ON THE MEDIAN AND THE ANTIMEDIAN OF A COGRAPH

this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G2 are any two cographs, then there is a cograph that is both Eulerian and Hamiltonian having Gl as its median and G2 as its antimedian. Moreover, the connected planar and outer planar cographs are characterized and the median and antimedian graphs of connected, planar cographs are listed.

The quantum effects in quadratically damped systems

A dynamical system with a damping that is quadratic in velocity is converted into the Hamiltonian format using a nonlinear transformation. Its quantum mechanical behaviour is then analysed by invoking the Gaussian effective potential technique. The method is worked out explicitly for the Duffing oscillator potential.

Electron-Phonon Interaction Within the Framework of the Fluctuating Valence of Copper Atoms — a Theoretical Model for High Temperature Superconductivity

Electron-phonon interaction is considered within the framework of the fluctuating valence of Cu atoms. Anderson's lattice Hamiltonian is suitably modified to take this into account. Using Green's function technique tbe possible quasiparticle excitations' are determined. The quantity 2delta k(O)/ kB Tc is calculated for Tc= 40 K. The calculated values are in good agreement with the experimental results.

Overtone Spectra of 1,2-Dichloro-And Dibromo-Ethanes in the Near Infrared Region

The vibrational overtone spectra 0f the liquid phase 1,2-dichloroethane and 1,2-dibromoethane in the spectral regions of CH stretching local mode overtones corresponding to delta v CH= = 2 to delta v CH=5 are reported. The observed spectral features are assigned using the local mode model. LocaI mode frequencies WCH and diagonal local mode anharmonicities XCH are obtained from an analysis of the spectra. The local-local combinations observed are interpreted on the basis of a coupled CH oscillator model hamiltonian. Local-normal combinations show complex structures and their possible assignments are given.

Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Synthesis, spectral characterization and crystal structure of copper(II) complexes of 2-benzoylpyridine-N(4)-phenylsemicarbazone

An interesting series of nine new copper(II) complexes [Cu2L2(OAc)2] H2O (1), [CuLNCS] ½H2O (2), [CuLNO3] ½H2O (3), [Cu(HL)Cl2] H2O (4), [Cu2(HL)2(SO4)2] 4H2O (5), [CuLClO4] ½H2O (6), [CuLBr] 2H2O (7), [CuL2] H2O (8) and [CuLN3] CH3OH (9) of 2-benzoylpyridine-N(4)-phenyl semicarbazone (HL) have been synthesized and physico-chemically characterized. The tridentate character of the semicarbazone is inferred from IR spectra. Based on the EPR studies, spin Hamiltonian and bonding parameters have been calculated. The g values, calculated for all the complexes in frozen DMF, indicate the presence of the unpaired electron in the dx2 y2 orbital. The structure of the compound, [Cu2L2(OAc)2] (1a) has been resolved using single crystal X-ray diffraction studies. The crystal structure revealed monoclinic space group P21/n. The coordination geometry about the copper(II) in 1a is distorted square pyramidal with one pyridine nitrogen atom, the imino nitrogen, enolate oxygen and acetate oxygen in the basal plane, an acetate oxygen form adjacent moiety occupies the apical position, serving as a bridge to form a centrosymmetric dimeric structure