Construction of Doubly Periodic Solutions via the Poincare-Lindstedt Method in the case of Massless Phi^4 Theory

Doubly periodic (periodic both in time and in space) solutions for the Lagrange-Euler equation of the (1+1)-dimensional scalar Phi^4 theory are considered. The nonlinear term is assumed to be small, and the Poincare-Lindstedt method is used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of a Jacobi elliptic function. It have been proved that the choice of elliptic cosine with fixed value of module k (k=0.451075598811) as the leading-order term puts the principal resonance to zero and allows us constructed (with accuracy to third order of small parameter) the asymptotic solution in the standing wave form. To obtain this leading-order term the computer algebra system REDUCE have been used. We have appended the REDUCE program to this paper.Comment: 16 pages, LaTeX 2.09. This paper have been published in the Electronic Proceedings of the Fourth International IMACS Conference on Applications of Computer Algebra (ACA'98) {Prague (Czech Republic)} at http://math.unm.edu/ACA/1998/sessions/dynamical/verno

Conditional Density Matrix in the Context of Noncontextuality

Conditional density matrix represents a quantum state of subsystem in different schemes of quantum communication. Here we discuss some properties of conditional density matrix and its place in general scheme of quantum mechanics.Comment: 10 pages, LaTe

Structure of 5-nitro-2-tosylaminobenzaldehyde di(morpholin-4-yl)aminal Complex with Carbon Tetrachloride

The 5-nitro-2-tosylaminobenzaldehyde di(morpholin-4-yl)aminal forms a stable complex with carbon tetrachloride in the crystal phase. X-ray structural study of this complex indicates an essentially shortened intermolecular contact of 2.89 Å between the oxygen atom of the nitro group and one of the chlorine atom of the CCI4 molecule. Quantum-chemical calculations by semiempirical AMI method showed that the formation of such complex did not cause considerable decrease of system energy or change of charge distribution in molecules. It was supposed that this associate has van der Waals character

Superconductivity in the Sn-Ba-Sr-Y-Cu-O system

Since Bednorz and Muller discovered high-T(sub c) superconductivity in the La-Ba-Cu-O compound, several families of superconducting oxides have been synthesized. Here, researchers report the results of search for superconductivity in the compounds based on tin, which has a lone electron pair like Bi, Tl, Pb. The following compounds were synthesized: Sn1Ba1Sr1Cu3Ox, Sn1Ba1Ca1Cu3Ox, Sn1Ba1Mg1Cu3Ox, Sn1Sr1Ca1Cu3Ox, Sn1Sr1Mg1Cu3Ox, Sn1Ca1Mg1Cu3Ox. The initial components were oxides and carbonates of the appropriate elements. Standard firing-grinding procedure was used. Final heating was carried out at 960 C during 12 hours. Then the samples were cooled inside the furnace. All the synthesis cycles were carried out in air atmosphere. Among the synthesized compounds only Sn1Ba1Sr1Cu3Ox showed remarkable conductivity. Other compounds were practically dielectrics. Presence of a possible superconductivity in Sn1Ba1Sr1Cu3Ox was defined by using the Meissner effect. At low temperature a deviation from paramagnetic behavior is observed. The hysteresis loops obtained at lower temperatures undoubtly testify to the presence of a superconductive phase in the sample. However, the part of the superconductive phase in the Sn1Ba1Sr1Cu3Ox ceramic turned out to be small, less than 2 percent, which agrees with the estimation from magnetic data. In order to increase the content of the superconductive phase two-valent cations Ba, Sr were partially substituted by univalent (K) and three-valent ones (Y)