共查询到20条相似文献，搜索用时 31 毫秒
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The states of radiation of a single frequency and polarization propagating in free space are very conveniently represented
by those of a quantum mechanical simple harmonic oscillator. This fact is exploited, together with the Ehrenfest theorem,
to map the time evolution of the radiation to the dynamics of the oscillator. This enables a graphical comparison of the behaviour
of classical and nonclassical states of radiation. 相似文献
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The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori. 相似文献
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B. Sury 《Resonance》2011,16(4):341-355
In this article, we discuss the basic theme of approximating functions by polynomial functions. Although it is exemplified
by the classical theorem of Weierstrass, the theme goes much further. Even on the face of it, the advantage of polynomial
approximations can be seen from the fact that unlike general continuous functions, it is possible to numerically feed polynomial
interpolations of such functions into a computer and the justification that we will be as accurate as we want is provided
by the theorems we discuss. In reality, this theme goes deep into subjects like Fourier series and has applications like separability
of the space of continuous functions. Marshall Stone’s generalisation to compact Hausdorff spaces is natural and important
in mathematics. Applications of the Weierstrass approximation theorem abound in mathematics — to Gaussian quadrature for instance. 相似文献
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Subhashis Nag 《Resonance》1998,3(11):18-29
This article explores the connection between the Archimedes principle in physics and Gauss’s divergence theorem in mathematics. 相似文献
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Dinesh Khurana 《Resonance》2012,17(7):691-693
In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. ??Classroom?? is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. 相似文献
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Bikash Chakraborty 《Resonance》2016,21(7):653-655
In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. 相似文献
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B. Sury 《Resonance》2014,19(4):338-346
In 1937, George Pólya wrote what is considered one of the most significant papers in 20th-century mathematics. The article contained one theorem and 100 pages of applications. It introduced a combinatorial method which led to unexpected applications to diverse problems in science like the enumeration of isomers of chemical compounds. Pólya’s theory of enumeration was discussed in detail in [1] by Shriya Anand, a summer student of the author. In what follows, we briefly recall the theory and complement the earlier article by adding some other applications not discussed there. 相似文献
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WANG Jin-hua LI Chong 《浙江大学学报(A卷英文版)》2007,8(6):978-986
The convergence criterion of Newton＇s method to find the zeros ofa mapffrom a Lie group to its corresponding Lie algebra is established under the assumption thatfsatisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of fare estimated. Owren and Welfert （2000） stated that if the initial point is close sufficiently to a zero off then Newton＇s method on Lie group converges to the zero; while this paper provides a Kantorovich＇s criterion for the convergence of Newton＇s method, not requiring the existence of a zero as a priori. 相似文献
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M. G. Narasimhan 《Resonance》2011,16(6):529-539
Damodar Dharmananda Kosambi (1907–1966) was an eminent mathematician, scientist, innovative Marxist, a maverick scholar, and
historian of contemporary India. Combining both versatility and a certain sense of virtuosity Kosambi made seminal contributions
to a wide variety of disciplines spread across from pure and applied mathematics to archaeology and Indology. In the course
of these writings he provided an incisive analysis of various developments in science and technology and novel perspectives
onmany topics related to mathematics (especially in number theory and statistics), genetics and India’s past history, present
concerns, and future growth. 相似文献
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高中英语中的阅读材料题材多样，体裁各异。从文学角度来分，有小说、戏剧、散文等。但从文章的写作方式上来看，一般都以记叙文、说明文、议论文和应用文为主。演讲稿是属于应用文一类的。对于应用文，学生感觉是比较容易的，因为大多数题目可以直接看题目找答案，但是对于演讲稿，这种方法是不适应的， 相似文献
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“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… 相似文献
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You-shi Liu You-hong Fang Ling-xiang Ruan You-ming Li Lin Li Ling-ling Jiang 《Journal of Zhejiang University. Science. B》2009,10(8):631-634
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.
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Deepanshu Kush 《Resonance》2017,22(9):879-887
The combinatorial problem discussed in this article is very simple to state but needs the algebraic machinery of characters of abelian groups. 相似文献