Hypercomplex algebras, hypercomplex analysis and conformal invariance
In this paper a complete characterization of hyperreflexive operators on finite dimensional Hilbert spaces is given.
In this paper we reexamine the concept of isostrophy. We connect it to the notion of term equivalence, and describe the action of dihedral groups that are associated with loops by means of isostrophy. We also use it to prove and present in a new way some well known facts on -inverse loops and middle Bol loops.
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward...
Almost completely decomposable groups with a critical typeset of type and a -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient , either no indecomposables if ; only six near isomorphism types of indecomposables if ; and indecomposables of arbitrary large rank if .
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set of all fully indecomposable matrices as a subsemigroup of the semigroup of all Hall matrices over the lattice are given.