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1.         Atmospheric and solar neutrino experiments favour neutrino oscillations, non-zero neutrino masses and lepton flavour mixing resulting CP violation in lepton sector which could possibly be explained in beyond standard gauge models. A typical texture of neutrino mass matrix could be achieved in the  left-right-symmetric gauge model with horizontal flavour chiral. More interestingly, CP violation in the lepton sector arises at TeV scale at tree level due to the exchange of horizontal gauge bosons exclusively paving the way for the experimentalists to look for new particles in forthcoming Large Hadron Collider experiments (RSP/PHY/KB-01/2015).

2.         Minimization of the Higgs potential, containing minimal interacting Higgs fields in a left-right-symmetric gauge model with SU(2)H horizontal symmetry confirms a particular  texture of lepton mass matrices with normal hierarchy of lepton masses, in particular, neutrino masses. The mixing matrix in the lepton sector is complex with non-vanishing phase factor. The phase term could never be rotated away resulting soft CP violation in the lepton sector. Furthermore, CP violation in the lepton sector arises at tree level due to horizontal gauge bosons only where as contributions from WL – WR mixing factor, lepton –Higgs coupling phase factor have been suppressed in the model. Thus, non-zero neutrino mass and non-diagonal lepton mixing matrix could be confirmed in the model from minimization of the  Higgs fields and heavy right-handed neutrinos are excluded in since their masses are connected to the breaking of SU(2)H symmetry. Higgs mass in the model is around 1TeV which could be interesting in NON SUSY GAUGE MODELS (RSP/PHY/KB-02/2015).

3.         The Eightfold scheme invented by Gell-Mann explained a strange feature of certain particles which appeared to be easily produced in cosmic radiation and accelerator reactions, but decayed slowly, as if something were hindering their decays. Meson octet and Baryon octet fit exactly to the “Eightfold way”. Great emphasis is put on the practical/experimental aspect, because it is only through practice that one can attain a higher level of understanding and finally get the concept of basic building blocks of particles i.e., quarks for Meson-(quark-anti quark system) and Baryon-(three quark system) octets and Nirvana in Buddhism. The eight aspects of the path are not to be understood as a sequence of single steps, instead they are highly interdependent principles that have to be seen in relationship with each other in both cases. This establishes that Basic Science and Philosophy are subsets of a set (Proc. Of  UGC (ERO) Sponsored National Seminar on Buddhist Philosophy at SSLNTM Mahavidyalya, Dhanbad,Dec.18-19,2014). 

4.         The evolution from scientific reductionism to monistic idealism, known so far as Advaita Vedanta, depends on the assumption that consciousness, not matter, is the building block of our universe. The fact of the matter is that matter is no longer a fact. This new paradigm for the working of human consciousness, if understood, has enormous epistemological repercussions and must change our views about our impact on the immanent world. Quantum physics is the link, the bridge, over the century-old chasm between science and religions, it is the “science of transcendence” we have been waiting for. The philosophy of Vedanta could only be realized if Quantum postulates are understood and the eternal phenomena could be well explained in the domain of both non-relativistic and relativistic Quantum mechanics subject to the understanding of space-time dimension or beyond it i.e., manifold dimension system (Proc. Of  UGC (ERO) Sponsored National Seminar on Vedanta Philosophy at SSLNTM Mahavidyalya, Dhanbad,Jan.22-23,2015).




Ref: Presented in An Interdisciplinary National Seminar on Vedanta philosophy (22nd and 23rd January 2015).

Highlight:        History of Mathematics reflect its Development step wise from Ancient Mathematics to Modern Mathematics and its wide applications to the interdisciplinary subjects as well as to the society from counting of numbers, Integers, Rational numbers, Real and Complex number,  Irrational numbers, Pythagoren Triangles, Diaphontine equations, Trigonometric function, Calculus, Probability(Statistics) etc. to applied mathematics computer development and Number theory.

            None can differ that when Indian mathematician were contributing the major basic problems, Kerala school of astronomy and mathematics founded by Madhava of sanganagrama in Kerala between 14 and 16th centuries, Trigonometric function given in Sanskrit “Tantra Sangrah” (sine, cosine and inverse tangent) in Malayalam Yuktibhasa like such several basic work had been investigated had not received proper recognition in proper time. Surely this ignorance harassed the Indian mathematician.

            But at present if we highlight the ancient mathematics (some one are usually/really saying Vedic Mathematics) as politically influenced or ignorance of the out come in near future. The student of Mathematics inclination towards Vedic Mathematics can deviate them from Sir Isacc Newton and G. Lebniz invention of Calculus which is most interesting and wide useful for modern age which gives the accurate calculation for astronomical constraint (Solar Eclipse, Lunar Eclipse etc.).

            So, my suggestion to encourage the Indian mathematicians by developing infrastructure and other facilities provided to research worker as well as students rather than to Indanise the Mathematics (Vedic mathematics).


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