Found 1,346 Documents (Results 1–100)
Quaternion convolutional neural networks: current advances and future directions. (English) Zbl 07912300
Block diagonalization of block circulant quaternion matrices and the fast calculation for T-product of quaternion tensors. (English) Zbl 07909817
A uniform characterization of the octonions and the quaternions using commutators. (English) Zbl 07903874
Nonlinear statics of three-dimensional curved geometrically exact beams by a hierarchal quadrature element method. (English) Zbl 07901023
Incremental quaternion singular value decomposition and its application for low rank quaternion matrix completion. (English) Zbl 07899242
A new structure-preserving algorithm based on the semi-tensor product of matrices for split quaternion matrix LDU decomposition and its applications. (English) Zbl 07890906
Invariant measures on \(p\)-adic Lie groups: the \(p\)-adic quaternion algebra and the Haar integral on the \(p\)-adic rotation groups. (English) Zbl 07880225
Perturbations of group inverses of quaternion tensors under the QT-product. (English) Zbl 1542.15005
Algebraic method for LU decomposition in commutative quaternion based on semi-tensor product of matrices and application to strict image authentication. (English) Zbl 07869365
On subgroup regular sets in Cayley sum graphs. (English) Zbl 07862959
MSC:
05C25
The 2-ruled hypersurfaces in Minkowski 4-space and their constructions via octonions. (English) Zbl 1539.53011
Extending Lasenby’s embedding of octonions in space-time algebra \(Cl(1, 3)\), to all three- and four dimensional Clifford geometric algebras \(Cl(p, q)\), \(n = p + q = 3, 4\). (English) Zbl 1537.15018
A note on polynomial equations over algebras. (English) Zbl 07836111
Reviewer: Joël Kabore (Ouagadougou)
Fixing numbers of graphs with symmetric and generalized quaternion symmetry groups. (English) Zbl 1531.05121
Some generalizations of Springer’s theorem in characteristic two. (English) Zbl 1540.11030
Reviewer: Detlev Hoffmann (Dortmund)
HAQTR: NTRU-like public key. (English) Zbl 1538.94029
MSC:
94A60
An efficient real structure-preserving algorithm for the quaternion weighted least squares problem with equality constraint. (English) Zbl 07886624
Direct methods of solving quaternion matrix equation based on STP. (English) Zbl 1533.15010
Moslehian, Mohammad Sal (ed.), Matrix and operator equations and applications. Cham: Springer. Math. Online First Collect., 185-209 (2023).
Structure preserving quaternion full orthogonalization method with applications. (English) Zbl 07790620
Lie group quaternion attitude-reconstruction of quadrotor UAV. (English) Zbl 1534.70023
Nielsen, Frank (ed.) et al., Geometric science of information. 6th international conference, GSI 2023, St. Malo, France, August 30 – September 1, 2023. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 14072, 3-11 (2023).
Algebraic structures in group-theoretical fusion categories. (English) Zbl 1530.18025
Reviewer: Liu Gongxiang (Nanjing)
Manifolds of Lie-group-valued cocycles and discrete cohomology. (English) Zbl 1540.22049
Reviewer: Chunguang Xia (Xuzhou)
Generalized quaternion algebras. (English) Zbl 07783245
General right-sided orthogonal 2D-planes split quaternionic wave-packet transform. (English) Zbl 1541.42038
Matrix and operator equations and applications. (English) Zbl 1533.15002
Mathematics Online First Collections. Cham: Springer (ISBN 978-3-031-25385-0/hbk; 978-3-031-25388-1/pbk; 978-3-031-25386-7/ebook). x, 765 p. (2023).
The perturbation of the Moore-Penrose inverse of quaternion tensor via the QT-product. (English) Zbl 1525.15003
Units in \(F(C_n \times Q_{12})\) and \(F(C_n \times D_{12})\). (English) Zbl 1535.16044
Reviewer: Leo Margolis (Madrid)
Dual quaternions for the kinematic description of a fish-like propulsion system. (English) Zbl 1523.70003
Splitting of differential quaternion algebras. (English) Zbl 1533.12002
Reviewer: Sergi Simon (Portsmouth)
Efficient iterative method for generalized Sylvester quaternion tensor equation. (English) Zbl 1538.65090
Hurwitz’s lectures on the number theory of quaternions. (English) Zbl 1526.01002
Heritage of European Mathematics. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-011-2/hbk; 978-3-98547-511-7/ebook). xvii, 293 p. (2023).
Reviewer: Franz Lemmermeyer (Jagstzell)
Involutions of \(\mathfrak{sl}(2,k)\) and non-split, three-dimensional simple Lie algebras. (English) Zbl 1521.17019
Reviewer: Dmitry Artamonov (Moskva)
MSC:
17B20
Local-global principle for projective homogeneous spaces of unitary groups. (English) Zbl 1516.11047
Classification of involutive automorphisms and anti-automorphisms of the Lie algebra of quaternions. (English) Zbl 1530.16041
Reviewer: Bijan Davvaz (Yazd)
Hodge operators and exceptional isomorphisms between unitary groups. (English) Zbl 1522.20193
Reviewer: Wilberd van der Kallen (Utrecht)
Approximation strategy based on the T-product for third-order quaternion tensors with application to color video compression. (English) Zbl 1524.65098
Harmonic multi-symplectic Lanczos algorithm for quaternion singular triplets. (English) Zbl 1522.65072
Relation between the row left rank of a quaternion unit gain graph and the rank of its underlying graph. (English) Zbl 1515.05096
Counting intersection numbers of closed geodesics on Shimura curves. (English) Zbl 1536.11090
Reviewer: Salman Abdulali (Greenville)
The \(\eta\)-(anti-)Hermitian solution to a constrained Sylvester-type generalized commutative quaternion matrix equation. (English) Zbl 1515.15013
Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform. (English) Zbl 1517.42010
Reviewer: Nikhil Khanna (Masqaṭ)
Splitting fields of differential symbol algebras. (English) Zbl 1525.12004
Reviewer: Sergi Simon (Portsmouth)
Semigroup algebras which are Azumaya algebras. (English) Zbl 1521.20138
Reviewer: Ulrich Knauer (Oldenburg)
Eigenvalues of quaternion tensors with applications to color video processing. (English) Zbl 1504.15023
Cohomology and deformation theory of \(\mathcal{O}\)-operators on Hom-Lie conformal algebras. arXiv:2312.04121
Preprint, arXiv:2312.04121 [math.RA] (2023).
Hyperpolyadic structures. arXiv:2312.01366
Preprint, arXiv:2312.01366 [math.RA] (2023).
Differential Central Simple Algebras. arXiv:2303.12430
Preprint, arXiv:2303.12430 [math.RA] (2023).
Computing square roots in quaternion algebras. (English) Zbl 07798897
MSC:
68-XX
\(\mathcal{L_C}\) structure-preserving method based on semi-tensor product of matrices for the QR decomposition in quaternionic quantum theory. (English) Zbl 1518.65047
Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform. (English) Zbl 1510.43002
Reviewer: Jinsong Wu (Beijing)
Exponential and logarithm of multivector in low-dimensional \((n = p + q < 3)\) Clifford algebras. (English) Zbl 1502.15016
Hecke operators acting on optimal embeddings in indefinite quaternion algebras. (English) Zbl 1536.11186
On the number of generators of an algebra over a commutative ring. (English) Zbl 1517.16014
Reviewer: Stefaan Caenepeel (Brussels)
Color image inpainting via robust pure quaternion matrix completion: error bound and weighted loss. (English) Zbl 1496.94007
Improved computation of fundamental domains for arithmetic Fuchsian groups. (English) Zbl 1501.11111
The sum and the product of two quadratic matrices: regular cases. (English) Zbl 1497.15013
Reviewer: John D. Dixon (Ottawa)
The algebra of \(2D\) Gabor quaternionic offset linear canonical transform and uncertainty principles: the algebra of \(2D\) Gabor quaternionic offset LCT and uncertainty principles. (English) Zbl 1493.42010
On a problem by Nathan Jacobson. (English) Zbl 1500.17025
Reviewer: Ivan Kaygorodov (Covilhã)
Quaternion quantum neurocomputing. (English) Zbl 1492.81036
MSC:
81P68
The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra. (English) Zbl 1492.15017
Several kinds of special least squares solutions to quaternion matrix equation \(AXB=C\). (English) Zbl 1490.15024
On the Gersten-Witt complex of an Azumaya algebra with involution. (English) Zbl 1493.11083
Reviewer: Stefan Gille (Edmonton)
Decomposition of topological Azumaya algebras. (English) Zbl 1521.16024
Reviewer: William Woods (Essex)
Equivalence between K-functionals and modulus of smoothness on the quaternion algebra. (English) Zbl 1487.42009
On generic \(G\)-graded Azumaya algebras. (English) Zbl 1503.16025
Reviewer: Uzi Vishne (Ramat Gan)
Morita theory for non-commutative Noetherian schemes. (English) Zbl 1498.14003
Reviewer: Wassilij Gnedin (Bochum)
Involutions on sheaves of endomorphisms of locally finitely presented \(\mathscr{O}_X\)-modules. (English) Zbl 1486.16020
Reviewer: Mart Abel (Tartu)
Splitting quaternion algebras defined over a finite field extension. (English) Zbl 1500.12003
Reviewer: Adam Chapman (Tel Hai)
New applications of Clifford’s geometric algebra. (English) Zbl 1490.15036
Reviewer: Morteza Shahpari (Adelaide)
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