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...In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place ...

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...Brightsen Nucleon Cluster Model – F. Smarandache & Dmitri Rabounski (Progress in Physics, vol. 2, www.ptep-online.com) 198 12. Yang-Mills field from Quaternion space geometry, and its Klein-Gordon representation – A. Yefremov, F. Smarandache, V. Christianto (Progress in Physics, vol. 3 no. 3, 2007, www.ptep-online.com) 208 13. Numerical solution of radial biquaternion Kl...

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...e 72 7.1. Relativity theory 72 7.2. Questions related to Modified Bell’s theorem 73 7.3. Mind-matter interaction, hidden mystery of water 77 7.4. Quaternion wave interpretation of superconductor 80 7.5. Solar dynamics 83 7.6. Science of Energy Conservation and Modified Coulomb-Newton Law 85 7.7. Do fundamental constants in Nature vary with time? 96 7.8. Scale invar...

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...orentin Smarandache1 and Vic Christianto, Progress in Physics, 28-30, Vol. 2, 2010. .......................64 A Derivation of Maxwell Equations in Quaternion Space, by Vic Chrisitianto1 and Florentin Smarandache, Progress in Physics, 23-27, Vol. 2, 2010. .................68 An Exact Mapping from Navier-Stokes Equation to Schrödinger Equation via Riccati Equation, by...

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...hrödinger Equation with PT-Symmetric Periodic Potential, and its Gamow Integral, by V. Christianto & F. Smarandache .............686 86. Generalized Quaternion Quantum Electrodynamics from Ginzburg-Landau Schrödinger type Equation, proposed research abstract, by V. Christianto, F. Smarandache ......................................694 87. Unleashing the Quark within: LENR...

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...hrödinger Equation with PT-Symmetric Periodic Potential, and its Gamow Integral, by V. Christianto & F. Smarandache .............686 86. Generalized Quaternion Quantum Electrodynamics from Ginzburg-Landau Schrödinger type Equation, proposed research abstract, by V. Christianto, F. Smarandache ......................................694 87. Unleashing the Quark within: LENR...

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...of H; x 2 = e. (iii) If x, y are in H and (x, y) ≠ e and x, y generate a quaternion group. (iv) If x, y, z are in H and (x, y, z) ≠ 1 then (x, y, z... ...z for which (x, y, z) = 1 are contained in a subgroup then H is either a quaternion group or a Cayley group. We define CA-loop, inner commutative l... ...8 normal subgroup, 11, 14, 53, 80-81, 93-95, 98-99, 110 normalizer, 9 quaternion group, 24 subgroup, 7, 9-11, 14, 19-21, 24, 36-37, 39, 47-48, 5... ... 27, 67 Pseudo commutative loop, 26, 61 Pseudo commutator, 26 Q Quaternion group, see Group, quaternion 124 R RALT-loop, 20 Rel...

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...an rings refer [15]. The reader may just recall the concept of integral quaternions which was introduced in section 2.1. Now we introduce the conc... ... = –1 = ijk, ij = – ji = k, jk = – kj = i, ki = –ik = j} be the ring of quaternions. Clearly QR is a S-commutative ring II and QR is also a S-ri... ...ht set of R. 112 Now we proceed on to define the concept of finite quaternion rings and skew fields as this concept would help in defining in... ... identity with respect to '.'. Now P is a ring called the ring of real quaternion of characteristic n i n a finite prime. If n is a composite nu... ...niv., Vol. 22, 123-125, (2000). 149. Vasantha Kandasamy W.B., On finite quaternion rings and skew fields, Acta Cienca Indica, Vol. XXIV, 133-135, ... ...er, 133 Quasi semi commutator, 133 Quasi semi commutative ring, 133-134 Quaternion, 32, 39, 112, 210 Quotient ring, 21, 28-29, 34, 62-63, 104, ... ...ing, see Quotient ring ring homomorphism, see Homomorphism ring of quaternions, 39 ring with A.C.C, see Chain condition ring with D.C.C, s...

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...tion which is known as the Dirac-Hestenes equation. Dirac’s equation using quaternions (related to Clifford algebras) was frst derived by Lanczos [91]... ... e. the choice of the spin quantization axis in the original Dirac-Lanczos quaternionic equation. How is such preferred orientation (spin quantization... ... Hopf quantum Clifford algebras [86], hypercomplex ex- tensions of QM like quaternionic and octonionic QM [99], [97], [98], exceptional group extensio... ...ikalische Zeitschrift, B. 31, 1930, 120–130. 92. Gursey F. Applications of quaternions to feld equations. Ph. D. thesis, University of London, 1950, 2... ...d Shiri- Garakaui M. Found. Phys., v. 33, 2003, 1267–1275. 97. Adler S. L. Quaternionic Quantum Mechanics and quantum felds. Oxford Univ. Press, New Y...

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...vision ring. Example 6.1.12: Let R = Z 3 ∪ Q' where Q' is the ring of quaternions and Z 3 = {0, 1, 2} prime field of characteristic 3. Clearly ...

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...when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him ...

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...r- riages derived from the reign of Charles II) that they, the illustrious quaternion, constituted a porcelain variety of the human race, whose dignit...

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...lic car- riages from the reign of Charles II.,) that they, the illustrious quaternion, constituted a porcelain variety of the human race, whose dignit...

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...tion, which often became ri- diculous from his misarranging the triads and quaternions with which he loaded his sentences. T o this personage Glossin ...

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...d, the others took Their treasure, swift or slow. At th’ other wheel, A band quaternion, each in purple clad, The Divine Comedy of Dante Purgatory ... ...en, Lord! are come!”responsive thus, The trinal now, and now the virgin band Quaternion, their sweet psalmody began, Weeping; and Beatrice listen’d, s... ...ements to hope must arise either from one or other of these. v. 125. A band quaternion.] The four moral or cardinal virtues, of whom Prudence direct...

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...d, the others took Their treasure, swift or slow. At th’ other wheel, A band quaternion, each in purple clad, Advanc’d with festal step, as of them on... ...en, Lord! are come!”responsive thus, The trinal now, and now the virgin band Quaternion, their sweet psalmody began, Weeping; and Beatrice listen’d, s... ...ements to hope must arise either from one or other of these. v. 125. A band quaternion.] The four moral or cardinal virtues, of whom Prudence direct...

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...rmined to fight himself through his inadvertency, rather than break up his quaternion of cases. ‘In speaking of Romanism as arising from a misapplicat...

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...’d up Light. Aire, and ye Elements the eldest birth Of Natures Womb, that in quaternion run Perpetual Circle, multiform; and mix And nourish all thing...

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...ight. Aire, and ye Elements the eldest birth 180 Of Natures Womb, that in quaternion run Perpetual Circle, multiform; and mix And nourish all t...

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... by geometry, by analytical geom- etry, by algebra, by the calculus, or by quaternions, and each time come out right? On this view religion and scienc...