The magnetic field,force and inductance of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid

The method of separation of variables has been applied to determine the magnetic field of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid of revolution. The inductance and the force acting between the coil and the ellipsoid are also examined.     

Graph Approach to the Computation of the Homology of Continuous Maps

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27].     

Non-trivial negative links have positive signature

A negative link is an oriented link that can be represented by a diagram with all the crossings negative. In this paper we prove the following theorem.     

EPR studies of Gd3+-doped Ce2(SO4)3.8H2O and La2(SO4)3.9H2O single crystals

EPR spectra of Gd³⁺-doped Ce₂(SO₄)₃.8H₂O and La₂(SO₄)₃.9H₂O single crystals have been measured with an X-band spectrometer at room and low temperatures. The absolute signs of spin Hamiltonian parameters have been determined for the La₂(SO₄)₃.9H₂O host from intensities of lines at liquid helium temperature; for the Ce₂(SO₄).8H₂O host the lines broaden considerably below 60 K, not permitting the determination of absolute signs of spin Hamiltonian parameters. The data are analysed using a rigourous least-squares procedure, fitting simultaneously all lines obtained for several orientations of the external magnetic field. The zero-field splittings have been computed for both the hosts. The characteristics of EPR spectra of Gd³⁺ in these hosts are compared with those obtained in other rare-earth trisulphate octahydrate hosts.     

The dichlorovinylation of enolates

The condensation of certain ketone and ester enolates with trichloroethylene proceeds with surprising ease to yield dichlorovinylation products. The $\text{trans}$ stereochemistry for one such product is established by X-ray, and subsequent transformations of these initial products to ethinyl or ω-chloroethinyl derivatives is described.     

Behaviour of LiF:Mg,Cu,P and LiF:Mg,Ti thermoluminescent detectors for electron doses up to 1 MGy

The behaviour of LiF:Mg,Cu,P and LiF:Mg,Ti detectors at ultra-high doses up to 1 MGy, has been investigated. The presence of the ultra-high-temperature peak (450 °C) of reproducible properties was observed in various batches of LiF:Mg,Cu,P, confirming earlier findings. The results indicate that this peak is not an effect of random impurities nor intrinsic effects of LiF, but it is rather connected with the doping.A parameter called ultra-high temperature ratio (UHTR) was defined in order to quantify the observed changes of LiF:Mg,Cu,P glow-curve shape at very high doses and very high temperatures. The use of this parameter allows to determine an absorbed dose in the range from 1 kGy to 1 MGy. This new method of high-dose dosimetry makes LiF:Mg,Cu,P a unique dosimeter, which is capable to cover at least 12 orders of magnitude of dose range: from a microgray to a megagray.     

On the correctness of the thermoluminescent high-temperature ratio (HTR) method for estimating ionization density effects in mixed radiation fields

The high-temperature ratio (HTR) method which exploits changes in the LiF:Mg,Ti glow-curve due to high-LET radiation, has been used for several years to estimate LET in an unknown radiation field. As TL efficiency is known to decrease after doses of densely ionizing radiation, a LET estimate is used to correct the TLD-measured values of dose. The HTR method is purely empirical and its general correctness is questionable. The validity of the HTR method was investigated by theoretical simulation of various mixed radiation fields.The LET_eff values estimated with the HTR method for mixed radiation fields were found in general to be incorrect, in some cases underestimating the true values of dose-averaged LET by an order of magnitude. The method produced correct estimates of average LET only in cases of almost mono-energetic fields (i.e. in non-mixed radiation conditions). The value of LET_eff found by the HTR method may therefore be treated as a qualitative indicator of increased LET, but not as a quantitative estimator of average LET.However, HTR-based correction of the TLD-measured dose value (HTR-B method) was found to be quite reliable. In all cases studied, application of this technique improved the result. Most of the measured doses fell within 10% of the true values. A further empirical improvement to the method is proposed. One may therefore recommend the HTR-B method to correct for decreased TL efficiency in mixed high-LET fields.     

Quantum Hall ferrimagnetism in lateral quantum dot molecules

We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.     

The small peptide-catalyzed direct asymmetric aldol reaction in water

Simple modular di- and tripeptides with a primary amine at the N-terminus catalyze the aqueous asymmetric aldol reaction between unmodified ketones and aldehydes to furnish the corresponding beta-hydroxy ketones with up to 86% ee in water and 99% ee in aqueous media.