From noncommutative κ-Minkowski to Minkowski space–time

We show that free κ-Minkowski space field theory, discussed in the context of κ-Poincaré algebra and Doubly Special Relativity is equivalent to a relativistically invariant free field theory on Minkowski space–time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy–momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.     

Inheriting independence and chi-squaredness under certain matrix orderings

Let x ～ N(μ, Z), and let S = (Σ:μ). It is shown that if x′A₁x is independent of x′Bx (x′A₁x is distributed as a chi-square variable), then this property is inherited by every x′A₂x for which S′A₂S precedes S′A₁S with respect to the range preordering (with respect to the rank subtractivity partial ordering).     

Exponential-like responses analysis method

An exponential-like responses analysis method is presented. The method enables one: 1) to evaluate the similarity of a curve to the ideal exponential characteristic; 2) to find the most appropriate final value of a curve; and 3) to find the value of Τ giving the best approximation between the analyzed curve and the ideal exponential one.     

The cyanide-catalyzed conversion of β-formylmuconates into triglochinates: A useful biomimetic synthesis

Upon treatment with cyanide under slightly basic conditions, β-formyl-cis,cis-muconic acid and esters, prepared from vanillin, undergo a sequence of prototropic shifts equivalent to an internal redox process in which 1,4-reduction of the diene system is blanaced by oxidation of the formyl group.     

The kinetics of tritium-hydrogen exchange between xanthine,theophylline,caffeine and water

Isotopic hydrogen exchange at C-8 of xanthine, theophylline and caffeine in water has been studied at several temperatures and constant pH. The rates of detritiation of these compounds have been determined over a pH range at constant temperature. The rate-pH profiles for theophylline and caffeine are interpreted in terms of rate determining attack by hydroxide ion on protonated substrate. For caffeine and xanthine at high pH an additional mechanism involving hydroxide catalysed exchange of the neutral compound is suggested.     

A tetranuclear 3d-4f single molecule magnet: [CuIILTbIII(hfac)2]2

We report now the first single molecule magnet (SMM) consisting of d-f elements. The present study demonstrates that the synthesis of the d-f polynuclear molecule is a very promising approach to SMMs. (1) The d-f polynuclear molecule can be easily synthesized by the assembly reaction of the d-component and the f-component, (2) the high-spin ground state can be generated by a smaller number of metal ions than the d complex, and (3) the molecular magnetic anisotropy is easily derived from the f-component.     

Computing the tame kernel of quadratic imaginary fields

J. Tate has determined the group (called the tame kernel) for six quadratic imaginary number fields where Modifying the method of Tate, H. Qin has done the same for and and M. Skaba for and

In the present paper we discuss the methods of Qin and Skaba, and we apply our results to the field

In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of for some other values of The results agree with the conjectural structure of given in the paper by Browkin and Gangl.

     

The construction of the Gilmore–Perelomov coherent states for the Kratzer–Fues anharmonic oscillator with the use of the algebraic approach

By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.