Cesàro α-Integrability and Laws of Large Numbers I

For a sequence of integrable random variables, we introduce a new set of conditions called Cesàro -Integrability and Strong Cesàro -Integrability and show that, for <1/2, these conditions that are strictly weaker than Cesàro Uniform Integrability and Strong Cesàro Uniform Integrability respectively, are sufficient for WLLN and SLLN to hold for a sequence of pairwise independent random variables. For some special kinds of dependent sequences of random variables also, Cesàro -integrability for appropriate is shown to be sufficient for WLLN to hold.     

Cumulative yields of short-lived ruthenium isotopes in the thermal neutron induced fission of233U,235U and239Pu

Cumulative yields of short-lived ruthenium isotopes in the thermal neutron induced fission of²³⁵U,²³⁵U and²³⁹Pu have been determined using a fast radiochemical separation technique followed by gamma spectrometry. The cumulative yields of¹⁰⁷Ru and¹⁰³Ru in²³³U (n_th, f) and¹⁰⁷Ru and¹⁰⁹Ru in²³⁹Pu (n_th, f) are determined for the first time. The measured cumulative yields are converted to chain yields assuming normal charge distribution systematics for comparison with the literature data on chain yields.     

Metal-promoted aromatic ring amination and deamination reactions at a diazo ligand coordinated to rhodium and ruthenium

Reactions of MCl(3).3H(2)O (M = Rh and Ru) with the ligand 2-[(2-N-arylamino)phenylazo]pyridine [HL(1); NH(4)C(5)N=NC(6)H(4)N(H)C(6)H(4)(H) (HL(1a)), NH(4)C(5)N=NC(6)H(4)N(H)C(6)H(4)(CH(3)) (HL(1b)), and NH(4)C(5)N=NC(6)H(4)N(H)C(5)H(4)N (HL(1c))] in the presence of dilute NEt(3) afforded multiple products. In the case of rhodium, two green compounds, viz. [Rh(L(1))(2)](+) ([2](+)) and [RhCl(pap)(L(1))](+) ([3](+)), where L(1) and pap stand for the conjugate base of [HL(1)] and 2-(phenylazo)pyridine, respectively, were separated on a preparative thin layer chromatographic plate. The reaction of RuCl(3).3H(2)O, on the other hand, produced two brown compounds, viz. [RuCl(HL(1))(L(1))] (4) and [RuCl(pap)(L(1))] (5), respectively, as the major products. The X-ray structures of the representative complexes are reported. Except for complex 2, and 4, the products are formed due to the cleavage of an otherwise unreactive C(phenyl)-N(amino) bond. In complex 4, one of the tridentate ligands (HL(1)) does not use its maximum denticity and coordinates as a neutral bidentate donor. Plausible reasons for the differences in their modes of coordination of the ligands as in 2 and 4 have been discussed. The ligand pap in the cationic mixed ligand complex [3](+) reacts instantaneously with ArNH(2) to produce an ink-blue compound, [RhCl(HL(2))(L(1))](+) ([6](+)) in a high yield. The ligand HL(2) is formed due to regioselective fusion of ArNH(2) residue at the para carbon of the phenyl ring (with respect to the azo fragment) of pap in [3](+). The above complexes are generally intensely colored and show strong absorptions in the visible region, which are assigned to intraligand charge transfer transitions. These complexes undergo multiple and successive one-electron-transfer processes at the cathodic potentials. Electrogenerated cationic complexes of ruthenium(III), [4](+) and [5](+), showed rhombic EPR spectra at 77 K.     

Separation of lanthanum and cerium on modified fly ash bed

The adsorption of lanthanum and cerium on modified fly ash bed has been studied. The effect of pH on the adsorption of both lanthanum and cerium by the bed material has been discussed. The exchange capacities of lanthanum and cerium have been determined. The method has been applied to monazite sand solution. The elution of both lanthanum(III) and cerium(IV) was studied using buffer and suitable eluting agent. The process is simple and may be considered as a low cost-methodology for separation of lanthanum and cerium.     

Drop size prediction in liquid membrane systems

The design of separation equipment using liquid membranes requires predictive methods for the estimation of drop diameters of the dispersed liquid membrane “macrodrop”. Existing models for drop breakage in liquid-liquid systems underpredict drop diameters of liquid membrane macrodrops even after incorporating the effects of dispersed phase viscosity and hold-up. By considering that the microdroplets within a liquid membrane macrodrop cause a damping of induced drop oscillations arising from external turbulence, the recently proposed model of Calabrese et al. (1986) has been modified and the resulting model equations have been shown to predict drop diameters of both oil as well as water liquid membrane macrodrops reasonably well.     

Blue dimetallic complexes of two heavy metal ions Cd(II) and Hg(II) with an extended nitrogen donor ligand. Preparation, spectral characterization, and crystallographic studies

In methanol, the metal salts CdCl2.H2O and HgCl2 react instantaneously with the deprotonated ligand, L-, producing molecular dimetallic ink-blue complexes of general formula M2Cl2L2, M=Cd(II), (1) and Hg(II), (2) (HL=2-[2-(pyridylamino)phenylazo]pyridine). Crystal structures of these two complexes are reported. The coordination sphere around each Cd(II) ion in 1 is a distorted square pyramidal. The metal ion (Cd1) sits above the basal plane of three nitrogen atoms, N(1), N(3), and N(4). The second cadmium ion (Cd2) in this compound lies below the plane of three nitrogen atoms, N(6), N(8), and N(9). The apical positions are occupied by two Cl atoms. Secondary intramolecular interactions between the metal ions and the anionic secondary amine nitrogen atoms (N(4) and N(9)) are noted. The geometry of each Hg(II) ion in the mercury complex, Hg2Cl2L2.0.5H2O, is also distorted square based pyramid with the metal ions lying out of planes of the three nitrogen atoms of the chelating ligands. Secondary Hg(1)...N(1A) (deprotonated amine) interactions are noted. The separation between the two Hg(II) ions in this complex is within the sum of their van der Waals radii. Solution properties of these blue complexes are reported. The origin of the intense blue color in these complexes is the intraligand transitions that occur near 615 nm. 1H NMR of Hg2Cl2L2.0.5H2O indicates that it undergoes exchange in solution with the coordinated ligands.     

A new spectrophotometric method for the determination of total and ferric iron in rain water at the ppb level

A new, simple, selective and sensitive spectrophotometric procedure for the on-site quantification of iron at nano-gram levels in atmospheric precipitations, i.e. rain as sample source is described. It is based on the color reaction of Fe3+ with SCN- ions in the presence of a cationic surfactant, i.e. cetylpyridinium chloride (CPC), in strong HCl solution, and subsequent extraction of the complex with N-octylacetamide into toluene or chloroform. The apparent molar absorptivity of the complex is 2.60 x 10(5) L mol(-1) cm(-1) at lambdamax = 480 nm at an enrichment factor (EF) of 10. The detection limit (causing higher absorbance than the sum of the blank absorbance (0.009) and 3 SD) is 5 ng mL(-1) Fe. Ions commonly associated with iron did not interfere in the present method. The effect of analytical variables, i.e. amount and type of the reagents, acidity, solvent, temperature, dilution, etc., in the determination of iron are discussed. The validity of the present method is checked with GF-AAS. The method has been applied to the determination of iron at the ppb level in rain water samples.     

Selinidin: Crystal structure generated by C–H···O, C–H···π and π-π interactions

The title compound, 9,10-dihydro-8,8-dimethyl-2-oxo-2H,8H-benzo[1,2-b:3,4-b']dipyran-9-yl-2-methyl-2-butenoate, C₁₉H₂₀O₅, was isolated from the roots of Selinum vaginatum. The compound crystallizes into monoclinic space group P2 ₁ with unit cell parameters: a = 12.830(2) Å, b = 9.041(1) Å, c = 14.983(1) Å, β = 95.09(1)°, Z = 4. The crystal structure has been determined using direct methods and refined by full-matrix least-squares to a final R value of 0.0529 for 3142 observed reflections. There are two independent molecules, A and B, per asymmetric unit. In both the molecules, the coumarin nucleus is planar. However pronounced differences are observed in the conformation of dihydropyran ring which has a half-chair conformation with an 8β-9α orientation in molecule A and is intermediate between half-chair and sofa in molecule B. Differences also occur in the conformation of the 2-methylbutenoyloxy side chain at C9 due to the different geometry of C–H···π interactions in molecules A and B. Molecules A and B are connected by π–π interactions between their coumarin fragments forming dimers. The dimers interact through C–H···O and C–H···πhydrogen bonds.     

Characterisation of semiconducting V2O5–Bi2O3–TeO2 glasses through ultrasonic measurements

Tellurite containing vanadate (50−x)V₂O₅–xBi₂O₃–50TeO₂ glasses with different bismuth (x=0, 5, 10, 15, 20 and 25 wt%) contents have been prepared by rapid quenching method. Ultrasonic velocities (both longitudinal and shear) and attenuation (for longitudinal waves only) measurements have been made using a transducer operated at the fundamental frequency of 5 MHz in the temperature range from 150 to 480 K. The elastic moduli, Debye temperature, and Poisson’s ratio have been obtained both as a function of temperature and Bi₂O₃ content. The room temperature study on ultrasonic velocities, attenuation, elastic moduli, Poisson’s ratio, Debye temperature and glass transition temperature show the absence of any anomalies with addition of Bi₂O₃ content. The observed results confirm that the addition of Bi₂O₃ modifier changes the rigid formula character of TeO₂ to a matrix of regular TeO₃ and ionic behaviour bonds (NBOs). A monotonic decrease in velocities and elastic moduli, and an increase in attenuation and acoustic loss as a function of temperature in all the glass samples reveal the loose packing structure, which is attributed to the instability of TeO₄ trigonal bipyramid units in the network as temperature increases. It is also inferred that the glasses with low Bi₂O₃ content are more stable than with high Bi₂O₃ content.     

Inhomogeneous and Radiating Composite Fluids

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems.