On Invariants of the Rotation Group

Any quantity transforming according to an irreducible representation of the space rotation group may be realized in three forms: i) as a multispinor χ…α_2l; ii) as a 3-tensor t…i_l (for 2l even) or, tensor-spinor t…i_l−1/2 (for 2l odd); iii) as an l-spinor Ψλ^(l) (λ = −l,…, l). Only one invariant may be constructed of three quantitites of a given kind; so the three invariants are equal up to a numerical factor that is found in the work. A number of invariants may be constructed of four quantities, not all of them independent. For applications it is of importance to be able to construct an independent set of invariants of every kind, as well as to relate the invariants of different kinds. This problem is solved in the present work for arbitrary angular momenta l₁, l₂, l₃, l₄.     

Isomeric states in the second well of the potential and long-lived superheavy elements

The data on long-lived isomeric states obtained via secondary reactions in CERN W targets irradiated with 24 GeV protons and also by the¹⁶O+¹⁹⁷Au and²⁸Si+¹⁸¹Ta reactions are summarized. Their consequences concerning the existence and the discovery of the long-lived superheavy element withZ=112 are discussed.     

Growth of buckytubes on the anode at are discharge

It is shown that for an arc discharge between carbon electrodes in an inert gas atmosphere the temperatures at the electrode surfaces play a key role in determining the structure and the electrode on which a deposit can grow. The heat balance equations determine that the anode temperature is higher due to the energy carried by the electrons. This leads to anode sublimation and deposition on the cathode. It is shown that by cathode heating, by anode cooling or by a combination of these, a deposit may be obtained on the anode due to cathode erosion. The deposit grown by the “inverse” method is compared with a deposit obtained on the cathode under the same conditions but at reverse supply voltage polarity. The material from both deposits, studied by TEM, shows that there are graphite crystals within the anode deposit, and that the carbon forms within have a relatively small number of structural defects while the buckytubes are greater in length than those within the cathode deposit. The reasons for these differences are discussed. In the “inverse” method, the constant decrease in cooling of the anode surface leads to an equalization of the anode and cathode temperatures. This creates conditions that favor buckytube growth.     

Investigation on the TeO2-MoO3-V2O5 System I. Phase Equilibrium

The phase equilibrium in the TeO₂-MoO₃-V₂O₅ system has been determined in air at atmospheric pressure. Differential thermal analysis (DTA), X-ray diffraction and optical microscopy were used for establishing the phase transitions. Two congruently melting ternary compounds (Te₃Mo₂V₂O₁₇ and TeMoV₂O₁₀) were identified by the above methods. Their fields of primary crystallization are entirely within the glass-formation range. The character and behaviour of the phases, the invariant points as well as the temperature maxima have been discussed. The glass-formation range correlates with the phase distribution in the system and includes all ternary invariant points.     

An approach to quanitzation of constrained systems

The dynamics of a classical system, specified by a HamiltonianH ₀(q,p) and a number of constraint functions _k (q,p) in Euclidean phase space (q,p), is described by means of a new HamiltonianH(q,p), which is an invariant of the (closed) Poisson-bracket Lie algebra (H ₀, _k ). Fixed values of _k (not necessarily zero) are given by initial conditions, and they are conserved along the trajectories determined by the Hamilton equations. The quantization is performed by the standard Heisenberg commutation relations in the embedding phase space, while the constraint functions are put in correspondence with constraint operators which generate the Lie algebra of quantum commutators. A subset of commuting constraint operators may be chosen to have certain values in the initial state; and as soon as the Hamiltonian operator is an invariant of the Lie algebra, these conditions are maintained permanently. Simple examples are presented. Systems with both Bose and Fermi degrees of freedom (and constraints) can be treated universally.     

S4N4 und seine Derivate: Darstellung und Röntgenstrukturanalyse von CuCl2 · S4N4

Phase equilibrium in the TeO₂? Cu₂O system was determined in air at atmospheric pressure. Differential thermal analysis (DTA), X-ray powder diffraction and optical microscopy were used to identify the phase transitions. Two congruently melting compounds Te₃Cu₂O₇ and TeCu₂O₃ were obtained. They possess monoclinic and hexagonal symmetry respectively. The morphology, optical properties and indexed powder pattern up to 1.3 Å are submitted for these compounds. Experiments realized by the DTA indicated the existence of an oxidation process with beginning and rate dependent on the composition. The glass formation limits determined for 2 g and 10 g tellurite glass melts correlate with the invariant points in the system.     

Contrary to Wilczyński,there is no aberration for comoving source and observer

The aberrational method for measurement of the Earth's absolute velocity proposed by Wilczyski cannot give a positive result.     

Influence of nonlinearly induced diffraction on spatial solitary waves

Spatial solitary waves carried by a TE mode in planar optical waveguides with Kerr-type of nonlinearity are investigated based on a modified nonlinear (1 + 1) Schrödinger equation. Looking for effects instigated by the spatial inhomogeneity of the nonlinear polarization, the nonzero divE-term is taken into account in the nonlinear guided wave equation together with the nonparaxial approach and vector model. It is shown that, at self-focusing of beams in a (1 + 1) geometry, the effect coming out from the divergence term predominates over modifications related to the nonparaxial vector model. This term is interpreted as nonlinearly induced diffraction which plays the role of an effective saturation. Analytical solutions supported by numerical results are found.