Transcendental values of class group <Emphasis Type="Italic">L</Emphasis>-functions

Let K be an algebraic number field and f a complex-valued function on the ideal class group of K. Then, f extends in a natural way to the set of all non-zero ideals of the ring of integers of K and we can consider the Dirichlet series \({L(s,f) =\sum_{{\mathfrak a}} f({\mathfrak a}){\bf N}({\mathfrak a})^{-s}}\) which converges for \({{\mathfrak R}(s) >1 }\). After extending this function to \({{\mathfrak R}(s)=1}\), and in the case that f does not contain the trivial character, we study the special value L(1, f) when f is algebraic valued and K is an imaginary quadratic field. Applying Kronecker’s limit formula and Baker’s theory of linear forms in logarithms, we derive a variety of results related to the transcendence of this special value.     

Permeability of R6G across Cx43 hemichannels through a novel combination of patch clamp and surface enhanced Raman spectroscopy

We have measured the permeability of rhodamine-6G across Cx43 hemichannels reconstituted on a pipette tip. Cx43 hemichannels were overexpressed in Sf9 cells, and affinity-purified. The hemichannels were reconstituted in a lipid bilayer on a pipette tip by the tip-dip method. R6G in the pipette permeated across the channels into the bath. The permeability of R6G was quantified by measuring R6G concentration in the bath after several hours by surface enhanced Raman spectroscopy (SERS) with 100 nm silver colloid particles. The ratio of the permeability of dye to salt, as extracted by this combined electrical-SERS technique, is compatible with similar ratios for other dyes across whole gap junction channels. The results for the permeability ratio were further compared to fluorescence measurements. The novel combination of patch and SERS techniques can be extended to quantifying the transport of biologically significant non-fluorescent molecules, such as cAMP and IP3, across 1 nm sized pores, such as the gap junction channel.     

Influence of temperature on the photometric determination of silicon by the molybdenum blue methods

Some systematic studies have been carried out on the influence of temperature on the photometric determination of silicon by the molybdenum blue procedure. It has been shown that temperature exerts a distinct influence on the colour intensities involved in the different procedures and the extent of this influence depends largely on the nature of the acid medium and the reducing agent employed. Ascorbic acid has been successfully employed to overcome the influence of temperature. Our thanks are due to the management of the Tata Iron and Steel Company for permitting the publication of this paper.     

On the normal vibrations of nonrigid molecule B(CH3)3

Treating the symmetry operations as transformations in higher dimensional space, it is shown that Wigner’s method can be straightaway extended to study the vibrations of nonrigid molecules exhibiting free or nearly free internal rotations. The molecule B(CH₃)₃ is illustrated.     

Molar extinction coefficients of some carbohydrates in aqueous solutions

Molar extinction coefficients of some carbohydrates viz. l-arabinose (C₅H₁₀O₅), d-glucose (C₆H₁₂O₆), d-mannose (C₆H₁₂O₆), d-galactose (C₆H₁₂O₆), d(-) fructose (C₆H₁₂O₆) and maltose (C₁₂H₂₄O₁₂) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well.