Analytic analysis of irregular discrete universes

In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric, thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model.     

Ru(II)-catalyzed cascade reactions in stereocontrolled construction of rigid as-indacene-bridged bis(alpha-amino acid) derivatives

The key construction in the preparation of as-indacene-bridged bis(alpha-amino acid) derivatives was effected by a Ru(II)-catalyzed RCM cascade reaction of appropriately substituted triynes. The latter were available after stepwise and stereocontrolled alkynylations of (2R)-2,5-dihydro-2-isopropyl-3,6-dimethoxypyrazine as chiral auxiliary. The regio- and stereochemical transformations have been verified by a single-crystal X-ray analysis.     

On the Foundation of the Principle of Relativity

The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call Aristotle's first and second laws. An Aristotelian universe in which all motion is relative to absolute space is considered. The first law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in true gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed.     

Nanowires for surface enlargement of narrow-bore fused-silica tubing

A method for preparation of silica nanowires with dimensions of d = 10-100 nm, l = 5-500 nm, is described. The nanostructured material is an integral part of the inner surface of narrow bore fused-silica capillary tubing. The wire preparation method is based on a decomposition of 2-chloro-1,1,2-trifluoroethyl methyl ether at elevated temperature and pressure. The silica bulk material is rearranged via a sustained silica-hydrogen fluoride chemistry, and reaction mechanisms for this process are proposed. The method is suitable for preparing long lengths of tubing with the modified surface. It is our belief that the texture of the capillary wall with its increased surface area is useful for applications such as microreactions, catalysis, and high-resolution pressure and/or electrodriven open-tubular liquid chromatography.     

Global rotation

Global rotation in cosmological models is defined on an observational basis. A theorem is proved saying that, for rigid motion, the global rotation is equal to the ordinary local vorticity. The global rotation is calculated in the space-time homogeneous class III models, with Gödel's model as a special case. It is shown that, with the exception of Gödel's model, the rotation in these models becomes infinite for finite affine parameter values. In some directions the rotation changes sign and becomes infinite in a direction opposite to the local vorticity. The points of infinite rotation are identified as conjugate points along the null geodesies. The physical interpretation of the infinite rotation is discussed, and a comparison with the behavior of the area distance at conjugate points is given.     

The classical and relativistic concepts of mass

An elementary presentation is given of classical and relativistic collision dynamics based upon the principle of conservation of momentum. The concepts of mass are shown to be implicitly defined and their basic properties are rigorously derived and discussed. Luxons and tachyons are treated on the same footing as material particles.     

Stereoselective preparation of (RP)-8-hetaryladenosine-3',5'-cyclic phosphorothioic acids

Cyclic adenosine monophosphate (cAMP) has been converted into its 8-bromo derivative and 2'O-TBDMS protected before activation of the phosphoric acid moiety with a reagent generated in situ from oxalyl chloride and DMF. Further reactions with primary amines furnished corresponding phosphoramidates with high stereoselectivity at the phosphorus atom. Cross-coupling reactions with the 8-bromopurine yielded 8-hetaryl derivatives. X-Ray analyses showed the amidates to possess the (S(P))-configuration. Carbon disulfide effected thiylation under strongly basic conditions stereospecifically provided the (R(P))-phosphorothioic acids.     

Ergot alkaloids in Norwegian wild grasses: a mass spectrometric approach

Ergot alkaloids are mycotoxins which are produced among fungi in the family Clavicipitaceae. Poisoning with ergot alkaloids is an important veterinary problem in animal husbandry and has recently also been recognised in wild animals. While the poisoning syndrome observed in domestic animals such as cattle, horses and sheep is usually caused by endophyte-infected grass, the recently observed ergotism among Norwegian cervids is probably due to infection of wild grasses with Claviceps. Mass spectrometry is today the method of choice for the rapid qualitative and quantitative determination of many natural compounds. This study uses tandem quadrupole mass spectrometry as well as ion trap mass spectrometry in connection with electrospray(+) ionisation for the quantification, screening and fragmentation of ergot alkaloids in extracts from Claviceps sclerotia that had been picked from wild grasses from several locations in Norway. Ergotamine, ergovaline, ergonovine and ergocryptine were available as standards and were quantified in the extracts, while ergocrystine, ergocornine, ergonine/ergosine, lysergic acid and lysergol were identified on the basis of their molecular weights and semi-quantified. Ergocrystine dominated the alkaloid spectrum of most extracts. Levels of the quantified alkaloids were in the range 0.2-9300 microg/g. Several unknown ergot alkaloids were found in the extracts. MS(n) experiments identified some as simple lysergic acid amide derivatives, while othes are probably related to ergocrystine and ergocryptine by dehydration, dehydrogenation and/or amino acid substitution at R(1) of the peptide moiety.     

The timing and deterrence of terrorist attacks due to exogenous dynamics

In this paper, we develop a model for the timing and deterrence of terrorist attacks due to exogenous dynamics. The defender moves first and the attacker second in a two-stage game which is repeated over T periods. We study the effects of dynamics of several critical components of counter-terrorism games, including the unit defence costs (eg, immediately after an attack, the defender would easily acquire defensive funding), unit attack costs (eg, the attacker may accumulate resources as time goes), and the asset valuation (eg, the asset valuation may change over time). We study deterministic dynamics and conduct simulations using random dynamics. We determine the timing of terrorist attacks and how these can be deterred.