On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator semigroup {Tt}_t?0 acting on a complex F-space, every Tt with t>0 is supercyclic. Moreover, the set of supercyclic vectors of each Tt with t>0 is exactly the set of supercyclic vectors of the entire semigroup.     

Radiometric enzyme assays: development of methods for extremely sensitive determination of types 1, 2 and 3 iodothyronine deiodinase enzyme activities

We elaborated novel, reliable radiometric methods for extremely sensitive determination of enzyme activities of iodothyronine deiodinases (IDs) of types 1, 2 and 3 in microsomal fractions of different rat and human tissues, as well as in homogenates of cultured mammalian cells. These radiometric enzyme assays were based on the use of high-specific-radioactivity ¹²⁵I-labeled iodothyronines as substrates; TLC separation of radioactive products from the unconsumed substrates; film-less autoradiography of radiochromatograms using storage phosphor screens; and quantification of the separated compounds with a BAS-5000 laser scanner. This methodology enabled us to determine IDs enzyme activities as low as 10⁻¹⁸ katals. The applicability of our sophisticated methods was demonstrated by following the alterations of IDs activities induced in cultured astroglial cells by a series of purinergic agonists, retinoic acid, and their combination. In addition, in case of ATP as a representative of purinergic agonists, we determined time-course and dose–response curves to characterize in more details the induction of each type of deiodinase by purines.     

Synthesis of N-phthalimido β-aminoethanesulfonyl chlorides: the use of thionyl chloride for a simple and efficient synthesis of new peptidosulfonamide building blocks

N-Phthalimido β-aminoethanesulfonyl chlorides, new building blocks for the synthesis of peptidosulfonamide peptidomimetics, were prepared in a straightforward manner from amino acids. In the crucial synthetic step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of refluxing thionyl chloride or thionyl chloride/DMF. This simple and effective chlorinating method is also applicable to β-aminoethane sulfonic acids and their sodium salts with other N-protecting groups.     

Absolutely continuous functions of several variables and diffeomorphisms

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.     

Dynamical stability of an elastic column and the phenomenon of bifurcation

The article studies the stability of rectilinear equilibrium shapes of a non-linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6] solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite-dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite-dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post-buckling).     

On some properties of 4-regular plane graphs

The d-distance face chromatic number of a connected plane graph is the minimum number of colors in such a coloring of its faces that whenever two distinct faces are at the distance at most d, they receive distinct colors. We estimate 1-distance chromatic number for connected 4-regular plane graphs. We show that 0-distance face chromatic number of any connected multi-3-gonal 4-regular plane graphs is 4. © 1995, John Wiley & Sons, Inc.     

A quantum chemical investigation of pyrolysis reactions of glyoxylic acid ethylester

Two possible reaction paths for the pyrolysis of the ethylester of glyoxylic acid have been studied by ab initio molecular orbital calculations. The basis sets 3-21G and 6-31G * have been used, and electron correlation has been included by Møller–Plesset calculations up to fourth order. Our calculations indicate that the reaction leading to acid and ethylene through a 6-membered ring transition state is favored relative to a process involving a formyl hydrogen transfer via a 5-membered ring to the alkyl unit leading to ethane, CO, and CO₂. The predicted activation energies for these two reactions obtained at the highest level of calculation, MP 4(SDTQ )/6–31G *, are 50.4 and 71.7 kcal/mol, respectively. The transition states have RHF wave functions that are stable relative to UHF solutions using the 3–21G basis. The geometry of the transition states and IRC following indicate that both reactions are strongly asynchronous: The C? O bond rupture is virtually completed before hydrogen transfer occurs. For comparative purposes, analogous calculations have been performed for the ethylester of formic acid, where it is confirmed that a 6-membered ring transition state is preferred relative to a 4-membered one by around 42 kcal/mol at the highest level of calculation.