Newton’s contributions to optics

Newton’s epochal work on dynamics and gravitation sometimes tends to eclipse his great contributions to optics. Also, his work in optics is rivalled by equally significant work by his contemporaries, especially Huygens. Yet his creativity is apparent, even in ideas and models in optics that were later abandoned in science. His main areas of interest are theoretical physics and physics education. He has been involved in the science olympiad programme in India from its inception in 1998.     

Algebra and geometry of Hamilton’s quaternions

Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three-dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.     

Ohm’s law, Kirchoff ’s law and the Drunkard’s walk

Recall from Resonance, Vol. 1, No. 7 that when the Drunkard asks: “Will I ever, ever get home again?”, Polya answers: “You can’t miss, just keep going and stay out of 3D!” In this two-part article we show how to look at this question of recurrence and transience of random walks (which was originally asked and solved by George Polya) through electrical networks. In the first part we look at the related electrical networks.     

Ohm’s law, Kirchoff’s law and the Drunkard’s walk

We change gears in this second part of the article and discuss one of the oldest problems in probability theory, viz. the simple random walk. The recurrence and transience of the random walk in different dimensions is later derived using the material from the first part.     

Shopping :Men’s and Women’s

“M en say they hate to shop,”says Zhukin,C ity U niversity of N ewY ork Sociology (社会学) professor. “Y et w hen you ask them deeperquestions,it turns out that they like to shop.M en generally like to shopfor books, m usic and hardw are. But ifyou ask them aboutthe shoppingthey do for books or m usic, they ll say, ‘W ell, thats not shopping.Thats research.’”In other words,what m en and w om en call “buying things”and howthey com plete thattask are different.W om en will wander thr…     

Deconstructing Arsovski’s proof of Snevily’s conjecture

The combinatorial problem discussed in this article is very simple to state but needs the algebraic machinery of characters of abelian groups.     

Takayasu’s arteritis associated with Crohn’s disease

Takayasu’s arteritis (TA), also known as the “pulseless disease,” is a chronic vasculitis of the aorta and aortic branches. TA with Crohn’s disease is rare and has not been documented in China before. In this paper we report on a case of Takayasu’s arteritis associated with concurrent Crohn’s disease. A 17-year-old Chinese male developed upper limb sourness and a sensation of fatigue, and his upper limb pulses were absent. He was diagnosed with TA and underwent an axillary artery bypass with autologous great saphenous vein on the left subclavian artery. After the surgery, he regained the normal blood pressure. This patient also had years of diarrhea and developed an anal canal ulcer, and was diagnosed with inflammatory bowel disease and ulcerative colitis before. Five months after the TA surgery, he was hospitalized for severe stomachache and diarrhea and was finally diagnosed with Crohn’s disease. The possible pathophysiological mechanisms responsible for concurrent existence of TA and Crohn’s disease may be associated with immune disorders, especially autoimmunity.      

Jensen’s和Graham’s等式的推广

本文对Jensen与、Graham等式进行了推广,并得到了恒等式:∑k≤mm+r()kxkym-k=∑k≤m-r()k(-x)k(x+y)m-k.     

Mother’s, father’s regulation and child’s self-regulation in a computer-mediated learning situation

This study has explored the parents’ regulation strategies that were more likely to support children’s self-regulation in learning situations with computers. These strategies have been analysed by means of new grids involving seven categories of behaviour: cognitive strategies relating to identification of objective, exploration of means, attention and evaluation; motivational strategies; and socio-communicative strategies such as joint attention and request. 62 7-year-old children from Quebec families were examined with their mothers and fathers. The children were asked to complete two learning tasks that involved using LOGO software to draw a picture. Results indicated that parents’ regulation varied depending on their gender; a higher directivity was observed in mothers, more specifically through some specific strategies. Analysis of variance on repeated measures showed that, during the session, there was a decrease in the specification of the objective, the initiation of joint attention and of behaviour regulation in parents; and an improvement of the identification of the objective, planning and self-evaluation in children. Correlations between parental regulation and children’s self-regulation strategies indicated positive links concerning strategies relating to joint attention and to motivation; and negative links concerning strategies relating to the exploration of means and evaluation. A good adjustment of the parents’ regulation and the children’s self-regulation correlated positivel with success in the task. Methodological implications are proposed for research and psycho-educative intervention.     

An Interpretation of Ben’s Function in Intensifying Willy’s Tragedy from Aristotle’s Poetics

The play Death of a Salesman is undoubtedly the most influential play of Arthur Miller which depicts a tragic life of Willy Loman, a travelling salesman, induced by his false American Dream of making a fortune out of business. Unlike many other essays focusing on the hero Willy, this one tries to explore Willy’s dead brother Ben’s function in this play so as to demonstrate that Ben plays an important role in Willy’s life by making Willy’s life more tragic in terms of Aristotle’s tragic theory. The first part of the essay illustrates Ben’s importance to Willy and the second part centers on the way Ben pushes Willy to a more tragic situation.