On perfect mappings from ℝ to ℝ

Perfect mappings from ℝ to ℝ and also mappings close to perfect ones are considered. Some of their properties are given.     

Conjugate functions

This is the author-review of a dissertation for the competition of the academic degree of Doctor of Physicomathematical Sciences (published with abbreviations). The dissertation was defended on June 30, 1976, in the academic council of the A. M. Razmadze Tbilisi Mathematics Institute of the Academy of Sciences of the Georgian SSR. The official opponents were: Professor N. N. Bakhaniya, Doctor of Physicomathematical Sciences; Professor Sh. S. Pkhakadze, Doctor of Physicomathematical Sciences; Professor A. A. Talalyan, Corresponding Member of the Academy of Sciences of the Armenian SSR and Doctor of Physicomathematical Sciences; and Professor S. A. Telyakovskii, Doctor of Physicomathematical Sciences.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 771–783, November, 1977.     

Two-dimension-like functions defined on the class of all Tychonoff spaces

Two-dimension-like functions are constructed on the class of all Tychonoff spaces. Several of their properties, analogous to those of the classical dimension functions, are established.     

Calorimetric study of the native and postdenatured structures in starches with different degree of hydration

DSC studies of melting process of annealed native structures and postdenatured ones in low-amylose starches with different degrees of hydration were carried out. The starch recrystallization at different thermal treatments of the samples was studied both after the complete and partial destroy of native structures. It has been shown that native structures as well as postdenatured ones possess the ability to perfection, which is most clearly seen at the annealing at temperatures inside their melting ranges. The results obtained demonstrate that at the same duration of annealing the process of crystal perfection for secondary starch structures proceed more intensively compared to the native ones. The presence of the remained native structures in partial melt in contrast to the remained gel ones restricts the ability of the recrystallized structures to perfection.     

Efficient linear algebra routines for symmetric matrices stored in packed form

Quantum chemistry methods require various linear algebra routines for symmetric matrices, for example, diagonalization or Cholesky decomposition for positive matrices. We present a small set of these basic routines that are efficient and minimize memory requirements.     

Calorimetric Study of the Glass Transition Process in Humid Proteins and DNA

By method of differential scanning calorimetry the absolute values of heat capacity for the systemwater–biopolymer (globular and fibrillar proteins and DNA) were measured in a wide range of temperatures (from -30 up to 130°C) and concentrations of proteins both in native and denatured states. Thermal properties of humid denatured biopolymers demonstrate a characteristic anomaly in the form of the heat capacity jump at temperature depending on the bound water content. It has been shown that in the systems studied a glass transition, where water serves as a native plasticizer, is observed. It has been established that the S-shaped character of all heat capacity curves obtained on dehydration for native and denatured biopolymers is due to the gradual transition to the glassy state of both native and denatured samples. It was found that thermally denatured humid small globular proteins at subsequent dissolving in water at room temperature are able to restore their native structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

The integrability of conjugate functions

For any functionf of L(0, 2), we prove that there is a function L(0, 2) such that ¦(x)¦ = ¦f(x)¦ almost everywhere and L(0, 2), where is the conjugate of.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 461–465, October, 1968.     

DSC Study of the Postdenaturated Structures in Biopolymer–water Systems

The temperature dependences of heat capacity for water–denaturated biopolymer (globular proteins, collagen and DNA) were measured in a wide range of temperatures (0–140°C) and water content of the systems. It has been shown that thermally denaturated globular proteins (lysozyme, myoglobin and catalase) are able to form the thermoreversible heat-set structures under the certain conditions studied. The additional endothermal maximum observed is the calorimetric manifestation of the phase transition related to the melting of these thermotropic non-native structures. The melting gels are completely formed just after denaturation during relatively short time and only their prolonged state at T>T _d leads to their transformation to thermoirreversible non-melting ones. The post denaturated structures from water-denaturated protein (Mb, Lys and RN-ase) systems with a different amount of free water were also studied. The thermoreversible cold-set gels are formed from both water-denaturated DNA and water-denaturated collagen systems. These thermotropic structures are metastable. A spatial gel network of both collagen and DNA is formed from the native-like renaturated structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dehydrated native biopolymers - a unique representative of glassy systems

DSC study of native and denatured biopolymers with different chemical and steric structure was carried out in a wide range of temperatures and water contents. It was shown that all the native and denatured humid biopolymers studied are glassy systems. The residues of native structures surviving after partial dehydration prevent the glass transition at the glass transition temperatures of the denatured biopolymers. In dehydrated native biopolymers the processes of melting and glass transition take place in the same temperature range that leads to a large change of the heat capacity across denaturation.