Finite groups in which a Sylow two-subgroup of the centralizer of some involution is of order 16

It is proved that the sectional two-rank of a finite group G having no subgroup of index two is at most four if a Sylow two-subgroup of the centralizer of some involution of G is of order 16. This implies the following assertion: If G is a finite simple group whose order is divisible by 2⁵ and the order of the centralizer of some involution of G is not divisible by 2⁵, then G is isomorphic to the Mathieu group M₁₂ or the Hall-Janko group J₂.     

Momentless elastic reinforced shells with a zero gaussian curvature

In [1], a number of statements were formulated of the problem of the attainment of a momentless stressed state in elastic reinforced shells with an arbitrary form of their middle surface. The present work is devoted to the solution of three of the statements advanced in [1], for the case where the middle surface has a zero Gaussian curvature.     

Thermodynamics of a dense plasma

Journal of Applied Spectroscopy -     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED-CLAMPED AND SIMPLY SUPPORTED-CLAMPED BEAMS

In a previous series of papers (Benamar 1990 Ph.D. Thesis, University of Southampton; Benamaret al. 1991 Journal of Sound and Vibration149, 179-195;164, 399-424 [1-3]) a general model based on Hamilton's principle and spectral analysis has been developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. The results obtained with this model corresponding to the first non-linear mode shape of a clamped-clamped (CC) beam and to the first non-linear mode shape of a CC plate are in good agreement with those obtained in previous experimental studies (Benamaret al. 1991 Journal of Sound and Vibration 149, 179-195;164, 399-424 [2, 3]). More recently, this model has been re-derived (Azar et al. 1999 Journal of Sound and Vibration224, 377-395; submitted [4, 5]) using spectral analysis, Lagrange's equations and the harmonic balance method, and applied to obtain the non-linear steady state forced periodic response of simply supported (SS), CC, and simply supported-clamped (SSC) beams. The practical application of this approach to engineering problems necessitates the use of appropriate software in each case or use of published tables of data, obtained from numerical solution of the non-linear algebraic system, corresponding to each problem. The present work was an attempt to develop a more practical simple “multi-mode theory” based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance. The purpose was to derive simple formulae, which are easy to use, for engineering purposes. In this paper, two models are proposed. The first is concerned with displacement amplitudes of vibrationW_max /H, obtained at the beam centre, up to about 0·7 times the beam thickness and the second may be used for higher amplitudes W_max/H up to about 1·5 times the beam thickness. This new approach has been successfully used in the free vibration case to the first, second and third non-linear modes shapes of CC beams and to the first non-linear mode shape of a CSS beam. It has also been applied to obtain the non-linear steady state periodic forced response of CC and CSS beams, excited harmonically with concentrated and distributed forces.     

Cascade unlooping of a low-pitch helical spring under tension

We study the force vs. extension behaviour of a helical spring made of a thin torsionally stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to unwind when pulled but rather to form hockles that pop out one by one and lead to a highly non-monotonic force-extension curve. Between abrupt loop pop-outs this curve is well described by the planar elastica whose relevant solutions are classified. Our results may be relevant for tightly coiled nanosprings in future micro- and nano(electro)mechanical devices.     

Study of the ion composition of an expanding magnesium plasma produced by a CO2 laser

The evolution of the ion composition of a laser plasma during its expansion over a large distance is studied. The plasma is produced by a TIR CO₂ laser with a pulse energy up to 100 J and duration of ～20 ns. X-ray diagnostics with the use of a spectrograph and X-ray PIN diodes was applied to study the plasma near the target surface. At large distances from the target surface, time-of-flight neutral-particle diagnostics with the use of an electrostatic analyzer and ion collector was applied. Calculations performed with the GIDRA-1 code agree well with experimental data.     

Embedding Uq(sl(2)) and Sine Algebras in Generalized Clifford Algebras

We establish the connection between certain quantum algebras and generalizedClifford algebras (GCA). To be precise, we embed the quantum tori Lie algebraand U _q (sl(2)) in GCA.