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1.
Rajani K. Samal R. R. Das M. C. Nayak G. V. Suryanarayana G. Panda D. P. Das 《Journal of polymer science. Part A, Polymer chemistry》1981,19(11):2751-2758
The kinetics of polymerization of acrylonitrile initiated by KHSO5 and catalyzed by Ag(I) have been investigated in an aqueous medium over the temperature range of 35–50°C. The rates of polymerization Rp have been calculated and studied with respect to monomer and initiator. The catalytic activity of various metal ions on the initiator has been determined from a comparison of Rp values. The effects of monomer, catalyst, neutral salts, various amines, and inhibitor (hydroquinone) on the initial rate as well as maximum conversion have been studied. From the kinetics results a suitable reaction scheme has been proposed. 相似文献
2.
3.
Rajani K. Samal M. C. Nayak G. Panda G. V. Suryanarayana D. P. Das 《Journal of polymer science. Part A, Polymer chemistry》1982,20(1):53-62
Vinyl polymerization of acrylonitrile initiated by the Ce(IV)/thioacetamide redox system has been investigated in aqueous sulfuric acid in the temperature range of 10–20°C. The rate of polymerization (Rp) and the rate of Ce(IV) disappearance (?RCe) were measured. The effect of certain water-soluble organic solvents, added electrolytes, and aromatic and heterocyclic organic nitrogen compounds on the rate of polymerization has been investigated. Depending on the experimental results, we have suggested a suitable reaction scheme for the system which involves the production of initiating radicals from the oxidation of thioacetamide (TAm) by ceric ion and the termination of the polymer chain by metal ions. 相似文献
4.
D. Suryanarayana 《Periodica Mathematica Hungarica》1983,14(1):69-75
LetL(x) denote the number of square-full integers not exceedingx. It is well-known that $$L\left( x \right) \sim \frac{{\zeta \left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right)}}{{\zeta \left( 3 \right)}}x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \frac{{\zeta \left( {{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \right)}}{{\zeta \left( 2 \right)}}x^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ,$$ whereζ(s) denotes the Riemann Zeta function, LetΔ(x) denote the error function in the asymptotic formula forL(x). On the assumption of the Riemann hypothesis (R.H.), it is known that $$\Delta x = O\left( {x^{13/81 + 8} } \right)$$ for everyε > 0. In this paper, we prove on the assumption of R.H. that $$\frac{1}{x}\int\limits_x^1 {\left| {\Delta \left( t \right)} \right|dt = O\left( {x^{1/10 + ^8 } } \right)} .$$ In fact, we prove a more general result. We conjecture that $$\Delta x = O\left( {x^{1/10 + ^8 } } \right)$$ under the assumption of the R.H. 相似文献
5.
Summary A method for the photometric estimation of molybdenum(V) by extraction of the complex formed with NaDDTC in 5 N HCl solution is discussed. The reduction of Mo(VI) to Mo(V) is achieved with hydrazine sulphate. The colour intensity of the chloroform extract of the complex is measured at 450 nm. Beer's law is obeyed up to 500 g/25 ml of molybdenum.
Zusammenfassung Zur photometrischen Molybdänbestimmung wird der Komplex mit Diäthyldithiocarbamidat verwendet, der in 5 N salzsaurer Lösung gebildet und mit Chloroform extrahiert wird. Mo(VI) wird mit Hydrazinsulfat zur fünfwertigen Stufe reduziert. Die Messung erfolgt bei 450 nm; das Beersche Gesetz ist bis zu 500 g Mo/25 ml erfüllt.相似文献
6.
D. Suryanarayana 《Periodica Mathematica Hungarica》1979,10(4):261-271
LetL(x) denote the number of square full integers ≤x. By a square-full integer, we mean a positive integer all of whose prime factors have multiplicity at least two. It is well known that $$\left. {L(x)} \right| \sim \frac{{\zeta ({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2})}}{{\zeta (3)}}x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \frac{{\zeta ({2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3})}}{{\zeta (2)}}x^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ,$$ where ζ(s) denotes the Riemann Zeta function. Let Δ(x) denote the error function in the asymptotic formula forL(x). On the basis of the Riemann hypothesis (R.H.), it is known that \(\Delta (x) = O(x^{\tfrac{{13}}{{81}} + \varepsilon } )\) for every ε>0. In this paper, we prove the following results on the assumption of R.H.: (1) $$\frac{1}{x}\int\limits_1^x {\Delta (t)dt} = O(x^{\tfrac{1}{{12}} + \varepsilon } ),$$ (2) $$\int\limits_1^x {\frac{{\Delta (t)}}{t}\log } ^{v - 1} \left( {\frac{x}{t}} \right) = O(x^{\tfrac{1}{{12}} + \varepsilon } )$$ for any integer ν≥1. In fact, we prove some general results and deduce the above from them. On the basis of (1) and (2) above, we conjecture that \(\Delta (x) = O(x^{{1 \mathord{\left/ {\vphantom {1 {12}}} \right. \kern-0em} {12}} + \varepsilon } )\) under the assumption of R.H. 相似文献
7.
R. K. Samal P. C. Dash B. Mishra G. V. Suryanarayana D. P. Das M. C. Nayak 《高分子科学杂志,A辑:纯化学与应用化学》2013,50(5):805-819
Polymerization of acrylonitrile initiated by the Cr6+/thioacetamide redox system was studied in nitrogen atmosphere in the temperature range 35–45°C. The rate of polymerization and the rate of Cr6+ ion disappearance were measured. The effect of certain water-miscible organic solvents, neutral electrolytes, and complexing agents on the rate of polymerization was investigated. Chromic acid alone did not initiate the polymerization under deaerated and undeaerated conditions. Depending on the results obtained, a suitable kinetic scheme was proposed and various rate parameters were evaluated. 相似文献
8.
9.
Summary Let k and l be integers such that 2k l. Let Sk and S
l
lbe two subsets of positive integers with SkQk and Sl Ql, where Qk denotes the set of k-free integers. Further suppose that the characteristic functions of Sk and S
l
l are multiplicative. Let T(n) denote the number of representations of n in the form n=a+b, where a Sk and b S
l
l. In this paper we establish an asymptotic formula for T(n), when n is sufficiently large; and deduce several known asymptotic formulae as particular cases. 相似文献
10.
M. B. Suryanarayana 《Journal of Optimization Theory and Applications》1976,19(1):125-140
In the context of a recent geometric condition of Cesari, used in the reduction of seminormality requirements in lower closure theorems, this paper shows that the existence of a strongly convergent selection from the sequence of orientor fields, under Kuratowski property (K), is adequate to guarantee lower closure theorems. This generalization is justified through examples. Several related remarks are made.This work was done in the framework of Research Project AFOSR-71-2122 at the University of Michigan, Ann Arbor, Michigan. The author wishes to thank Professor L. Cesari for helpful discussions during the writing of this paper. 相似文献