Crystallographic and magnetic structure of HAVAR under high-pressure using diamond anvil cell (DAC)

Annealed (H1) and cold-rolled (H2) HAVAR has been studied using high-pressure synchrotron X-ray diffraction. A structural phase transformation was discovered at ～13 GPa at ambient temperature, transforming from m ??3 m (S.G. 225) to P 63/m m c (S.G. 194) symmetry. The transition was not reversible on pressure release. The low-pressure cubic phase was found to be more compressible than the high-pressure hexagonal phase. Conventional Mössbauer and NFS shows that the HAVAR is not magnetic at room temperature and no splitting is observed. The SQUID indicates a huge difference in the temperature dependence of the magnetic susceptibility between the cold Rolled HAVAR compared to the annealed HAVAR.     

Exact scaling relations in relativistic hydrodynamic turbulence

We consider the steady state statistics of turbulence in general classes of dissipative hydrodynamic equations, where the fluctuations are sustained by a random source concentrated at large scales. It is well known that in some particular cases, such as non-relativistic incompressible turbulence, a Kolmogorov-type exact scaling relation for a correlation function holds. We show that all such scaling relations follow from a general relation on the current-density correlation function. The derivation does not require an energy cascade picture and suggests that this traditional interpretation of the Kolmogorov relation for incompressible turbulence may be misleading. Using this we derive exact scaling results for compressible turbulence in relativistic hydrodynamics, which reduce in the slow motion limit to the Kolmogorov relation. We discuss the experimental implications of the results.     

Polybromostryl macromers and their anionic polymerization

The decomposition of polybromostyryl carbanions (PBS^?), obtained by anionic polymerization of 4-bromostyrene in tetrahydrofuran (THF), was investigated in the dark in a temperature range of ?6–?21°C. It was accompanied by the evolution of bromine anions and by the formation of polymeric allylic carbanions (λ_max = 575 nm; ε_max = 6800 eq^?1·L·cm^?1). The reaction mechanism was elucidated. The rate constant of the unimolecular rate-determining step of the process was 1.3 × 10^?5 s^?1 and 9.7 × 10^?5 s^?1 at ?21 and ?6°C, respectively. Its apparent energy of activation E_app = 18.38 Kcal/mol. The polybromostyrenes with allylic carbanions at their ends may decompose further. Their “dark” decomposition yielded 1,3-butadiene-1,3-diphenyl-macromers. The mechanisms of decomposition of the PBS^? carbanions and the dark decomposition of the polybromostyryl allylic carbanions are analogous. The rate constant of the latter process was 2.5 × 10^?6 s^?1 at ?6°C. The anionic polymerization of prepared macromers can be initiated in THF at ?78°C by α-methylstyryl carbanions, which do not react, however, with PBS^? carbanions. “Comblike” polymacromers were prepared in which each branch had a molecular weight of about 50,000. The overall molecular weight of the polymacromer was estimated to be about 1 × 10⁶. It has been assumed that the 2–1 mode of addition to the diene group of the macromer is predominant during its polymerization. The 3–4 mode of addition followed by proton shift represents the termination step. The 4–3 mode of addition was ruled out on the basis of spectroscopic evidence.     

A universe embedded in a five-dimensional flat space

Since a homogeneous isotropic universe can be embedded in a flat space of five dimensions, the question is considered under what conditions a more general universe can be embedded in a five-dimensional flat space. On the assumption that the deviation from homogeneity is small, it is found that real inhomogeneities can occur only in the case of a universe filled with radiation, or a universe containing at least two different substances with different equations of state, as for example radiation and matter. In the case of a radiation-filled universe, the inhomogeneities can be of arbitrary size and can conceivably be the precursors of galaxies.     

Optimal multi-period insurance contracts

In multi-period insurance contracts (such as automobile insurance contracts), unlike single-period ones, the premiums that the insured must pay increase whenever he files a claim. Hence, the buyer faces a problem that is absent in one-period models, namely: he must determine for which damages he should file a claim and for which he should not.The optimal claims policy of the buyer is presented for a large class of insurance contracts. It is shown that the buyer will file a claim only if it is larger than some critical value. Based on this it is shown that the buyer prefers a contract that provides full coverage above a deductible for damages that exceed his critical value. In this case the optimal contract is not unique since the buyer is indifferent to the form of the contract for damages below his critical value. It is shown, however, that as in one-period models (Arrow (1963, 1974)) there exists an optimal contract that provides full coverage above a deductible. In multi-period setting, however, the buyer will file a claim only if the damage is sufficiently higher than the deductible.It is also shown that the buyer prefers a strictly positive deductible. Unlike the one-period case (Mossin (1968)), this result holds true even if the premium rates equal the expected payments.     

Some cosmological models in the bimetric theory of gravitation

It is shown that the field equations of the bimetric theory of gravitation have solutions corresponding to a class of homogeneous isotropic cosmological models with negative spatial curvature (k=–1). Some examples are given.     

A polynomial algorithm for minimal interval representation

The following problem arises in the context of object representation: given two endpoints of an interval in a Gray code table, find a Boolean function in DNF that represents this interval, with as few prime implicants as possible. This paper shows that there is a unique minimal representation and presents a polynomial algorithm that finds it.