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      Mechanical EngineeringAerospace EngineeringMeasurement ErrorPose Estimation
Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conjectures about their rationality properties. Moreover, if K... more
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      Number TheoryAlgebraic GeometryPure MathematicsElliptic Curve Cryptography
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      Dirac equationClifford algebraQuaternion Algebra
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      Degree of FreedomQuaternion Algebra
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      EngineeringAlgebraModelingFinite element method
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      Mechanical EngineeringAlgebraSensitivity AnalysisMeasurement Errors
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      Pure MathematicsQuaternion Algebra
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      MathematicsAlgorithmsDentistryBiomedical Engineering
Aragona-Fernadez-Juriaans showed that a generalized holomorphic function has a power series. This is one of the ingredients use to prove the identity theorem.
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      Mathematical AnalysisPower SeriesBoolean SatisfiabilityContemporary Mathematics
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      Number TheoryAlgebraic GeometryPure MathematicsStability of Functional Equation
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      MathematicsGroup Ring TheoryPure MathematicsNon-commutative Geometry
Let f be a modular eigenform of even weight k>0 and new at a prime p dividing exactly the level, with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D_FM(f) and an... more
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      Number TheoryAlgebraic GeometryStability of Functional EquationLocal Cohomology
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      Non-commutative GeometryPublic key cryptographyMulti DimensionalQuaternion Algebra
In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence... more
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      Linear EquationsQuaternion Algebra
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      MathematicsNumber TheoryInformation TheoryFace
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra... more
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      MathematicsLie AlgebraPhysicsPure Mathematics
Is "Gravity" a deformation of "Electromagnetism"? Deformation theory suggests quantizing Special Relativity: formulate Quantum Information Dynamics SL(2,C)_h-gauge theory of dynamical lattices, with unifying gauge... more
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      PhysicsQuantum InformationSpecial RelativityGauge theory
In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence... more
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      Linear EquationsQuaternion Algebra
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      Number TheoryDifferential GeometryPure MathematicsFuchsian group
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      Computer ArithmeticDifferential GeometryFinite VolumeQuaternion Algebra
Abstract. It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a number field of bounded degree. We explore this conjecture when restricted to... more
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      Elliptic Curve CryptographyQuaternion Algebra
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      Number TheoryAlgebraic GeometryPure MathematicsIndexation
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal... more
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      MathematicsPhysicsPure MathematicsQuaternion
I consider differential of mapping f of continuous division ring as linear mapping the most close to mapping f. Different expressions which correspond to known deffinition of derivative are supplementary. I explore the Gateaux derivative... more
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      Taylor SeriesDifferential equationQuaternion AlgebraHigher order
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      MathematicsInverse ProblemsInverse KinematicsIndustrial Robots
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      HumansSpace flightMovementEye Movements
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      Applied MathematicsMatrix TheoryPort Hamiltonian systemQuaternion Algebra
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      AlgebraGroup Ring TheoryPure MathematicsFree Group
We propose an algebraic framework for studying coherent space-time codes, based on arithmetic lattices on central simple algebras. For two transmit antennas, this algebra is called a quaternion algebra. For this reason, we call these... more
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      AlgebraArithmeticQuaternion Algebra
Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as $E^{3}$ (Euclidean 3-space), $H^{3}$ (hyperbolic 3-space) and $ E^{2,1}$ (Minkowski 3-space), using quaternion algebra theory, are... more
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      Pure MathematicsRepresentation TheoryRepresentationSpace Use
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      Associative AlgebraBoundary ConditionQuaternion Algebra
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      Mathematical AnalysisPower SeriesBoolean SatisfiabilityContemporary Mathematics
The basics on the arithmetic on quaternion algebras is introduced: (maximal) orders, (principal) ideals, (reduced) norm/discriminant, ideal classes, etc.
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    • Quaternion Algebra
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      MathematicsPure MathematicsQuaternion Algebra
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      MathematicsLie AlgebraPhysicsPure Mathematics
In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence... more
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      MathematicsLinear EquationsQuaternion Algebra
We give a simplified and a direct proof of a special case of Ratner's theorem on closures and uniform distribution of individual orbits of unipotent flows; namely, the case of orbits of the diagonally embedded unipotent subgroup acting on... more
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      Number TheoryRepresentation TheoryLocally Compact GroupsQuaternion Algebra
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      Lie AlgebraPure MathematicsEdge ColoringQuaternion Algebra
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      Algebraic GeometryDifferential GeometryPure MathematicsAlgebraic Variety
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      Quantum InformationSpecial RelativityGauge theoryFine Structure Constant
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      Algebraic Number TheoryFuchsian groupQuaternion AlgebraAnalysis on Manifolds
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      GeophysicsFractureMolecular DynamicsSimulation
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      GeophysicsFractureMolecular DynamicsSimulation
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      Quantum ChemistryParticle PhysicsTHEORETICAL AND COMPUTATIONAL CHEMISTRYQuaternion Algebra
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      EngineeringChemical PhysicsPhysical sciencesCHEMICAL SCIENCES
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      Pure MathematicsEJCHamming weightQuaternion Algebra
We give a simplified and a direct proof of a special case of Ratner's theorem on closures and uniform distribution of individual orbits of unipotent flows; namely, the case of orbits of the diagonally embedded unipotent subgroup... more
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      MathematicsNumber TheoryRepresentation TheoryLocally Compact Groups
In this paper, we analyze the performance of an Algebraic Space Time Codes (ASTC), called the Golden code. Due to its Algebraic construction based on Quaternionic algebra, the code has a full rate, full diversity, non-vanishing constant... more
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      AlgebraComputer ScienceLeast squares estimationChannel Estimation
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      MathematicsAlgebraKinematicsInverse Kinematics
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      Non-commutative GeometryPublic key cryptographyMulti DimensionalQuaternion Algebra