanted.