Kinetics of Thallium (III) oxidation of aromatic ketones

The kinetics of oxidation of acetophenone and six substituted acetophenones by Thallium (III) acetate have been studied in 95% (v/v) aqueous acetic acid. The reaction is first order with respect to the oxidant as well as the organic substrate and acid catalysed. The probable nature of Tl (III) species in aqueous acetic acid has been indicated. The rate data fitted well with Brown’sσ ⁺ values withρ ⁺ = ?0.70. A mechanism for the Tl (III) oxidation of aromatic ketones has been proposed.     

Salt effects in the alkaline hydrolysis of dicarboxylic esters in aqueous DMSO—The mechanism of half-ester hydrolysis

The effect of addition of several salts on the rate of hydrolysis of dicyclohexyl phthalate and sodium monobenzyl phthalate in aqueous DMSO has been studied. It is found that the rate of the second step of the hydrolysis is dependent on the character and the concentration of the cation of the electrolyte added while the rate of the first step is not much affected. The results are taken to point to the operation of an iondipole mechanism in the half-ester hydrolysis rather than an ion-ion mechanism.     

Numerical studies of slow viscous rotating fluid past a sphere

Navier-Stokes equations for steady, viscous rotating fluid, rotating about the zaxis with angular velocity ω are linearized using Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity component. Only one parameterR _eω =2ωa ²/v enters the resulting equations. Even the linearized equations are difficult to solve analytically and the method of matched asymptotic expansions is to be applied. Central differences are applied to the two-dimensional partial differential equations and are solved by the Peaceman-Rachford ADI method. The resulting algebraic equations are solved by successive over relaxation method. Streamlines are plotted for Ψ=0·01, 0·05, and 0·25 andR _eω =0·1, 0·3, 0·5.     

Studies in the hydrolysis of metal ions

The hydrolysis of cupric ion has been studied at various ionic strengths (0·01, 0·05, 0·1 and 0·5 M). The results are analyzed employing ‘core + links’ theory, log-log plot, normalization plot, and extrapolation method for obtaining the pure mononuclear curve. The stability constants of Cu₂(OH) ₂ ⁺⁺ , Cu₃(OH) ₄ ⁺⁺ , Cu(OH)⁺ and Cu(OH)₂ have been reported.     

Characteristics ofπ −-nucleon collisions at a primary energy of 4·4 GeV

Eight hundred and sixteen nuclear interactions produced by 4·4 GeVπ ^?-mesons in nuclear emulsion have been obtained by “along the track” scanning procedure. Favourable secondary particles from a selected 290π ^?-N (pion-nucleon) collisions have been identified by blob-density and multiple scattering measurements. It is found that the pion often persists in theseπ ^?-N collisions, the average persistence is estimated to be 0·24 per collision. It is estimated thatπ-N andπ-π collisions account for 60% and 28% respectively of the secondary particles. The average number of charged shower particles is 〈n _s〉=2·09±0·12, the average number of created charged particles is 〈n _e±〉=1·94±0·12, the average number of protons with energy greater than 300 MeV is 〈n _p〉=0·15±0·05 and the average number of charged kaons is found to be 〈n _k±〉=0·11±0·06. The integral energy spectra of pions in C-system as well as in L-system are well represented by exponential forms. The average inelasticity of the proton in C-system is found to be 0·52±0·10. The charge retention probability for protons inπ ^?-p collisions is 0·45±0·07.     

Acidity function in dipolar aprotic media

The H₀ acidity function has been determined for hydrochloric and trichloroacetic acids in dimethyl sulphoxide (DMSO) and acetonitrile using three amine class of indicators. The variation of H₀ with solvent composition at a fixed concentration of 0.1 M HCI in DMSO-water, acetonitrile-water and DMSO acetonitrile mixtures was also studied. Approximate medium effects on the proton in all these solvents were computed from the H₀ data and the results are discussed.     

Mixed complexes of iron (III)—thiocyanate with some nitrogen and oxygen donors and their analytical applications

Methods for the determination of iron (III) as thiocyanate complex in the presence of neutral donors like isoquinoline and antipyrine have been developed. The two methods are of equal sensitivity (ε=18,000±100 lit. mole^?1 cm^?1) but operate at widely different hydrogen ion concentrations ranging from 10^?5 N(pH 5·0) to 7N. The interference of various foreign substances has been studied in the two methods. The application of these methods in the analysis of alloys and commercial HCl for iron has been explored and the composition of the extracting species established.     

Microwave spectrum of pentafluorobenzonitrile

The absorption spectrum of pentafluorobenzonitrile has been investigated in the frequency range of 18–26·5 GHz using a 100 KHz stark modulated microwave spectrometer. The analysis of the spectrum is based on the rigid asymmetric rotor theory. The rotational constants obtained are A=1026·82±0·3 MHz, B=776·34±0·1 MHz, C=442·06±0·1 MHz and the asymmetry parameterχ=+0·1433. The inertial defect is I _o ?I _a ?I _b =0·081 amu Ų. The bond distances ared _CF=1·328 Å andd _CN=1·157 Å. The results are in good agreement with the assumed planarity of the molecule and the normal values of bond distances.     

On an approximate identity of Ramanujan

In his second notebook, Ramanujan says that $$\frac{q}{{x + }}\frac{{q^4 }}{{x + }}\frac{{q^8 }}{{x + }}\frac{{q^{12} }}{{x + }} \cdots = 1 - \frac{{qx}}{{1 + }}\frac{{q^2 }}{{1 - }}\frac{{q^3 x}}{{1 + }}\frac{{q^4 }}{{1 - }} \cdots $$ “nearly” forq andx between 0 and 1. It is shown in what senses this is true. In particular, asq → 1 the difference between the left and right sides is approximately exp ?c(x)/(l-q) wherec(x) is a function expressible in terms of the dilogarithm and which is monotone decreasing with c(0) = π²/4,c(1) = π²/5; thus the difference in question is less than 2· l0^?85 forq = 0·99 and allx between 0 and 1.     

Microwave spectrum of pentafluorobenzene

The microwave spectrum of pentafluorobenzene has been measured in the frequency region 12·5 to 18·00 KMHz. The spectrum is analysed on the basis of rigid asymmetric rotor theory. The rotational constants obtained are A=1471·963 MHz, B=1026·278 MHz, C=604·693 MHz and the asymmetry parameterκ=?0·0278. The inertial defect is Δ=I _c -I _a -I _b =?0·014 amu Ų. The bond distances ared _CF=1·328 Å andd _CH=1·089 Å, assumingd _CC=1·395 Å.     

Flow of a viscous incompressible fluid between two parallel plates,one in uniform motion and the other at rest with uniform suction at the stationary plate

In the present paper an exact solution of the Navier-Stoke’s equations reduced to third and second order non-linear differential equations with appropriate boundary conditions is obtained. The longitudinal and transverse velocity profiles for λ=0·1, 1 and R=100 are drawn. It is noted that for large values of\(\bar x\), an adverse pressure gradient is developed which causes a back flow. There is increase in pressure even for very small fluid suction along the stationary plate. The skin friction and the flow coefficient decrease with reference to the suction velocity and the distance along the stationary plate. For λ=0, the results transform to the known results for plane couette flow without suction.     

Emission spectrum of chlorine excited in the presence of argon

The spectrum of chlorine excited in the presence of argon has been photographed with a 21-ft. grating spectrograph in the first order. Two band systems in the region 2600–2390 Å and 2365–2239 Å are observed which appear to be respectively analogous to the 2950–2670 Å and 2660–2590 Å systems of bromine reported earlier by Venkateswarlu and Verma. The wavelengths and the wavenumbers of all the bands in the system 2600–2390 Å are given. The vibrational scheme along with the corresponding Franck-Condon parabola is also given. The analysis suggests that the lower state of the system is the 3π(O _u ⁺_ state established by Elliott at 17658 cm.^?1 and that the upper state is at 67773 cm.^?1 The vibrational constants obtained arew ₀′ = 246·6 cm.^?1,w ₀′x ₀′ = 0·615 cm.^?1,w ₀″ = 255·2 cm.^?1,w ₀″x ₀″ = 5·5 cm.^?1,w ₀″y ₀″ = ?0·0155 cm.^?1 andw ₀″z ₀″ = 0·00115 cm.^?1     

On the Relative Waiting Times in the GI/M/s and the GI/M/1 Queueing Systems

The expected steady-state waiting time, Wq(s), in a GI/M/s system with interarrival-time distribution H(·) is compared with the mean waiting time, Wq, in an "equivalent" system comprised of s separate GI/M/1 queues each fed by an interarrival-time distribution G(·) with mean arrival rate equal to 1/s times that of H(·). For H(·) assumed to be Exponential, Gamma or Deterministic three possible relationships between H(·) and G(·) are considered: G(·) can be of the "same type" as H(·); G(·) can be derived from H(·) by assigning new arrivals to the individual channels in a cyclic order; and G(·) may be obtained from H(·) by assigning customers probabilistically to the different queues. The limiting behaviour of the ratio R = Wq/Wq(s) is studied for the extreme values (1 and 0) of the common traffic intensity, ρ. Closed form results, which depend on the forms of H(·) and G(·) and on the relationships between them, are derived. It is shown that Wq is greater than Wq(s) by a factor of at least (s + 1)/2 when ρ approaches one, and that R is at least s(s!) when ρ tends to zero. In the latter case, however, R goes to infinity (!) in most cases treated. The results may be used to evaluate the effect on the waiting times when, for certain (non-queueing) reasons, it is needed to partition a group of s servers into several small groups.     

Complex formation between cadmium and thiosalicylic acid

Polarographic measurements on the system Cd-thiosalicylic acid (TSA) reveal the formation of a complex, 1:2:: metal: ligand (ammonia buffer pH 9·1,µ=0·2 M, 50% alcoholic medium), dissociation constant of the complex being 6·3 × 10^?8 at 30° C. Potentiometric titrations confirmed this stoichiometry, stepwise stability constants, logk ₁ and logk ₂ being 7·85 and 8·10 respectively. The complex has also been isolated and studied in solid state.     

Electrodeposition of copper on copper single crystal (100) face in presence of chloride ions

Observations of copper electrodeposits on to the (100) plane of copper was made from highly purified solutions of copper sulphate containing known concentration of hydrochloric acid from 10^?10 to 10^?1 m/L. In pure solutions at current densities of 5 and 10 mA/cm.² layers and pyramids were noticed. In the presence of hydrochloric acid of concentration 10^?9 to 10^?5 m/L there is a gradual decrease of distance between successive steps. At 10^?4 m/L of HCl there was the breaking of layers giving rise to ridge type of growth. With the increase of concentration to 3·5×10^?3 m/L pyramids appear again. On increasing the concentration of HCl to 10^?2 m/L there was the formation of triangular pyramids of cuprous chloride and on still increasing the concentration, polycrystalline type of deposit was noticed. The transition from layer to ridge, ridge to pyramids and to polycrystalline deposit occurs at all c.d. studied but the critical concentration of HCl needed for the transition depends upon the current density.     

Cosmic ray nuclei of chargeZ⩾3 during the period of low solar activity

A detailed study of the composition and energy spectra of heavy nuclei of charge Z?3 in the primary cosmic rays has been made during the period of low solar activity, using two stacks of nuclear emulsions exposed in balloon flights from Fort Churchill, Canada, in June 1963. Each of the stacks was composed of 120 nuclear emulsions of three different sensitivities and was exposed at about 3·5 g. cm.^?2 of residual air for about 11.1 hr. Reliable resolution of charges of nuclei from lithium to oxygen was obtained; for heavier nuclei, charge groups were determined. From the analysis of 793 tracks of nuclei with Z?3, results on the following aspects were obtained:

1. The differential energy spectra of L (Z=3–5), M (Z=6–9) and H (Z=10–28) nuclei were measured in the energy intervel 150–600 MeV/nucleon; integral fluxes were obtained for energy >600 MeV/nucleon;
2. The energy dependence of the L/M ratio at the top of the atmosphere was determined; the ratios were obtained as 0·45 ± 0·06 and 0·29 ± 0·03 in the energy intervals of 200–575, and >575 MeV/nucleon respectively;
3. Relative abundances of individual nuclei of Li, Be, B, C, N and O at the top of the atmosphere were determined as 36, 29, 55, 100, 60 and 106 respectively in the energy interval 150–600 MeV/nucleon; corresponding values were also obtained for energy >600 MeV/nucleon.
4. The differential fluxes of multiply charged nuclei measured by us and by other investigators were used to determine the solar modulation between solar maximum to solar minimum. It was found that solar modulation of the fluxes of M and He nuclei were consistent with Rβ dependence and that the modulation parameter Δη between 1965 and 1957 was about 1·1.

The implications of these results are discussed.     

Viscosities of binary solutions of non-electrolytes

Viscosities and molar volumes of binary solutions,viz., Toluene-Nitrobenzene, Toluene-Bromobenzene, Toluene-Cyclohexanone, Cyclohexane-Cyclohexanone, Cyclohexane-Nitrobenzene, Cyclohexane-Acetic acid, Cyclohexane-Propionic acid and Cyclohexane-Butyric acid have been measured. The experimental results have been discussed in terms of viscosity-composition relations developed for binary solutions by Grunberg and Nissan and Katti and Chaudhri.     

Electron spin resonance of Cr5+ in CaWO4

Electron Spin Resonance of CaWO₄ with 0·1% of Cr has been investigated at liquid nitrogen and liquid helium temperatures. The observed ESR spectrum is attributed to Cr⁵⁺ ion in the substitutional site of W which has a compressed tetrahedral surroundings. A simple point charge calculation based on this geometry explains the observedg anisotropy and hyperfine anisotropy and places the magnetic electron in a predominantly \(3d_{z^2 } \) orbital. A comparison of these results with those obtained on other isoelectronic systems in similar and different co-ordinations justifies our assignment.     

Properties of finite unrefinable chains of ring topologies

Let R(+, ·) be a nilpotent ring and $ \left( {\mathfrak{M}, < } \right) $ be the lattice of all ring topologies on R(+, ·) or the lattice of all such ring topologies on R(+, ·) in each of which the ring R possesses a basis of neighborhoods of zero consisting of subgroups. Let ?? and ??? be ring topologies from $ \mathfrak{M} $ such that $ \tau = {\tau_0}{ \prec_\mathfrak{M}}{\tau_1}{ \prec_\mathfrak{M}} \cdots { \prec_\mathfrak{M}}{\tau_n} = \tau ^{\prime} $ . Then k????n for every chain $ \tau = {\tau ^{\prime}_0} < {\tau ^{\prime}_1} < \cdots < {\tau ^{\prime}_k} = \tau ^{\prime} $ of topologies from $ \mathfrak{M} $ , and also n?=?k if and only if $ {\tau ^{\prime}_i}{ \prec_\mathfrak{M}}{\tau ^{\prime}_{i + 1}} $ for all 0????i?<?k.     

A rotation theorem in the class of bounded univalent functions

Let S_M, M > 1, be the class of functionsf(z) which are regular and univalent in the disk ¦z¦ < 1 and satisfy the conditionsf(0) = 0,f'(0) = 1, and ¦f(z)¦ < M. In the present note we will obtain an exact estimate for the argument of the derivative of a function of the class S_M.