A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Polypyrazolylborate analogues without boron: Structural diversity in ligand design and metal complexes

Structural chemistry of organometallic complexes containing pyrazolederived polydentate ligands (without boron) has been reviewed in the context of current results from this laboratory. NCL Communication No. 6137     

Mass spectrometric investigation of polyfluorinated C60. Evidence for the existence of C60F2n (n = 0–30)

Electron-capture negative ion chemical ionization (EC-NICI) and field desorption (FD) mass spectrometric techniques were utilized to examine polyfluorinated C₆₀. Two different samples from the same preparation, one prior to sublimation and the other sublimed material, were investigated. From the raw non-sublimed product in EC-NCI six series of ions corresponding to different numbers of attached oxygen atoms were obtained, which are represented by the formula [C₆₀F_2nO_m]^?, where n ranged from 0 to 30 and m from 0 to 5. The sublimed material in EC-NICI produced the same six series of ions with up to 48 fluorine atoms attached to C₆₀. The field desorption of the same sample produced similar results, but the signal-to-noise ratios of the spectra were low. Both samples, in the two different techniques examined, yielded C₆₀F₆₀ ions with only an even number of fluorine atoms attached. The present investigation, for the first time, provides direct experimental evidence for the existence of higher fluorinated C₆₀ up to C₆₀F₆₀ and multiple oxides of polyfluoro-C₆₀ with up to five oxygen atoms attached.     

Analysis of Low-energy α-4He Elastic Scattering Process in Direct Channel Regge-Pole Formalism

The elastic scattering of low-energy α-particles by a ⁴He target has been analysed within the frame-work of a modified Regge-Pole model which reproduces the partial wave phaseshifts in an elegant and simple way and describes all other relevant features of the scattering phenomena.     

Loop Algebra of Lie symmetries for a short-wave equation

It is demonstrated that Lie point symmetries associated with a nonlinear equation for short waves in three dimensions generate an infinite-dimensional Lie algebra—a loop Algebra. Classification of the independent sets of the subalgebra is done through the adjoint action of the corresponding generators. Different forms of similarity solutions are discussed.     

Painleve Analysis and the Yang-Mills Equation in Two Specific Cases

Two important configurations of Yang-Mills fields are discussed applying to them the Painleve test of Ablowitz. The case with a constant electric E-field does not admit an exact solution while the cylindrically symmetric self-dual system admits an inverse scattering approach for instanton solution.     

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.