On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euclidean spaces $R_q^N$ with the quantum groups of rotation $U_qso(N)$ of $R_q^N$, for which it has no classical analog.Comment: Latex file, 27 pages. Final version to appear in J. Phys.

Unidirectional Rotation Neurones in the Optomotor System of the Crab, Carcinus

1. Among the optomotor fibres to the eye muscles in Carcinus a class was found which responds to unidirectional fast rotations around various body axes. All had large signals and are therefore of large diameter. 2. In one set of these fibres which fires especially for rotations around the dorsoventral axis, it could be shown that discharges take place especially during accelerations and that, when a rotation in the null direction is suddenly stopped, a short discharge occurs. The fibres for other axes behave in a similar manner. 3. For rotations around the ventro-dorsal axis, but not for other directions, mediumsized fibres are present which, in contrast to the fast fibres, respond to visual stimulation, as well as to body rotations in darkness, thus combining the input properties of the unidirectional fast rotatory and the unidirectional purely optokinetic small fibres. Their sensitivity to visual input is for low rotation velocities, to body rotations is for high rotation velocities

Factors Regulating the Discharge Frequency in Optomotor Fibres Of Carcinus Maenas

The influence of the excited state of the animal on various motor neurone discharges and accompanying muscle action potentials was studied in the eyestalk of the crab, Carcinus maenas. In most cases large increases in firing frequency could be obtained during such states. An exception is the tonic eye-withdrawal system in which an inhibitory effect is caused. A pronounced difference in habituation to constant stimuli between spring and summer was found for the position fibres; in spring it was slow and in summer much quicker

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Iron line emission in X-ray afterglows

Recent observations of X-ray afterglows reveal the presence of a redshifted Kalpha iron line in emission in four bursts. In GRB 991216, the line was detected by the low energy grating of Chandra, which showed the line to be broad, with a full width of ~15,000 km/s. These observations indicate the presence of a >1 solar mass of iron rich material in the close vicinity of the burst, most likely a supernova remnant. The fact that such strong lines are observed less than a day after the trigger strongly limits the size of the remnant, which must be very compact. If the remnant had the observed velocity since the supernova explosion, its age would be less than a month. In this case nickel and cobalt have not yet decayed into iron. We show how to solve this paradox.Comment: 3 pages, to appear in the proceedings of the the 2nd Workshop on Gamma-Ray Bursts in the Afterglow Era, Rome, Oct. 200

An aging evaluation of the bearing performances of glass fiber composite laminate in salt spray fog environment

The aim of the present paper is to assess the bearing performance evolution of pinned, glass-composite laminates due to environmental aging in salt-spray fog tests. Glass fibers/epoxy pinned laminates were exposed for up to 60 days in salt-spraying, foggy environmental conditions (according to ASTM B117 standard). In order to evaluate the relationship between mechanical failure mode and joint stability over increasing aging time, different single lap joints, measured by the changing hole diameter (D), laminate width (W) and hole free edge distance (E), were characterized at varying aging steps. Based on this approach, the property-structure relationship of glass-fibers/epoxy laminates was assessed under these critical environmental conditions. Furthermore, an experimental 2D failure map, clustering main failure modes in the plane E/D versus W/D ratios, was generated, and its cluster variation was analyzed at each degree of aging