Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

Some developments in reaction and solution microcalorimetry,with particular reference to its use in biochemistry and cellular biology

The field of isothermal microcalorimetry as applied to systems of interest for aqueous solution chemistry, biochemistry and in cellular biology is briefly reviewed. Some techniques recently developed in the author's laboratory are described.     

A new general-purpose isothermal microcalorimeter for use at temperatures up to 200 °C

The design and some properties of a new general-purpose isothermal microcalorimeter are reported. The instrument is a twin thermopile heat conduction calorimeter, which is designed for use up to 200 °C. The calorimetric units and surrounding heat sink are suspended inside a hollow aluminium construction, which is thermostated. Above that unit a second thermostated block is positioned and the whole assembly is suspended inside a Dewar vessel. When the instrument is used at room temperature and below, the thermostated units are cooled by use of an insertion Peltier effect cooler. The instrument can be used with a wide range of different reaction vessels (diameter 14 mm). Baseline experiments have been conducted in the temperature range 15-200 °C. Typical values obtained during 10 h periods at 200 °C are ±3 and ±10 nW for the baseline drift and baseline fluctuations, respectively. The heat detection limit, determined by release of electrical energy, is about 2 μJ. Preliminary stability measurements have been conducted at 100 °C on samples of stabilised and non-stabilised polyamide film.     

Strange reality: Ashtekar's variables with variations

I give a very brief review of Ashtekar's variables, with an emphasis on the non-trivial reality condition. As a toy model a formulation of spin 1/2 fields is presented, in which the Dirac equation appears as a reality condition. Then, some new ways to modify complex general relativity are mentioned. It is not known whether the new theories admit any reality condition at all.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 211–213, May, 1993.     

Molecular gradients: an efficient approach for optimizing the surface properties of biomaterials and biochips

A variety of molecular gradients of alkanethiols with the structure HS-(CH(2))(m)-X (m = 15; X = COOH, CH(2)NH(2), or CH(3)) and oligo(ethylene glycol)-terminated alkanethiols with the structures HS-(CH(2))(15)-CO-NH-Eg(n) (n = 2, 4, or 6), HS-(CH(2))(15)-CO-NH-Eg(2)-(CH(2))(2)-NH-CO-(CH(2))(4)-biotin, and HS-(CH(2))(15)-CO-NH-Eg(6)-CH(2)-COOH were prepared on polycrystalline gold films. These gradients were designed to serve as model surfaces for fundamental studies of protein adsorption and immobilization phenomena. Ellipsometry, infrared spectroscopy, and X-ray photoelectron spectroscopy, operating in scanning mode, were used to monitor the layer composition, gradient profiles, tail group conformation, and overall structural quality of the gradient assemblies. The gradient profiles were found to be 4-10 mm wide, and they increased in width with increasing difference in molecular complexity between the thiols used to form the gradient. The oligo(ethylene glycol) thiols are particularly interesting because they can be used to prepare so-called conformational gradients, that is, gradients that display a variation in oligo(ethylene glycol) chain conformation from all trans on the extreme Eg(2,4) sides, via an amorphous-like phase in the mixing regimes, to helical at the extreme Eg(6) sides. We demonstrate herein a series of experiments where the above gradients are used to evaluate nonspecific binding of the plasma protein fibrinogen, and in agreement with previous studies, the highest amounts of nonspecifically bound fibrinogen were observed on all-trans monolayers, that is, on the extreme Eg(2,4) sides. Moreover, gradients between Eg(2) and a biotinylated analogue have been prepared to optimize the conditions for the immobilization of streptavidin. Ellipsometry and infrared spectroscopy reveal high levels of immobilization over a fairly broad range of compositions in the gradient regime, with a maximum between 50 and 60% of the biotinylated analogue in the monolayer. A pI gradient composed of (NH(3)(+)/COO(-))-terminated thiols was also prepared and evaluated with respect to its ability to separate differently charged proteins, pepsin, and lysozyme, on a solid surface.     

Synthesis of 2•,3•-Dideoxy-3•-<Emphasis Type="Italic">C</Emphasis>-hydroxymethylcytidine Phosphonomethyl Derivatives

Phosphonomethyl substituted 2?,3?-Dideoxy-3?-C-hydroxymethylcytidines have been synthesized and evaluated for their anti HIV-1 activities. The sugar moiety was synthesized starting from (S)-5-hydroxymethylfuran-2-(5H)-one using photocatalyzed addition of methanol. Reduction of the lactone, condensation with silylated 4-methoxy-2(1H)pyrimidinone, followed by phosphonomethylation and deprotection gave the title compounds. The compounds were tested for inhibition of HIV-1 activity but did not show any significant antiviral activity.     

A Kochen-Specker inequality from a SIC

Yu and Oh (eprint) [1] have given a state-independent proof of the Kochen-Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute a SIC (symmetric informationally-complete positive operator-valued measure) and a complete set of MUB (mutually unbiased bases). A theory-independent inequality is also presented using the same 21 rays, as required for experimental tests of contextuality.     

Synthesis of C 2 Symmetric Potential Inhibitors of HIV-1 Protease From D-Mannitol

ABSTRACT

D-Mannitol was used as precursor for the synthesis of acyclic C ₂ symmetric potential HIV-1 protease inhibitors. The 1- and 6-hydroxy groups of D-mannitol were substituted by -NHBoc, -NHValZ, -SAr, -SOAr and -SO₂Ar and the 2-and 5-hydroxy groups were benzylated. In some products one of the central hydroxyl groups was either inverted or deoxygenated. Despite a close structural similarity to previously published inhibitors none of the products showed significant inhibitory activity against HIV-1 protease.

     

Some observations on degenerate metrics

There are some polynomial formulations of Einstein's equations in which the metric is allowed to become degenerate. We examine some known exact solutions to see whether they may be smoothly joined to solutions with degenerate metrics. If one uses a lapse function which is a spatial scalar, this is very easy. If the lapse function has a small and negative tensor density weight, the joining together may take place across the horizons in the Schwarzschild and Kerr solutions. For large and negative weights, we have been unable to find any examples.