The localization of energy in gauge field theories and in linear gravitation

It is shown how the energy-positivity criterion enables us to localize the energy in various field theories. For this purpose the role of surface integrals in a canonical formalism is investigated. The same techniques are applied to linearized gravity, where the mixed Cauchy-boundary value problem in a finite volume is analyzed. Unconstrained degrees of freedom and boundary data which have to be controlled are found. This paper is part of a program to analyze the possibility of localization of gravitational energy in complete General Relativity.     

Polymerization of acrylonitrile by catalytic systems consisting of triphenylphosphine and a lewis acid

Polymerization of acrylonitrile in the presence of systems that consisted of triphenylphosphine (PPh₃) and a Lewis acid R_mMX_n (ZnCl₂, Me₃Al, Et₃Al, Et₂AlCl, EtAlCl₂, AlCl₃) was studied. The systems that contained Me₃Al and Et₃Al (i.e., Lewis acid of moderate acidity) were the most efficient catalysts. Conductometric measurements carried out in the polymerization systems showed the presence of ions. The presence of phosphonium cation in the polyacrylonitrile chain formed by the PPh₃–R_mMX_n catalytic systems was determined by IR, ¹H-NMR, and ³¹P-NMR spectroscopy. The average molecular weight measurements and kinetic chain lengths of polyacrylonitrile formed within the reaction time in the presence of PPh₃–Et₃Al showed that transfer reactions occur. According to the results obtained, the polymerization reaction of acrylonitrile by PPh₃–R_mMX_n involved a zwitterion formed by the attack of PPh₃ on acrylonitrile complexed by Lewis acid [Ph₃P^⊕? CH₂? C^?H? C?N → MR_mX_n] and the anion [CH₂?C^?? C?N] formed by the proton abstraction from the monomer.     

The kinetics of tritium-hydrogen exchange in xanthosine,theobromine and monomethylated derivatives of xanthine

Tritium exchange at C-8 of xanthosine, theobromine, 1-, 3- and 7-methylxanthine in water has been studied. The rates of detritiation of these compounds have been determined over a pH range at constant temperature. Several mechanisms of exchange involving various ionic forms of substrate operating at different pH have been suggested.     

Conformational equilibria and photoinduced tautomerization in 2-(2′-pyridyl)pyrrole

Depending on the polarity and protic abilities of the solvent, 2-(2′-pyridyl)pyrrole can exist in either syn or anti rotameric forms. In nonpolar solvents, intramolecular excited state single proton transfer is observed, manifested by the appearance of low-energy tautomeric emission. The solvent-assisted excited state double proton transfer reaction is also detected. DFT calculations confirm low barriers for both single and double proton transfer processes in the lowest excited singlet state and show different character of the tautomerization in both cases: in the intramolecular reaction, mutual approach of two nitrogen atoms plays an important role.     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.     

Duality transformations in electrodynamics

Electrodynamics admitting a duality transformation group is considered. For such an electrodynamics an extension of the classical Rainich-Misner-Wheeler theory is presented.On leave of absence from the University of Warsaw, Warsaw, Poland.     

Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies

The paper is focused on the phenomena of various steady-state oscillations exhibited by the twin-well potential system. Regions of existence of different attractors in the system parameter domain are examined and a picture book of different steady states for fixed damping and forcing is presented: 20 different combinations of single or coexisting, small orbit or large orbit, periodic and chaotic attractors are displayed. Computer simulations are followed by an approximate analytical analysis: A study of various forms of instability of periodic solutions gives close form approximate criteria for occurrence of T-periodic small orbit and large orbit oscillations, and for cross-well chaos.