Filtering formulas

Translated from algebra i Logika, Vol. 30, No. 6, pp. 693–704, November–December, 1991.     

Specific features of the thermal physical properties of relaxor ceramics based on lead zirconate titanate

The heat capacity and thermal expansion of ferroelectric relaxors based on lead zirconate titanate are studied near the diffuse phase transition. It is shown that no spontaneous phase transitions from the paraelectric phase to the ferroelectric phase and from the relaxor state to the normal ferroelectric state occur in an ensemble of nanometer-sized polar regions. It is noted that the transitions can be caused only by external electric fields or storage for a fairly long time.     

On the Dynamics of Two Oscillating Cosmic Strings

We present the spacetime interval of thenonradiated cosmic string oscillating as standing waves.The influence of string oscillations on the dynamics ofa probe cosmic thread that performs free oscillations and moves in its vicinity, isdiscussed.     

Effective characteristics of layered composites with allowance for structural changes

In moment linear theory of viscoelasticity for layered composites whose components undergo structural changes in the deformation process, we explicitly determine the effective characteristics. The corresponding boundary value problem is solved by the averaging method.     

Specific features of thermal resistance of silicon in the temperature range 105–130 K

Careful experimental investigations into the behavior of the thermal resistance of single-crystal silicon are carried out in the immediate vicinity of the temperature of an anharmonicity sign inversion (T _i =121.1 K), where phonon thermal resistance approaches zero. An anomalous positive deviation of the total thermal resistance (W) from the linear part of the temperature dependence with a maximum at 121.1 K is found in the temperature range 105–130 K. The temperature behavior of W in this range indicates that the mean free path of phonons is limited by a characteristic size of structural defects and that its temperature dependence exhibits specific features in the vicinity of T _i . It is established that the character of the temperature dependence of W above and below T _i is different. A linear functional relation between the total thermal resistance and the isobaric thermal strain is revealed at positive and negative anharmonicities of atomic vibrations.     

Scheme of creep experiments in nonlinear theory of viscoelasticity taking account of structural changes

We suggest a scheme for creep experiments for a viscoelastic medium whose nonlinear constitutive relations contain the damageability parameter.     

Syntheses of some substituted sym-triazines

The synthesis of various -substituted propionimidic esters has been effected and the conditions of their conversion into the corresponding 2,4,6-triethyl-sym-triazine derivatives have been studied.     

Crystal and molecular structure of 6,6-dimethyl-cis-2,4-diphenyl-3-aza-7-oxabicyclo[3.3.1]nonan-9-one

A method is presented for synthesizing 6,6-dimethyl-2,4-diphenyl-3-aza-7-oxabicyclo[3.3.1]nonan-9-one. The x-ray structure shows that the compound in the crystal exists in the chair-boat conformation with the piperidine ring in the boat form. The two phenyl substituents in the 2- and 4-positions are responsible for such a conformation.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1400–1402, October, 1990.