The radial force on a charged particle in superimposed magnetic fields on Schwarzschild spacetime

Following the approach of optical reference geometry we derive the expression for the total force in the radial direction acting on a charged particle in magnetic fields superimposed on the static Schwarzschild background and show the possible existence of bound orbits for particles in the field of ultra compact objects at distancesr?3m wherein the Lorentz force counterbalances both the gravitational and centrifugal forces.     

Dalzin as an analytical reagent for estimation of trace quantities of bismuth in lead and nickel

Dalzin forms coloured complexes with many metal ions. The present work deals with its use for determining microgram quantities of bismuth by solvent extraction followed by spectrophotometry. A method for estimation of bismuth in lead and nickel is presented.     

Thermal noise in the linear graded channel junction FET

The limiting noise mechanism in field effect transistors is thermal noise of the conducting channel. An analysis of the thermal noise in a linearly tapered inhomogeneous channel FET is presented leading to a solution for the open circuit noise voltage and the short circuit noise current. Improvement in the open circuit noise voltage for the inhomogeneous FET is shown directly from a comparison with the solution for a homogeneous channel FET.     

Use of the augmented penalty function in mathematical programming problems,part 1

In this paper, the problem of minimizing a functionf(x) subject to a constraint (x)=0 is considered. Here,f is a scalar,x ann-vector, and aq-vector, withq<n. The use of the augmented penalty function is explored in connection with theordinary gradient algorithm. The augmented penalty functionW(x, ,k) is defined to be the linear combination of the augmented functionF(x, ) and the constraint errorP(x), where theq-vector is the Lagrange multiplier and the scalark is the penalty constant.The ordinary gradient algorithm is constructed in such a way that the following properties are satisfied in toto or in part: (a) descent property on the augmented penalty function, (b) descent property on the augmented function, (c) descent property on the constraint error, (d) constraint satisfaction on the average, or (e) individual constraint satisfaction. Properties (d) and (e) are employed to first order only.With the above considerations in mind, two classes of algorithms are developed. For algorithms of Class I, the multiplier is determined so that the error in the optimum condition is minimized for givenx; for algorithms of Class II, the multiplier is determined so that the constraint is satisfied to first order.Algorithms of Class I have properties (a), (b), (c) and include Algorithms (I-) and (I-). In the former algorithm, the penalty constant is held unchanged for all iterations; in the latter, the penalty constant is updated at each iteration so as to ensure satisfaction of property (d).Algorithms of Class II have properties (a), (c), (e) and include Algorithms (II-) and (II-). In the former algorithm, the penalty constant is held unchanged for all iterations; in the latter, the penalty constant is updated at each iteration so as to ensure satisfaction of property (b).Four numerical examples are presented. They show that algorithms of Class II exhibit faster convergence than algorithms of Class I and that algorithms of type () exhibit faster convergence than algorithms of type (). Therefore, Algorithm (II-) is the best among those analyzed. This is due to the fact that, in Algorithm (II-), individual constraint satisfaction is enforced and that descent properties hold for the augmented penalty function, the augmented function, and the constraint error.This research was supported by the National Science Foundation, Grant No. GP-27271. The authors are indebted to Dr. J. N. Damoulakis for analytical and numerical assistance. Discussions with Professor H. Y. Huang are acknowledged.     

Application of fission track registration technique in the estimation of fissile materials

Analysis of fissile materials in solution by fission track registration technique has been extended to plutonium in solution of its alloys. In these estimations, the results agreed within 1–4% with the average of those obtained by other chemical and instrumental methods like potentiometry, mass-spectrometry and X-ray fluorescence. Some special practical problems encountered in the analysis of plutonium solutions are noted. Various factors affecting the results have been investigated and the necessary precautions for reducing these errors have been indicated. The advantages of the method over some other conventional methods have also been discussed. It is suggested that a source of about 10 μg of²⁵²Cf corresponding to a neutron flux of about 10⁷ n·cm⁻²·sec⁻¹ is ideal for these experiments.     

Allenyl azide cycloaddition chemistry. synthesis of pyrrolidine-containing bicycles and tricycles via the possible intermediacy of azatrimethylenemethane species

Thermolysis of 5-azidoallenes bearing a C(1) methyl group and either an aryl ring or an alkene on C(1) furnishes tricyclic (from the aryl substrates) or bicyclic (from the alkenyl substrates) pyrrolidine products following formal H-CN addition across an intermediate imine. High levels of diastereoselectivity are observed in all cases studied. This reaction cascade presumably passes through unobserved triazoline and azatrimethylenemethane diyl intermediates en route to product.     

Birefringence of native cellulosic fibers. Part II. Spiral structure of cotton

Interferometric studies have been made on cotton fibers as well as on twisted nylon filaments. The results so obtained provide strong evidence that the fibrils in the cotton fiber become less inclined to the fiber axis as one proceeds from the surface to the core. Also, studies on twisted nylon filaments by the fiber refractometer and Becke line techniques indicate that the latter, as practiced in this laboratory, does give values of refractive index which are heavily weighted towards the fiber periphery.     

Allenyl azide cycloaddition chemistry. Synthesis of annelated indoles from 2-(allenyl)phenyl azide substrates

[reaction: see text] Thermolysis of 2-(allenyl)phenyl azides leads to a cascade cyclization sequence furnishing both C(2)-C(3) and N-C(2) cyclopentannelated indoles.