Keywords: Maxwell equations; Quantum mechanics; Dirac equation' Klein-Gordon equation; Lorentz transformations; New formalism; Quaternions;
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Keywords: Attitude parameters; Attitude kinematics; Rotational transformation; Coning motion; Quaternions; Euler angles;
Keywords: 15A86; 15A60; Quantum states; Density operators; Convex functions; Von Neumann entropy; Preservers; Quaternions;
Keywords: Interference; Interferometric propagation; Probability amplitude; Quantum communications; Quantum entanglement; Quaternions;
Keywords: 17B62; 17B37; 11E04; 11E10; 11E25; Lie bialgebra; Compact type; Quantum group; Belavin-Drinfeld cohomology; Pfister form; Quaternions; Brauer group;
Keywords: Fredholm's equation; Functional equation of proportionality; Real; Complex; Quaternions; Octonions;
Keywords: Orientation control; Exceptional algebras; Quaternions; Fractal surface;
Keywords: Fingerprinting; Quaternions; Joint fingerprinting and decryption; Collusion attack; Traitor tracing
Keywords: Euler-Rodrigues formula; Quaternions; Exponential map; Lie groups; Lie algebras; Kinematics;
Keywords: 62G15; 62E20; 62P30Influence function; Orientation data; Pivotal bootstrap; Projected arithmetic mean; Quaternions
Keywords: Rotational spinning process; Viscous fiber; Special Cosserat theory; Partial differential algebraic equations; Quaternions; Finite volume scheme
Keywords: Isotropic elasticity; Quaternions; Monogenic potential; Meshless; Residual stress; Thermal load;
Keywords: Newton method; Quaternions; Radial derivative
Keywords: Pythagorean-hodograph; Rational curves; Dual parametric curve form; Frenet frame; Quaternions
Keywords: Rotation-minimizing frames; Pythagorean-hodograph curves; Quaternions; Angular velocity; Rigid body motion; Ruled surfaces
Keywords: Deductive program verification; Automated theorem proving; Floating-point computations; Quaternions
Weyl and Browder S-spectra in a right quaternionic Hilbert space
Keywords: primary; 47A10; 47A53; 47B07; Quaternions; Quaternionic Hilbert spaces; S-spectrum; Weyl S-spectrum; Browder operator;
Generating five-dimensional Myers-Perry black hole solution using quaternions
Keywords: Myers-Perry black holes; Newman-Janis algorithm; Giampieri's simplification; Quaternions;
S-Spectrum and the quaternionic Cayley transform of an operator
Keywords: primary; 81R30; 46E22; Quaternions; Quaternionic Hilbert spaces; Symmetric operator; Cayley transform; S-spectrum;
A finite element/quaternion/asymptotic numerical method for the 3D simulation of flexible cables
Keywords: Cables; Finite element method; Asymptotic numerical method; Quaternions;
Pseudo-simple heteroclinic cycles in R4
Keywords: Equivariant dynamics; Quaternions; Heteroclinic cycle; Periodic orbit; Stability;
A novel kinematics analysis method using quaternion interpolation-a case study in frog jumping
Keywords: Frogs; Jumping; Kinematics; Simulation; Forward kinematics; Quaternions; Spherical linear interpolation;
A new quaternion based kinematic model for the operation and the identification of an articulated arm coordinate measuring machine inspired by the geodetic methodology
Keywords: AACMM; Identification; Quaternions; Least-squares;
Further investigation of the six-DOF hollow gravity anchor: Impact of the internal slant angle
Keywords: Hollow gravity anchor; Dynamic mesh update method; Six-DOF; Quaternions;
Quaternion-based disorientation coloring of orientation maps
Keywords: Electron backscatter diffraction (EBSD); Disorientations; Quaternions; Deformation; Strain;
Quaternions and joint angles in an analysis of local stability of gait for different variants of walking speed and treadmill slope
Keywords: Nonlinear time series analysis; Phase space reconstruction; Deterministic chaos; Human gait analysis; Local dynamic stability; Quaternions; Joint angles;
Interpolation of three dimensional kinematics with dual-quaternions
Keywords: 3D; Three Dimensional; CT; Computed Tomography; DQHAM; HAM with Dual-quaternion; FD; Finite Difference; HAM; Helical axis of motion; HFZ; High Flexibility Zone; HSZ; High Stiffness Zone; NME; Normalized Maximum Error; NRMSE; Normalized Root Mean Square Er
Quaternionic B-splines
Keywords: 15A66; 30G35; 65D07; 42C40; Quaternions; B-splines; Clifford algebra; Quaternionic binomial; Quaternionic Gamma function; Multiresolution analysis;
Frequency domain quaternion adaptive filters: Algorithms and convergence performance
Keywords: Adaptive Filters; Frequency Domain; Hypercomplex; Quaternions; Quaternion-Valued Adaptive Filtering;
Singularities of slice regular functions over real alternative â-algebras
Keywords: Slice regular functions; Quaternions; Alternative *-algebras; Power series and expansions; Laurent series and expansions; Spherical series and expansions; Singularities; Semiregular functions;
A uniform estimate for general quaternionic Calabi problem (with appendix by Daniel Barlet)
Keywords: Monge-Ampère equation; Quaternions; HKT-manifolds;
On a new generalization of Fibonacci quaternions
Keywords: Fibonacci sequence; Generalized Fibonacci sequence; Recurrence relations; Quaternions; 11B39; 05A15; 11R52;
Rational rotation-minimizing frames—Recent advances and open problems
Keywords: Rotation-minimizing frame; Pythagorean-hodograph curve; Angular velocity; Quaternions; Hopf map; Spatial motion design
Dual Cayley-Klein parameters and Möbius transform: Theory and applications
Keywords: Clifford algebra; Cayley-Klein parameters; Quaternions; Kinematics;
A quaternion approach to polynomial PN surfaces
Keywords: Pythagorean-normal surfaces; Pythagorean-hodograph; Quaternions; Minimal surfaces;
R3DG features: Relative 3D geometry-based skeletal representations for human action recognition
Keywords: Action recognition; Skeletal representations; Lie groups; Special orthogonal group; Special Euclidean group; Quaternions; Dual quaternions;
Representation of Dupin cyclides using quaternions
Keywords: Dupin cyclide; Quaternions; Implicitization; Willmore energy
Symmetry and quaternionic integrable systems
Keywords: Integrable systems; Quaternions; Hyperkahler manifolds; Symmetry
S-spectrum and associated continuous frames on quaternionic Hilbert spaces
Keywords: primary, 42C40, 42C15S-spectrum; Quaternions; Quaternion Hilbert spaces; Frames
On the solutions of the quaternion interval systems [x]=[A][x]+[b][x]=[A][x]+[b]
Keywords: Intervals; Quaternions; The systems of equations
Corrigendum to “Rational rotation-minimizing frames on polynomial space curves of arbitrary degree” [J. Symbolic Comput. 45 (8) (2010) 844-856]
Keywords: Rotation-minimizing frames; Pythagorean-hodograph curves; Spatial motion planning; Quaternions; Polynomial identities;
Boundary identification in EBSD data with a generalization of fast multiscale clustering
Keywords: Electron backscatter diffraction; Quaternions; Fast multiscale clustering; Mahalanobis distance; Clustering;
Solvability of the quaternionic Monge–Ampère equation on compact manifolds with a flat hyperKähler metric
Keywords: Quaternions; Monge–Ampère equations; Calabi type problem
A Quaternion-Based LOS Guidance Scheme for Path Following of AUVs
Keywords: Autonomous underwater vehicles; path following; LOS guidance; quaternions
Modified firefly algorithm using quaternion representation
Keywords: Quaternions; Representation of individuals; Firefly algorithm; Optimization
On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme
Keywords: Pythagorean Hodograph; Quaternions; Hermite interpolation
Corisco: Robust edgel-based orientation estimation for generic camera models
Keywords: Grid mask; Edgels; Orientation estimation; Omnidirectional vision; Monocular vision; Quaternions
Algorithms for quaternion polynomial root-finding
Keywords: Quaternions; Polynomial roots; Fundamental theorem of algebra; Newton’s method; Recurrence relation; Polynomiography
Continuation of equilibria and stability of slender elastic rods using an asymptotic numerical method
Keywords: Elastic rods; Quaternions; Path-following techniques; Equilibrium; Stability
On the stability and stabilization of quaternion equilibria of rigid bodies
Keywords: Quaternions; Output feedback; Density functions; Rigid body