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Displaying 61 – 80 of 86

On the Singularities of Functions with Values in a Clifford Algebra.

Richard Delanghe (1972)

Mathematische Annalen

$p$ -adic Clifford algebras

Bertin Diarra (1994)

Annales mathématiques Blaise Pascal

Pairs of Clifford algebras of the Hurwitz type

Wiesław Królikowski (1996)

Banach Center Publications

For a given Hurwitz pair $[S (Q_{S}), V (Q_{V}), o]$ the existence of a bilinear mapping $⭑ : C (Q_{S}) \times C (Q_{V}) \to C (Q_{V})$ (where $C (Q_{S})$ and $C (Q_{V}$ ) denote the Clifford algebras of the quadratic forms $Q_{S}$ and $Q_{V}$ , respectively) generated by the Hurwitz multiplication “o” is proved and the counterpart of the Hurwitz condition on the Clifford algebra level is found. Moreover, a necessary and sufficient condition for "⭑" to be generated by the Hurwitz multiplication is shown.

Pfaffians, central simple algebras and similtudes.

R. Sridharan, M.-A. Knus, R. Parimala (1991)

Mathematische Zeitschrift

Plane waves, biregular functions and hypercomplex Fourier analysis

Sommen, F. (1985)

Proceedings of the Winter School "Geometry and Physics"

Quadratic forms and Azumaya algebras.

R. Sridharan, M. Ojanguren, M.A. Knus (1978)

Journal für die reine und angewandte Mathematik

Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»

(1974/1975)

Séminaire Jean Leray

Relativistic wave equations with fractional derivatives and pseudodifferential operators.

Závada, Petr (2002)

Journal of Applied Mathematics

Representations of the covering groups of the symmetric groups and their combinatorics.

Bessenrodt, Christine (1994)

Séminaire Lotharingien de Combinatoire [electronic only]

Résultats récents sur la théorie des formes quadratiques

Artibano Micali (1972/1973)

Séminaire Dubreil. Algèbre et théorie des nombres

Revêtements «spinoriels» du groupe symplectique et indices de Maslov

A. Crumeyrolle (1974/1975)

Séminaire Jean Leray

Some partial differential equations in Clifford analysis

Elena Obolashvili (1996)

Banach Center Publications

Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.

Some sharp $L^{2}$ inequalities for Dirac type operators.

Balinsky, Alexander, Ryan, John (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, $σ \in E n d (V^{\otimes 2})$ be a pre-braid operator and let $F \in l i n (V^{\otimes 2}, ℂ) .$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $C l (V, σ, 0) \equiv V^{\land} (σ)$ . If $σ \neq σ^{- 1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

Structure fractals and para-quaternionic geometry

Julian Ławrynowicz, Massimo Vaccaro (2011)

Annales UMCS, Mathematica

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...

Support vector machine skin lesion classification in Clifford algebra subspaces

Mutlu Akar, Nikolay Metodiev Sirakov (2019)

Applications of Mathematics

The present study develops the Clifford algebra ${Cl}_{5, 0}$ within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the ${Cl}_{5, 0}$ we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto...

Currently displaying 61 – 80 of 86

Previous Page 4 Next

Displaying 61 – 80 of 86

On the Singularities of Functions with Values in a Clifford Algebra.

$p$ -adic Clifford algebras

Pairs of Clifford algebras of the Hurwitz type

Pfaffians, central simple algebras and similtudes.

Plane waves, biregular functions and hypercomplex Fourier analysis

Quadratic forms and Azumaya algebras.

Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»

Relativistic wave equations with fractional derivatives and pseudodifferential operators.

Representations of the covering groups of the symmetric groups and their combinatorics.

Résultats récents sur la théorie des formes quadratiques

Revêtements «spinoriels» du groupe symplectique et indices de Maslov

Some partial differential equations in Clifford analysis

Some sharp $L^{2}$ inequalities for Dirac type operators.

Spinors in braided geometry

Structure fractals and para-quaternionic geometry

Support vector machine skin lesion classification in Clifford algebra subspaces

Sur les algèbres de Clifford. II.

Sur les deux premiers invariants d'une forme quadratique

Sur les idéaux à gauche des algèbres de Clifford et les produits scalaires des spineurs

Sur les n-normes

Currently displaying 61 – 80 of 86