Bivariate Gonarov polynomials and integer sequences

Univariate Gonarov polynomials arose from the Gonarov interpolation problem in numerical analysis.They provide a natural basis of polynomials for working with u-parking functions,which are integer sequences whose order statistics are bounded by a given sequence u.In this paper,we study multivariate Gonarov polynomials,which form a basis of solutions for multivariate Gonarov interpolation problem.We present algebraic and analytic properties of multivariate Gonarov polynomials and establish a combinatorial relation with integer sequences.Explicitly,we prove that multivariate Gonarov polynomials enumerate k-tuples of integers sequences whose order statistics are bounded by certain weights along lattice paths in Nk.It leads to a higher-dimensional generalization of parking functions,for which many enumerative results can be derived from the theory of multivariate Gonarov polynomials.     

A polarised SUSANS facility to study magnetic systems

Using a right-angled magnetic air prism, we have achieved a separation of ～10 arcsec between ～2 arcsec wide up and down-spin peaks of 5.4 Å neutrons. The polarised neutron option has thus been introduced into the SUSANS instrument. Strongly spindependent SUSANS spectra have been observed over ±1.3 × 10^?4 Å^?1 range for several magnetic alloy samples. Spatial pair-distribution functions for the up and down-spins as well as the nuclear and magnetic scattering length density distributions in the micrometer domain, have been deduced from these spectra.     

Thermal,IR, cation exchange and adsorption studies of new synthetic zeolite (Deolite)

Cadmium(II) and Pb(II) ions replace the sodium(I) ion in commercial molecular sieve deolite. These exchanged derivatives have been interacted with adsorbates like CO₂ and NH₃ and the new exchanged and adsorbed derivatives characterized by their TG and IR spectral data. It is concluded that deolite can be effectively employed for removal of hazardous Cd(II) and Pb(II) ions as well as the gaseous adsorbates.     

Multiplicities of mod p Galois representations

We study the multiplicity with which 2-dimensional mod p Galois representations occur in Jacobians of modular curves. Received: 26 February 1997 / Revised version: 2 July 1997     

Pregnane and pregnane tetraglycoside from Marsdenia roylei

Pregnane oligoglycoside, namely roylinine, and a pregnane derivative, namely marsgenin, have been isolated from chloroform-soluble extract of dried stem of Marsdenia roylei, and their structures were determined using 1H-NMR, 13C-NMR, 1H-1H COSY, HSQC, TOCSY and FABMS spectral techniques as well as chemical degradation and derivatisation.     

P.M.R. relaxation time studies in some binary liquid systems

Proton magnetic resonance relaxation time measurements have been carried out in mixtures of water with formic acid, acetic acid, propionic acid and n-butyric acid. On account of molecular association, the results reveal strong deviation of these mixtures from the ideal behaviour. The molecular association effect is discussed in some detail. The molecular association ratios determined from the present studies are in excellent agreement with those obtained by the ultrasonic absorption technique. It is further shown that N.M.R. relaxation time studies reveal more information about molecular interactions in liquids than the ultrasonic absorption studies.     

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.     

Study of magnetoresistance and conductance of bicrystal grain boundary in La0.67Ba0.33MnO3 thin film

La_0.67Ba_0.33MnO₃ (LBMO) thin film is deposited on a 36.7°C SrTiO₃ bicrystal substrate using laser ablation technique. A microbridge is created across bicrystal grain boundary and its characteristics are compared with a microbridge on the LBMO film having no grain boundary. Presence of grain boundary exhibits substantial magnetoresistance ratio (MRR) in the low field and low temperature region. Bicrystal grain boundary contribution in MRR disappears at temperature T>175 K. At low temperature, I-V characteristic of the microbridge across bicrystal grain boundary is nonlinear. Analysis of temperature dependence of dynamic conductance-voltage characteristics of the bicrystal grain boundary indicates that at low temperatures (T<175 K) carrier transport across the grain boundary in LBMO film is dominated by inelastic tunneling via pairs of manganese atoms and tunneling through disordered oxides. At higher temperatures (T>175 K), magnetic scattering process is dominating. Decrease of bicrystal grain boundary contribution in magnetoresistance with the increase in temperature is due to enhanced spin-flip scattering process.     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

Mod pq Galois representations and Serre's conjecture

We consider linear representations of the Galois groups of number fields in two different characteristics and examine conditions under which they arise simultaneously from a motive.