Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ _n ^∞ =1a_n λ _n ^−s be a generalized Dirichlet series with 1 =λ ₁ <λ ₂ < …,λ _n≤Dn, andλ _n+1 -λ _n ≥D ^{− 1} λ _n+1 ^{− a} where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.     

Donor properties of some flexidentate hydroxyimino-β-diketones in their rhodium(III) complexes

Summary A series of rhodium(III) complexes of certain hydroxyimino--diketones were synthesised and their structures assigned on the basis of elemental analyses and i.r. and¹H n.m.r. spectral studies, The complexes exhibit coordination through carbonyl oxygen and nitrogen of the hydroxy-imino groups in the ligands.¹H and¹³C n.m.r. studies show that the ligands exist in the isonitroso form in CDCl₃.     

Spectrophotometric determination of sulfur dioxide in air, using thymol blue

A simple and sensitive spectrophotometric method was developed for the determination of trace amounts of sulfur dioxide. The method is based on the reaction of SO2 with a known excess of ICI as the oxidant. The unreacted ICI iodinates thymol blue under acidic conditions. The lambdamax of thymol blue is at 545 nm under acidic conditions, and on lodination lambdamax shifts to 430 nm. This shift results in a decrease in the absorbance at 545 nm. The amount of uniodinated thymol blue present depends on the concentration of unreacted ICI, which in turn depends on the SO2 concentration. The system obeys Beer's law in the range 0-30 microg SO2 in a final volume of 25 mL, having a molar absorptivity of 3.2 x 10(4) L/mol cm with a relative standard deviation (RSD) of 2% at 24 microg SO2 (n = 10). The uniodinated dye can be extracted into 5 mL isoamyl alcohol under acidic conditions for measurement of absorbance. The extraction method obeys Beer's law in the range 0-5 microg SO2, having a molar absorpitivity of 4.16 x 10(4) L/mol x cm with an RSD of 1.9% at 4 microg SO2 (n = 10). The method has been successfully applied to the determination of atmospheric SO2.     

Synthesis of Novel N‐Morpholinoacetyl‐2,6‐diarylpiperidin‐4‐ones

A series of N‐chloroacetyl‐2,6‐diarylpiperidin‐4‐ones (10–18) obtained from the corresponding 2,6‐diarylpiperidin‐4‐ones upon base‐catalyzed condensation with morpholine afforded N‐morpholinoacetyl‐2,6‐diarylpiperidin‐4‐ones (19–27). The synthesized compounds have been characterized by their elemental, analytical, and spectral data.     

Pressure dependent study of semiconductors using semiempirical equations of state

Abstract

Variation of bulk modulus of Si, Ge and GaAs with pressure is studied using four semiempirical equations of state, two of which being proposed very recently. Hence an expression for bulk modulus for arbitrary pressure for the semiconductors similar to Cohen's formula for zero pressure is arrived at. The applicability of these equations of state for the high pressure phases of Si and Ge is tested using the recent experimental and theoretical pressure-volume data of these phases.     

Bioanalytical method development,validation and quantification of dorsomorphin in rat plasma by LC‐MS/MS

The present investigation describes the development and validation of a sensitive liquid chromatography–mass spectrometry/mass spectrometry (LC‐MS/MS) method for the estimation of dorsomorphin in rat plasma. A sensitive LC‐MS/MS method was developed using multiple reaction monitoring mode, with the transition of m/z (Q1/Q3) 400.2/289.3 for dorsomorphin and m/z (Q1/Q3) 306.2/236.3 for zaleplon. Chromatographic separation was achieved on a reverse phase Agilent XDB C₁₈ column (100 × 4.6 mm, 5 µm). The mobile phase consisted of acetonitrile and 5 mm ammonium acetate buffer (pH 6.0) 90:10 v/v, at a flow rate of 0.8 mL/min. The effluence was ionized in positive ion mode by electrospray ionization (ESI) and quantitated by mass spectrometry. The retention times of dorsomorphin and internal standard were found to be 2.13 and 1.13 min, respectively. Mean extraction recovery of dorsomorphin and internal standard in rat plasma was above 80%. Dorsomorphin calibration curve in rat plasma was linear (r² ≥ 0.99) ranging from 0.005 to 10 µg/mL. Inter‐day and intra‐day precision and accuracy were found to be within 85–115% (coefficient of variation). This method was successfully applied for evaluation of the oral pharmacokinetic profile of dorsomorphin in male Wistar rats. Copyright © 2013 John Wiley & Sons, Ltd.     

What We Don’t Know About Time

String theory has transformed our understanding of geometry, topology and space-time. Thus, for this special issue of Foundations of Physics commemorating “Forty Years of String Theory”, it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.     

Reaction of Dichlorocarbene with Substituted Cyclopentadienones Under Phase Transfer Conditions

The cycloaddition reactions involving dichlorocarbene generated under phase transfer conditions have been studied extensively in the past few years due to the simplicity of the procedure involved.¹ The facile formation of dichlorocyclopropanes provides an easy entry to functionalised aromatics and expanded carbocyclic compounds.² The dichlorocarbene generated under phase transfer conditions is capable of adding even to electron deficient olefins. We describe here the cyclo-addition reaction of dichlorocarbene to tetrasubstituted cyclopentadienones.