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.     

N.M.R. and I.R. studies of 1, 1, 1 trifluoroacetone in proton donor solvents

Interactions of 1, 1, 1 trifluoroacetone with proton donor solvents of the type RH [where R=HO, CH₃S, CH₃CH₂CH₂CH₂S, CH₃O, (CH₃)₂N, (C₂H₅)₂N] have been investigated using NMR and infra-red techniques. Evidence of the formation of addition products of the type CF₃.C(OH)R.CH₃ where OH group is hydrogen-bonded with the fluorine of the CF₃ group has been obtained.     

Infra-red spectroscopic studies of solvent-solute interactions in parachlorophenol and thiophenol with tertiary amides

Hydrogen bonding of O-H ... O=C and S-H ... O=C type has been studied in parachlorophenol and thiophenol with dimethyl and diphenyl amides and from the equilibrium constants, variation in the integrated absorption intensities and frequency shifts, the strength of the interaction in these complexes is discussed. In these systems diphenyl amides form weaker H-bond compared to that with the corresponding dimethyl amides. In dimethyl amides, the interaction is in the order dimethyl acetamide > dimethyl propionamide > dimethyl formamide. Similar results are obtained with diphenyl amides.     

Raman spectrum of dimethyl sulfoxide (DMSO) and the influence of solvents

The Raman spectrum of DMSO is recorded with a Hilger two-prism spectrograph andλ 4358 Å excitation. In addition to all the Raman lines reported earlier, six new lines at 898, 925, 1223, 1309, 2811 and 2871 cm.^?1 are observed and tentative assignments are given. The influence of solvents (CCl₄, CHCl₃, CH₃COOH) on the S=O bond is also studied. A shift from the liquid phase value,i.e., 1043 cm.^?1 to 1054, 1052 and 1009 cm.^?1 in the respective solvents is observed. The possibilities of association effects and hydrogen bonding are discussed.     

The equatorial anomaly in ionospheric total electron content and the equatorial electrojet current strength

Faraday Rotation of 40 and 41 MHz signals from the satellite BE-B (Explorer 22) recorded simultaneously at Ahmedabad (dip 34° N) and Kodaikanal (dip 3·4° N) during the years 1964–69 are used to derive the latitudinal profiles of Total Electron Content (TEC) over the Indian equatorial anomaly region. From these profiles the diurnal development of the equatorial anomaly and its correlation with equatorial electrojet strength are studied. The anomaly is found to maximise around 1400 LT,i.e., two-three hours after the electrojet attains its peak. The anomaly parameters such as the dip latitude of the anomaly peak,φ, the normalised depth,d, of the anomaly and the strength of the anomaly defined asS=? _xd are found to be well correlated with the electrojet strength.     

Sorption-desorption hysteresis in fibrous silica gel (Santocel C) with isomeric monohydric aliphatic alcohols

By employing the quartz fibre spring technique, sorption-desorption hysteresis at 35° has been studied of Iso-propyl, Iso-Butyl, Sec-Butyl, Tert-Butyl, Active Amyl and Iso-Amyl alcohols on fibrous silica gel (Santocel C) activated at 250°. The isotherms of all the alcohols have clearly defined “knees”. By the application of BET theory, the monolayer capacities are determined. Knowing the specific surface area of fibrous silica gel, assuming oriented sorption of the isomeric alcohols with the OH group attached to surface; the cross-sections of the alcohol molecules are calculated. Excepting Iso-Propyl and Sec-Butyl alcohols, all others have cross-sections greater than that of normal aliphatic alcohols. These higher values are to be expected in view of the side CH₃ groups. The exceptional behaviour of Iso-Propyl and Sec-Butyl alcohols is not clear. Permanent and reproducible hysteresis loops have been obtained in all the cases. Cohan’s theory of hysteresis cannot explain the observations satisfactorily. Cavity theory however explains all the cases of hysteresis. The shapes of the isotherms of the different alcohols in the high relative vapour pressure region indicate a variation in contact angles of the alcohols.     

Vinyl polymerization

Polymerization of Acrylamide initiated by cobaltic ions in aqueous solution at 15° C. and 20° C. in HClO₄ and H₂SO₄ media have been studied. Kinetics have been followed by determining the rate of cobaltic ion disappearance as well as monomer disappearance with variations in cobaltic, monomer and hydrogen ion concentrations, temperature, ionic strength, etc. Besides polymer reaction it has been observed that side reactions like water oxidation and monomer oxidation also contribute to rate of cobaltic ion disappearance. Certain anomalous results in H₂SO₄ medium have been observed. A reaction scheme involving CoOH²⁺ and Co³⁺ as initiators in HClO₄ and H₂SO₄ media respectively and mixed termination—mutual and linear—has been suggested. Certain rate parameters involving rate constants for initiation, propagation, termination and the corresponding activation energies have been evaluated.     

The microwave spectrum of methyl cyanide andl-type doubling in CH3CN,CH3NC,CH3CCH and CF3CCH

The microwave spectrum of Methyl cyanide molecule has been obtained corresponding to the transitions J=0→1, J=1→2 and J=2→3 in the ground vibrational state as well as in the excited degenerate vibrational statesv ₈=1 andv ₈=2. The frequencies of the lines are measured by using a secondary standard spectrograph taking mostly the ammonia lines as standards. The value of the vibration-rotation interaction constanta ₈ has been found to be ?27·3±0·4 mc./sec. The spectrum obtained for the transitions J=1→2 and J=2→3 withv ₈=1 has been understood on the basis of Nielsen’s theory ofl-type doubling in symmetric top molecules. The assignments give a value of 0·94 for the coriolis interaction constant which is consistent with the value obtained from the infra-red spectral data. The earlier work on similar transitions involvingl-type doubling in the molecules CH₃NC, CH₃CCH and CF₃CCH has been reviewed and the inconsistencies in the values of some parameters like coriolis interaction constant ζ and the rotation constant D_JK obtained by earlier workers from their assignments are pointed out. A reassignment of the transitions and the involved parameters removes these inconsistencies and yields coriolis interaction constants which are in close agreement with those obtained from infra-red spectral data. The following are the different ζ values obtained:

$$\begin{gathered}\zeta _8 in CH_3 NC = 0 \cdot 93 \hfill \\\zeta _{10} in CH_3 CCH = 1 \cdot 00 \hfill \\\zeta _9 in CH_3 CCH = 0 \cdot 95 \hfill \\\zeta _{10} in CF_3 CCH = 0 \cdot 6 \hfill \\\end{gathered}$$     

Ionospheric total electron content and slab-thickness at low latitudes in Indian zone

Observations of Faraday rotation of beacon signals from low orbiting satellite BE-B recorded at one station near the dip equator (Kodaikanal, dip 3·4° N) and at another station near the peak of the equatorial anomaly (Ahmedabad, dip 34° N) give a complete coverage of the equatorial anomaly belt in Indian zone. Contours of total elctron content (TEC) are obtained on a grid of latitudeversus local time for the different seasons of low (1964–66) and high (1967–69) solar activity epochs in the latitude belt 10° S to 26° N dip latitude. The development of the equatorial anomaly and its dependence on season and solar activity are discussed. Using similar contours of F₂ layer critical frequency, f₀F₂ contours of equivalent slab-thickness, τ are also constructed. The dependence of τ on season and solar activity and its implications on temperature are discussed.     

A simple proof of Ramanujan’s summation of the1ψ1

A simple proof by functional equations is given for Ramanujan’s₁ ψ ₁ sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.     

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.     

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.     

Fourier coefficients of Siegel cusp forms of genus n

Let F(Z) be a cusp form of integral weight k relative to the Siegel modular group Sp_n(Z) and let f(N) be its Fourier coefficient with index N. Making use of Rankin's convolution, one proves the estimate (1) $$f(\mathcal{N}) = O(\left| \mathcal{N} \right|^{\tfrac{k}{2} - \tfrac{1}{2}\delta (n)} ),$$ where $$\delta (n) = \frac{{n + 1}}{{\left( {n + 1} \right)\left( {2n + \tfrac{{1 + ( - 1)^n }}{2}} \right) + 1}}.$$ Previously, for n ≥ 2 one has known Raghavan's estimate $$f(\mathcal{N}) = O(\left| \mathcal{N} \right|^{\tfrac{k}{2}} )$$ In the case n=2, Kitaoka has obtained a result, sharper than (1), namely: (2) $$f(\mathcal{N}) = O(\left| \mathcal{N} \right|^{\tfrac{k}{2} - \tfrac{1}{4} + \varepsilon } ).$$ At the end of the paper one investigates specially the case n=2. It is shown that in some cases the result (2) can be improved to, apparently, unimprovable estimates if one assumes some analogues of the Petersson conjecture. These results lead to a conjecture regarding the optimal estimates of f(N), n=2.     

Lacunary subsets of orthonormal sets

В РАБОтЕ РАссМАтРИВА УтсьS _Р-пОДсИстЕМы О. Н.с. В ЧАстНОстИ, ДОкАжыВА Етсь слЕДУУЩАь тЕОРЕ МА, кОтОРАь НЕУсИльЕМА. тЕОРЕМА.пУсть Р>2 —ЧЕ тНОЕ ЧИслО, δ — пРОИжВО льНОЕ ЧИслО, 0<δ≦p?2,Φ= {Φ _n(x)} _n=1 ^N —O.H.C.,x?[0,1],пРИЧЕМ ∥ Φ _n∥_p≦M, n=1,2,...,N, гДЕР=Р+δ, 0М<∞. тОгДА Иж сИстЕМы Ф МОж НО ВыБРАть пОДсИстЕМ У \(\Phi ' = \left\{ {\varphi _{n_k } } \right\}_{k = 1}^{N'} ,N' \geqq N^{\alpha (\delta )} ,\alpha (\delta ) = \frac{{2\delta }}{{p(p - 2 + \delta )}}\) , тАкУУ, ЧтО Дль лУБОгО п ОлИНОМА \(P(x) = \sum\limits_{k = 1}^{N'} {a_k \varphi _{n_k } (x)} \) ИМЕЕ т МЕстО ОцЕНкА $$(\mathop \sum \limits_{k = 1}^{{\rm N}'} a_k^2 )^{1/2} \leqq \left\| P \right\|_p \leqq c_{p,M,\delta } (\mathop \sum \limits_{k = 1}^{{\rm N}'} a_k^2 )^{1/2} $$ (c _p, m, δ — пОстОьННАь, жАВИ сьЩАь тОлькО Отp, M, δ, НО НЕ От N ИлИ кОЁФФИцИЕНтОВ пО лИ-НОМА). пРИВОДьтсь И ДРУгИЕ РЕжУльтАты А НАлОгИЧНОгО хАРАктЕ РА.     

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.     

Strength and deformation properties of fiberglass-plastic in the flat stressed state as a function of reinforcement structure

Conclusion Limiting strength values have been ascertained in the flat stressed state as a function of reinforcement structure. The change in each strength surface tensor component as a function of reinforcement intensity has been approximated by the piecewise-linear approximation method. A strength condition has been derived which can be used in optimization problems. The problem of the optimum reinforcement structure of a composite at various ratios of the stresses ₁₁, ₂₂, and ₁₂ has been examined. By using the strength condition, one can predict strength values for structures which appear in the class of materials in question with various reinforcement intensities. The procedure developed can be used in designing composite materials.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 848–859, September–October, 1978.     

Spectrophotometric and potentiometric investigations of copper (II)-Ethanolamine complexes

Spectrophotometric and potentiometric investigations have been carried out on copper-diethanolamine system. Job plots at 900, 900 and 580 mμ have indicated the formation of CuD⁺⁺, CuD₂ ⁺⁺ and CuD₃ ⁺⁺. Then- pA curves obtained indicate the formation of CuD⁺⁺, CuD₂ ⁺⁺, CuD₃ ⁺⁺, CuDOH⁺, CuD₂OH⁺ and CuD₃OH⁺. Then- pA curves have been analyzed to obtain the stability constants of these complexes. Absorption curves of pure complexes have been computed by a graphical method. Gaussian analysis of the absorption curves of pure and hydroxy complexes show the presence of a second band, indicating that the structure is that of a distorted octahedron.     

On non-measurability of in its second dual

We show that with the weak topology is not an intersection of Borel sets in its Cech-Stone extension (and hence in any compactification). Assuming (CH), this implies that has no continuous injection onto a Borel set in a compact space, or onto a Lindelöf space. Under (CH), this answers a question of Arhangel'ski.

     

NMR studies of reorientational correlation times in dimethyl sulphoxide

The spin lattice relaxation times have been measured in a mixture of (CH₃)₂ SO and (CD₃)₂ SO. The (T₁)_inter and (T₁)_inter are found to be 5.0 seconds each. The correlation time π has been estimated from these data. A time interval measurement unit to measure pulse separation is described.     

Vibrational spectra and normal vibrations of acetanilide and N-deuterated acetanilide

The Raman and infra-red spectra of acetanilide and N-methylacetamide and of their N-deuterated compounds have been recorded. The vibrational frequencies of acetanilide have been assigned and the nature of the Amide I, II and III bands in acetanilide and N-methylacetamide has been investigated by the study of the changes in the frequencies of these bands in the spectra of their deuterated compounds. Acetanilide and deuterated acetanilide molecules have been subjected to normal co-ordinate treatment and the mixing up of the skeletal frequencies arising out of the in-plane vibrations has been determined. These results indicate that as in secondary amides, the amide II and amide III bands in acetanilide are due to the combined contribution ofδ (NH) andν (C-N) vibrations, but the contribution ofν (C-N) to the amide II band is less in acetanilide and deuterated acetanilide than in cases of N-methylacetamide and deuterated N-methylacetamide.