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      Volume 21, Issue 12

      December 2016,   pages  1063-1153

    • Editorial

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    • Hermann Weyl (1885-1955): Mathematician, Physicist, Philosopher and Poet

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    • Science Smiles

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    • Hermann Weyl and Representation Theory

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      Weyl was a universal mathematician whose fundamental contributionsto mathematics encompassed all areas, and provideda unification seldom seen. His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on the infinitesimal, and he strove to bringin a global perspective. Time and again, Weyl’s ideas arisingin one context have been adapted and applied to wholly newcontexts. In 1925–26, Weyl wrote four epochal papers in representationtheory of Lie groups which solved fundamentalproblems, and also gave birth to the subject of harmonic analysisof semisimple Lie groups. In these papers, Weyl provedcomplete reducibility theorems and introduced many techniqueswhich have become the standard way to study representationsof Lie groups and their various generalizationsin the last seven decades. Weyl’s work covers several parts ofmathematics, as well as parts of physics. In this article, wediscuss mainly his contributions to the representation theoryof Lie groups via the four papers mentioned above.

    • Mycorrhiza: The Oldest Association Between Plant and Fungi

      Jagnaseni Barman Aveek Samanta Babita Saha Siraj Datta

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      The symbiotic association between plant and fungi (mycorrhizalassociation) is an amazing phenomenon observed innature. The mycorrhizal association is one of nature’s boonsfor sustainable agriculture. In today’s changing environment,indiscriminate use of pesticides and chemicals pose a greatthreat to the existence of mycorrhizal species. There is a needto spread awareness in order to save mycorrhizal fungi fromextinction.

    • Geometry of Spin: Clifford Algebraic Approach

      Rukhsan-Ul-Haq

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      Spin is a fundamental degree of freedom of matter and radiation.In quantum theory, spin is represented by Pauli matrices.Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a geometrical and henceintuitive way to understand quantum theory of spin, and isa natural formalism to study spin. Clifford algebraic formalismhas lot of applications in every field where spin plays animportant role.

    • The Arithmetic Mean - Geometric Mean - Harmonic Mean: Inequalities and a Spectrum of Applications

      Prithwijit De

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      The Arithmetic Mean – Geometric Mean – Harmonic Meaninequality, AM–GM–HM inequality in short, is one of thefundamental inequalities in Algebra, and it is used extensivelyin olympiad mathematics to solve many problems. Theaim of this article is to acquaint students with the inequality,its proof and various applications.

    • Tables Turned: Physics in the Service of Mathematics

      J Madhusudana Rao T V N Prasanna

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      E T Bell, the famous author of ‘Men of Mathematics’, hasdescribed mathematics as the ‘Queen of Arts and Servant ofScience’. What he meant is that mathematics serves scienceby entering into the picture as soon as a proper mathematicalmodel is set up by the scientist, and then after a purely mathematicalanalysis of the model, the final mathematical step isinterpreted scientifically. The purpose of the present articleis to convince the readers that sometimes the roles of scienceand mathematics are reversed, and a mathematical problemis interpreted as a physics problem; the laws of physics areutilized for a physical analysis, and the final result of thephysical analysis is interpreted mathematically. We shall illustratethis by means of few examples.

    • Science Academies' Refresher Course in Experimental Physics

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    • Aphananthe cuspidata

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