Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

Electro-elastic interactions and second order anisotropic constitutive equations

Piezoelectricity is usually expressed as an interaction between mechanical and electrical variables. The physics involved is hence governed by a coupling between Maxwell's equations of electromagnetism and the equations of elasticity. Such a coupling takes us through the piezoelectric constitutive relations. In this work, the second order anisotropic constitutive equations are treated, and in particular, the number of independent material constants is computed for all the 32 crystallographic classes.Paper presented, in reduced version, at the 12th Italian National Congress of Theoretical and Applied Mechanics (AIMETA '95), October 1995, Naples, Italy.     

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are δ2 =4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ=4.669.     

Design,synthesis of novel quinazolin-4-one derivatives and biological evaluation against human MCF-7 breast cancer cell line

A new series of 6,8-dibromo-2-(4-chlorophenyl)quinazolin-4(3H)-one derivatives VI–XIII were synthesized. Their chemical structures were confirmed by spectral and elemental analysis. The cytotoxic effect of the newly synthesized compounds was tested in vitro against human breast cancer cell line (MCF-7). Most of the tested compounds have shown promising cytotoxic activity. Compounds X and XIIIb exerted a powerful cytotoxic effect against MCF-7 with a very low IC50 (0.0015 and 0.0047 µmol/ml), while compounds VI, VII, VIII, XIIb, XI, XIIIc and IX exerted a moderate cytotoxic effect (IC50 0.01523, 0.0213, 0.031, 0.0478, 0.049, 0.068 and 0.079 µmol/ml respectively), compared to doxorubicin (0.0025 µmol/ml). Exploring their apoptotic effect; interestingly,all compounds activated apoptotic cascade in MCF-7. Compounds VI, XIIIb, XIIb, XI, XIIa, VII, V and VIII showed potent effect even much more than doxorubicin by 12.87–5.91 folds, while compounds XIIIc, IX, XIIIa, XIIc and X showed moderate increase in CASP3 activity by 4.96–3.22 folds relative to untreated cells more or less similar to doxorubicin (5.57 folds).     

Ultra-low-frequency dust-electromagnetic modes in self-gravitating magnetized dusty plasmas

Obliquely propagating altra-low-frequency dust-electromagnetic waves in a self-gravitating, warm, magnetized, two fluid dusty plasma system have been investigated. Two special cases, namely, dust-Alfvén mode propagating parallel to the external magnetic field and dustmagnetosonic mode propagating perpendicular to the external magnetic field have also been considered. It has been shown that effects of self-gravitational field, dust fluid temperature, and obliqueness significantly modify the dispersion properties of these ultra-low-frequency dust-electromagnetic modes. It is also found that in parallel propagating dust-Alfvén mode these effects play no role, but in obliquely propagating dust-Alfvén mode or perpendicular propagating dust-magnetosonic mode the effect of self-gravitational field plays destabilizing role whereas the effect of dust/ion fluid temperature plays stabilizing role.     

Obliquely propagating ion-acoustic shock waves in a degenerate quantum plasma

A theoretical investigation has been carried out on the propagation of non-linear ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system composed of inertial non-relativistic positively charged light and heavy ions, inertialess non-relativistically or ultra-relativistically degenerate electrons and positrons. The reductive perturbation method has been employed to derive the Burgers' equation. It has been observed that under consideration, our plasma model supports only positive potential shock structure. It is also found that the amplitude and steepness of the IASHWs have been significantly modified by the variation of ion kinematic viscosity, oblique angle, number density, and charge state of the plasma species. The results of our present investigation will be helpful for understanding the propagation of IASHWs in white dwarfs and neutron stars.     

Commensurability oscillations in NdBa2Cu3Oy single crystals

Commensurability between inter-vortex distance and crystal lattice constant is investigated by angular dependent magnetization in very pure twinned and twin-free NdBa₂ Cu₃ O_y single crystals. With increasing temperature the incommensurate states split up and become finally commensurate with half the vortex distance. These new commensurate states are related to a substructure of the intrinsic pinning potential within the unit cell and discussed with respect to temperature, field, anisotropy, and twin structure.     

Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Off-axis pumping of a photonic crystal fiber laser

We present a new method for free space pumping of double-clad photonic crystal fiber lasers and amplifiers. The method is based on off-axis injection of the pump beam, exploiting the relatively high numerical aperture of the photonic crystal fiber cladding. It prevents feedback from the laser into the pump source, does not require any special treatment to the fiber, and could lead to a more compact resonator. Experimental results with the new pumping method show improved laser performance.