Existence of solutions to (k, n − k − 2) discrete boundary value problems

We provide general existence criteria to solutions for a class of higher-order discrete boundary value problems. Our results supplement as well as improve several recent results established in the literature.     

Parallel superposition of small- and large-amplitude oscillations upon steady shear flow of polymer fluids

The parallel superposition of small- and large-amplitude oscillations upon steady shear flow of elastic fluids has been considered. Theoretical results, obtained by numerical methods, are based upon the Leonov viscoelastic constitutive equation. Steady-state components, amplitude, and phase angle of oscillatory components of the shear stress, the first and second normal-stress differences as a function of shear rate, deformation amplitude, and frequency have been calculated. These oscillatory components include the first harmonic of the shear stresses and the first and second harmonic of the normal stresses. In the case of small-amplitude superposition, the effect of the steady shear flow upon frequency-dependent storage and loss moduli has been determined and compared with experimental data available in the literature for polymeric solutions and melts. In the case of large-amplitude superposition, the effect of oscillations upon the steady shear flow characteristics has been determined and compared with our experimental data for a polymeric melt. The experimental results for shear stress components have been found to be in good agreement with theoretical predictions, although there are some deviations for storage modulus at high shear rates. The deviations seem to be dependent on material. Moreover, the theory is unable to describe experimental data available for the first harmonic of normal stresses.     

Toluene solvent system for the headspace gas chromatographic determination of styrene monomer in polystyrene

The use of toluene as a solvent to dissolve polystyrene for the determination of styrene monomers is studied. Compared with the modified solution headspace method using dimethylacetamide as solvent, with toluene the system is slightly less sensitive. However, there appeared to be minimal matrix effect when toluene is used, so a simpler external calibration method can be applied.     

New chemistry of mitomycin C

Novel and significant analogues of mitomycin C were prepared based on new chemistry utilizing mitomycin C in its anion form.     

Emission of positive ions from KCl and NaCl crystals exposed to high electric fields

It is demonstrated by means of combined optical microscopy and field desorption mass spectrometry that alkali ions and cluster ions are emitted from microcrystals of KCl and NaCl exposed to positive high electric fields. The ion emission is very strong at temperatures where the sublimation of the sample is optically observable, indicating that an enhanced sample sublimation is a key precondition for enhanced ion emission.     

High efficiency and high brightness Raman conversion of dye laser radiation

A technique for efficient Raman conversion of an excimer pumped dye laser is described, based on the use of a Raman oscillator/amplifier combination. A photon conversion efficiency of 90% to first Stokes is demonstrated, with diffraction-limited beam quality.     

Texture dependence of capillary instabilities in nematic liquid crystalline fibres

Static and dynamic linear analyses of axisymmetric capillary instabilities in textured nematic liquid crystalline fibres are performed using the equations of nemato-statics and inviscid nemato-dynamics. Three representative textures, viz. axial, onion, and radial, are analysed to show all possible effects of Frank gradient elasticity on the wavelength selection and growth rate of peristaltic modes driven by surface area reduction. It is found that Frank elasticity may tend to stabilize or destabilize the fibre, depending on the initial fibre texture. Axial textures tend to stabilize the fibre through the director splay-bend distortions driven by surface tilting. Onion textures are destabilized by decreasing azimuthal bend elastic energy caused by surface displacement. Radial textures exhibit a stabilizing tilt mechanism due to bend modes and a destabilizing displacement mechanism due to splay modes, but the former is predicted to be dominant. The static analysis provides good estimates of the instability thresholds while the transient energy balance provides information on the fastest growing modes. The static and dynamic results are compared and shown to be fully consistent. The couplings between splay and/or bend distortions, surface tilting, and surface displacement in nematic fibres are characterized and used to explain the deviations from the classical Rayleigh instability.