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Dhananjay Shantaram Janorkar - One of the best experts on this subject based on the ideXlab platform.

  • the theorem with regards the definite complete and rational value of circumference of circle 6 283185306o straight diameter 2o goba 3 141592653 from arc radius straight radius 1 047197551 su s j constant
    Social Science Research Network, 2016
    Co-Authors: Dhananjay Shantaram Janorkar
    Abstract:

    “The self-proving theorem of Goba and its explanation on the basis of a formula (Goba Cha Swayamshidha Sidhanta Wa Sutrachya Aadharache Spastikaran, (in Marathi),” which is researched by my father and researcher Late Shri Shantaram Bapurao Janorkar and compiled by me with providing different examples and putting them in scientific and Mathematical Language. While thinking over this research paper prepared by me, I am getting new concepts through this research and that inspires me to do research and prepare research papers on different new subjects. The theorem with regards the definite, complete and rational value of circumference of circle 6.283185306o ÷ straight diameter 2o = Goba 3.141592653 from Arc Radius ÷ Straight Radius = 1.047197551 Su. S. J. Constant, [Kauns Trigha ÷ Saral Trigha = Yenara Sthirank, 1.047197551 Sula.Sha.Ja.Sthiranka Varun, Wartul Parigha 6.283185306o ÷ Saral Vahyas 2o = Goba Chi 3.141592653 Nichit, Purna Wa Parimay Kimath, cha Shidhanta, (In Marathi)], I am putting this formula before the world and I have tried to explain clearly this formula in scientific and Mathematical Language by giving different examples in this research paper.

  • the theorem with regards however small or large the straight radius or arc radius may be the constant 1 047197551 su s j constant arc radius straight radius 1 047197551 su s j constant
    Social Science Research Network, 2016
    Co-Authors: Dhananjay Shantaram Janorkar
    Abstract:

    “The self-proving theorem of Goba and its explanation on the basis of a formula (Goba Cha Swayamshidha Sidhanta Wa Sutrachya Aadharache Spastikaran, (In marathi),” which is researched by my father and researcher Late Shri Shantaram Bapurao Janorkar and compiled by me with providing different examples and putting them in scientific and Mathematical Language. While thinking over this research paper prepared by me, I am getting new concepts through this research and that inspires me to do research and prepare research papers on different new subjects. However small or however large the straight radius and arc radius may be, ‘arc radius divided by straight radius constant = 1.047197551 the Su. S. J. Constant is the same and it can be found from given formula. From this constant it is proved that arc radius is proportionate to straight radius, therefore the circumference of circle is proportionate to the diameter. It has come to my notice and I am putting before the world, The theorem with regards however small or large the straight radius or arc radius may be, the constant 1.047197551 Su. S. J. Constant (Arc Radius ÷ Straight Radius = 1.047197551 Su. S. J. Constant), [Saral Trigha Wa Kauns Trigha Kitihi Lahanath Lahan Aaso Athawa Kitihi Mothyat Mothi Aaso, Kauns Trigha Bhagila Saral Trighecha Sthirank = 1.047197551 Sula.Sha.Ja.Sthirank, Cha Shidhanta, (In Marathi)], and I have tried to explain clearly this formula in scientific and Mathematical Language by giving different examples in this research paper.

Chris Doran - One of the best experts on this subject based on the ideXlab platform.

  • geometric algebra for physicists
    2003
    Co-Authors: Chris Doran, A N Lasenby
    Abstract:

    Geometric algebra is a powerful Mathematical Language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.

  • a unified Mathematical Language for physics and engineering in the 21st century
    Philosophical transactions - Royal Society. Mathematical physical and engineering sciences, 2000
    Co-Authors: Joan Lasenby, A Lasenby, Chris Doran
    Abstract:

    The late 18th and 19th centuries were times of great Mathematical progress. Many new Mathematical systems and Languages were introduced by some of the millennium9greatest mathematicians. Amongst these were the algebras of Clifford and Grassmann. While these algebras caused considerable interest at the time, they were largely abandoned with the introduction of what people saw as a more straightforward and more generally applicable algebra: the vector algebra of Gibbs. This was effectively the end of the search for a unifying Mathematical Language and the beginning of a proliferation of novel algebraic systems, created as and when they were needed; for example, spinor algebra, matrix and tensor algebra, differential forms, etc. In this paper we will chart the resurgence of the algebras of Clifford and Grassmann in the form of a framework known as geometric algebra (GA). Geometric algebra was pioneered in the mid-1960s by the American physicist and mathematician, David Hestenes. It has taken the best part of 40 years but there are signs that his claim that GA is the universal Language for physics and mathematics is now beginning to take a very real form. Throughout the world there are an increasing number of groups who apply GA to a range of problems from many scientific fields. While providing an immensely powerful Mathematical framework in which the most advanced concepts of quantum mechanics, relativity, electromagnetism, etc., can be expressed, it is claimed that GA is also simple enough to be taught to schoolchildren! In this paper we will review the development and recent progress of GA and discuss whether it is indeed the unifying Language for the physics and mathematics of the 21st century. The examples we will use for illustration will be taken from a number of areas of physics and engineering.

Marie Amalric - One of the best experts on this subject based on the ideXlab platform.

Stanislas Dehaene - One of the best experts on this subject based on the ideXlab platform.

Mario Ziman - One of the best experts on this subject based on the ideXlab platform.

  • the Mathematical Language of quantum theory from uncertainty to entanglement
    2012
    Co-Authors: Teiko Heinosaari, Mario Ziman
    Abstract:

    For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on Mathematically precise formulations, the book summarises the relevant mathematics.

  • the Mathematical Language of quantum theory from uncertainty to entanglement
    2012
    Co-Authors: Teiko Heinosaari, Mario Ziman
    Abstract:

    Introduction 1. Hilbert space refresher 2. States and effects 3. Observables 4. Operations and channels 5. Measurement models and instruments 6. Entanglement Bibliography Index.

  • the Mathematical Language of quantum theory
    mlqt, 2012
    Co-Authors: Mario Ziman, Teiko Heinosaari
    Abstract:

    This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instru- ments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on Mathematically precise formulations, the book summarises the relevant mathematics.