An approach to numerical solution of multipoint boundary-value problems

An approach is proposed to solving multipoint boundary-value problems for linear differential equation of w-th order, based on reduction to two-point boundary-value problems. The two-point problems are solved by the stable discrete orthogonalization method. Some numerical examples are considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 36–45, 1986.     

A Parabolic Spline on a Nonuniform Grid

We obtain estimates for errors of interpolation on a nonuniform grid for a parabolic nonperiodic spline of defect 1.     

Book reviews

Ohne Zusammenfassung

---

Book reviews

     

The case of missing incommensurate smectic A phases

Two binary mixtures of polar liquid crystal materials were previously reported to exhibit three incommensurate smectic A phases predicted for such materials on the basis of phenomenological theory. Results of our recent high-resolution X-ray scattering experiments show that no incommensurate phases exist in the two systems. Wide coexistence regions are found at first order transitions between various frustrated smectic phases of these mixtures. These regions were previously identified as the incommensurate smectic A phases. The phase diagrams of the two systems determined with high-resolution X-ray technique are shown to be in excellent agreement with Baroisa-Prost-Lubensky theory.     

Liquid crystalline hexa-amides and side chain polysiloxanes of azacrown [18]-N6

The hexa-4-dodecyloxybenzoyl derivative 1 of azacrown [18]-N₆ was originally reported to have a 'tubular' mesophase on the basis of its large central ring and 6-fold symmetry. Starting in the mesophase, annealing of 1 under a cover slip results in formation of a new crystalline phase that melts directly to an isotropic liquid at the temperature previously observed for the mesophase to isotropic transition. Thus the phase behaviour of 1 is kinetically controlled. The analogous hexa-3,4-bisdodecyloxybenzoyl derivative 2 of azacrown [18]-N₆ has no kinetic limitations to its phase changes and has an enantiotropic columnar liquid crystalline phase. We have synthesized side chain copolysiloxanes with a (CH₂)₁₁ spacer and 75-84 per cent by weight of the same 4-dodecyloxybenzoyl-[18]-N₆ mesogen. The polysiloxanes also display a liquid crystalline phase.     

The nitrogen pentoxide dissociation equilibrium

The third-law method is used to assess the authenticity of available equilibrium constants for the thermal dissociation of N₂O₅ ? NO₂ + NO₃. © 1994 John Wiley & Sons, Inc.     

Temperature-dependent behavior of birefringence and rotation of the optical indicatrix in crystals of deuterated triglycinesulfate

On the basis of a complex null-polarimetric method, the natural birefringence and the rotation of the optical indicatrix in crystals of deuterated triglycinesulfate are measured in the temperature range of 300–340 K. The temperature-dependent behavior of the optical parameters is shown to be close to that observed previously in triglycinesulfate crystals. Changes in them upon the ferroelectric phase transition can be accounted for by the spontaneous quadratic electro-optic effect, with the values of the electro-optic coefficients being larger by a factor of 1.4 than in triglycinesulfate crystals.