Extraction of thorium(IV) as perchlorate and chloroacetate complexes with 1-phenyl-2,3-dimethyl-5-pyrazolone (antipyrine)

Summary Thorium was extracted quantitatively with the neutral ligand 1-phenyl-2,3-dimethyl-5-pyrazolone (Apy) in the presence of perchlorate (ClO₄^-) and di/trichloroacetates (DCA/TCA) at pH 2.5 into an organic solvent. Optimization of experimental parameters like pH, equilibration time, solvents, reactant concentrations, best suited conditions for back extraction, interference due to the presence of different anions and cations and effect of metal ion concentration were studied. The composition of the complexes has been established using log-log plots and are represented as [Th(Apy)₂(ClO₄)₄], [Th(Apy)₂(TCA)₄], [Th(Apy)(H₂O)(DCA)₄]. The respective conditional stability constants of the effectively extracted complexes have also been calculated as 9.4±0.03 and 10.4±0.04, respectively . The method has been extended for the separation of thorium from a number of cations in binary and multicomponent mixtures. The method is simple, rapid, selective and has a good reproducibility (±0.5%).     

Field and Frequency Effects in a Nematic Mixture of Negative and Positive Dielectric Anisotropy

The molecular alignment in the nematic liquid crystal mixture of p-ethoxy benzylidene p′-n-butyl aniline (EBBA) and p-ethoxy benzylidene p′-cyano aniline (EBCA) has been investigated by measuring the dielectric constant at 1 MHz. Detailed investigation has been carried out for a composition of 2.74%, of EBCA in EBBA for different electric and magnetic field strengths and at different frequencies of the applied electric field. Both parallel and perpendicular electric and magnetic field configurations have been employed. Temperature and frequency dependence of the dielectric anisotropy have been studied.

Two interesting features have been observed. I) In the crossed field configuration complete molecular alignment could be observed by suitably changing the electric field strength. The range of electric field strength required to change the molecular ordering, is frequency dependent. This range shows a minimum in the neighbourhood of 2 kHz. 2) It has also been observed that in the parallel field configuration minimum dielectric constant change is observed apparently independent of frequency and electric field strength. Detailed results of the field and frequency effects and of optical studies in this mixture are reported.     

Alignment studies on p-ethoxy phenyl azophenyl butyrate in the presence of electric and magnetic fields

Dielectric permittivity studies on the nematic liquid crystal p-(ethoxy phenyl azophenyl) butyrate were carried out at 1 MHz. The effect of parallel and perpendicular magnetic fields on the alignment of the molecules was studied. The threshold voltage for domain formation in the presence of a magnetic field is estimated.     

Effective equidistribution of eigenvalues of Hecke operators

In 1997, Serre proved an equidistribution theorem for eigenvalues of Hecke operators on the space S(N,k) of cusp forms of weight k and level N. In this paper, we derive an effective version of Serre's theorem. As a consequence, we estimate, for a given d and prime p coprime to N, the number of eigenvalues of the pth Hecke operator Tp acting on S(N,k) of degree less than or equal to d. This allows us to determine an effectively computable constant Bd such that if J₀(N) is isogenous to a product of Q-simple abelian varieties of dimensions less than or equal to d, then N?Bd. We also study the effective equidistribution of eigenvalues of Frobenius acting on a family of curves over a fixed finite field as well as the eigenvalue distribution of adjacency matrices of families of regular graphs. These results are derived from a general “all-purpose” equidistribution theorem.     

Linear independence of digamma function and a variant of a conjecture of Rohrlich

Let ψ(x) denote the digamma function. We study the linear independence of ψ(x) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series.     

In situ nucleophilic substitution reaction of N,N-dialkylaminoethyl-2-chlorides monitored by gas chromatography/mass spectrometry

The detection and identification of degradation products of scheduled chemicals, which are characteristic markers of Chemical Warfare agents (CWAs), plays a key role in verification analysis. Identification of such non-scheduled but specific markers of CWAs helps in deciphering the kind of agent that was present in the sample submitted for off-site analysis. This paper describes the stability of N,N-dialkylaminoethyl-2-chlorides, which are precursors for highly toxic chemicals like VX, in different solvents. These compounds are stable in chloroform, acetonitrile, hexane and dichloromethane but tend to undergo in situ nucleophilic substitution reaction in the presence of alcohols giving the corresponding alkyl ether. The study shows that N,N-dialkylaminoethyl alkyl ethers can be used as markers of N,N-dialkylaminoethyl-2-chlorides. A detailed degradation study of these compounds in the presence of alcohols was carried out and it was found that the reaction follows pseudo-first order kinetics. Electron ionization mass spectral data for the methyl ethers of all the compounds are briefly discussed.     

On the Uniform Distribution of Certain Sequences

We investigate the uniform distribution of the sequence n as n ranges over the natural numbers and is a fixed positive real number which is not an integer. We then apply this in conjunction with the Linnik-Vaughan method to study the uniform distribution of the sequence p as p ranges over the prime numbers.