Studies on the Dd antigen-antibody system. I. The nature of antigen Dd and its antibodies

Summary The nature of antigen Dd, an antigen present in the extracts of human dandruff which precipitates human sera selectively, and antibodies reacting with it are reported.This work was supported through U.G.C. Grant No. F.23-230/75/SR II. H.K. participated in this study, first as J.R.F. of U.G.C. and then as S.R.F. of I.C.M.R. We are grateful to Dr Baruch S. Blumberg for his invaluable suggestions and to Professor H. Walter for the gift of IgG, IgM and IgA immune sera.     

A study of macromolecular diffusion through native porcine mucus.

A diffusion chamber technique based on time-lag analysis for the estimation of effective diffusion coefficients of radiolabelled macromolecules of varying molecular weights through native mucus gel is reported. For all solutes studied, a reduction in effective diffusion coefficients was observed with a retardation of solute flux in both aqueous and mucus layers. Over the molecular weight range of solutes investigated (126-186,000 Daltons), a consistent effect of molecular weight was evident with regard to the retarding effect of mucus. No apparent or absolute molecular weight cut-off for macromolecular transfer was exhibited. However, at high molecular weights (greater than 30,000 Daltons) the retardation was greatly enhanced. The results confirm that mucus can be regarded as a gel with finite pores, but that it does not constitute an absolute barrier to even high molecular weight solutes.     

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method.     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

STABILITY CRITERIA FOR A CLASS OF UNCERTAINSYSTEMS WITH TIME—DELAY

Some stability criteria are obtained for a class of uncertain systems with time-delay usingLyapunov functional and analytic techniques. It is easy to check the criteria by making use of theboundedness of the uncertainties.     

Technical Notes ：STUDIES ON THE VALUE OF SECONDARY MARKET TO THE SUPPLY CHAIN

This paper investigates the impact of a secondary market, where retailers can buy and sell excessinventories, on the supply chain. We develop a two-period model with a single manufacturer and tworetailers. At the beginning of the first period the retailers order and receive products from themanufacturer, but at the beginning of the second period, they can trade surplus products betweenthemselves in the secondary market. We investigate the impact of the correlated dependence ofretailers' demand on both the quantity effect and the allocation effect under the secondary market.Lastly,we study potential strategies for the manufacturer to increase sales with the existence of thesecondary market.     

Non-Minimum Phase Nonlinear System Predictive Control Based on Local Recurrent Neural Networks

Abstract: After a recursive multi-step-ahead predictor for nonlinear systems based on local recurrent neural networks isintroduced, an intelligent PID controller is adopted to correct the errors including identified model errors and accumulatederrors produced in the recursive process. Characterized by predictive control, this method can achieve a good controlaccuracy and has good robustness. A simulation study shows that this control algorithm is very effective.     

Dynamic Characteristics of Inter-Satellite Links in LEO Networks

To establish an efficient inter-satellite link (ISL) in an LEO network, the effect of geometric characteristics of ISL on the ISLs and the devices on the LEO satellite should be examined. Because of the continuous movement of the LEO satellite, the time-varying behaviours of the ISL's geometric charactersistics continuously change with the changes of the satellite's position on the orbit. These dynamic geometric characteristics of the ISLs are important for ISL's performance analyzing and the design of the devices on the LEO satellite. This paper describes dynamic geometric characteristics of ISL, analyzes the impact of these regulations on the tracking system of the satellite's antenna and the power adjusting system of the satellite's transmitter, with the Iridium system as an example.