Mobius Transforms for Linear Ordinary Differential Equations

The Mobius transforms for linear ordinary differential equations of the second order are examined. It is shown that this transform has some quasi-isospectral properties. Solutions of the Heun equation with one apparent singularity are constructed. Bibliography: 15 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 67–88.     

Polyethylene with improved environmental stress cracking resistance

The stress cracking resistance of low-pressure polyethylene can be improved by introducing finely dispersed mineral additives (TiO₂, SiO₂, Al₂O₃ · SiO₂) and surface-active agents (anthranilic, adipic, and sebacic acids; mannitol). The amounts needed to effectively increase the cracking resistance without detriment to the principal physicomechanical and other characteristics of the material have been determined.Mekhanika Polimerov, Vol. 4, No. 1, pp. 67–71, 1968Communication V of the series "Modification of the Structure and Properties of Polyolefins."     

Formation of ceramic solid solutions in a SrTiO<Subscript>3</Subscript>-BiScO<Subscript>3</Subscript> system

X-ray structural, X-ray phase, and dilatometric analyses were used to explore specific features of the formation of solid solutions in the (1 − x)SrTiO₃−xBiScO₃ system with x = 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5. It was found that the synthesis of solid solutions from the initial Bi₂O₃, Sc₂O₃, TiO₂, and SrCO₃ components is accompanied by a considerable increase in the linear dimensions of the samples, depending on their composition. Solid solutions with x > 0.1 are formed through intermediate phases (Sr₅Bi₆O₁₄ at x = 0.2; Sr_0.78Bi_2.22O₄ at x = 0.3; and Sr_2.25Bi_6.75O_12.38 at x = 0.4 and 0.5). It was shown that the samples with x = 0.2, 0.3, 0.4, and 0.5 have two phases: one with a cubic Pm3m structure and one with a tetragonal I4/mcm structure.     

Parametric amplification of ultrasound in ferromagnetic piezoelectric composites at the vicinity of the orientational phase transition

Direct parametrical amplification of ultrasound was theoretically considered for the ferromagnetic/piezoelectric thin-layered structure composites, for which within the long-wavelength approach some, material specific, yet homogeneous bulk properties could be assumed. Having chosen appropriate homogeneous components, it is possible to construct a desirable composite with such properties that are absent in the starting-up “building blocks” (components).Sound frequencies are assumed to be such that only the dispersion due to magnetic subsystem is thought relevant; the piezoelectric components are set to have a nonlinear dielectric response. Presence of orientational phase transition for the ferromagnetic subsystem allows to vary frequency of a ferromagnetic resonance, and consequently to alter the dispersion at the chosen frequency of sound.While solving coupled equations describing dynamics of mechanical, magnetic and piezoelectric subsystems, an effective sound amplification for realistic values of physical parameters is shown possible.     

Thermal and Infrared Study of Desorption of Pyridine and Pyridine Derivatives from Ni-exchanged Montmorillonite

Thermal analysis (TG, DTG) and infrared absorption spectra were used to study desorption of pyridine (py), 4-methylpyridine (4-Mepy) and 4-ethylpyridine (4-Etpy) from Ni(II)-exchanged montmorillonite (Ni-MMT). It is shown that the bonds between the derivatives of pyridine (R-py) and the montmorillonite exhibit predominantly Lewis acid character. The thermal stability of studied samples and the total amounts of R-py inserted in the porous structure of Ni-MMT increase in the following sequence: py/Ni-MMT<4-Mepy/Ni-MMT<4-Etpy/Ni-MMT, i. e. the influence of the substituent on the pyridine ring is evident. This revised version was published online in August 2006 with corrections to the Cover Date.