Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−comple...

where P is a positive definite hermitian matrix and U is a unitary matrix. In this polar representation of the matrix A, as it is called, the two matrices P and U are unique. Since the matrix P is positive definite and nonsingular, it has the same signature as the identity matrix E while the unitary matrix U is a conjunctive automorph of E. From (1) we may deduce a somewhat similar representati...

The eigenproblems of the rank-one updates of the matrices have lots of applications in scientific computation and engineering such as the symmetric tridiagonal eigenproblems by the divide-andconquer method and Web search engine. Many researchers have well studied the algorithms for computing eigenvalues of Hermitian matrices updated by a rank-one matrix [1–6]. Recently, Ding and Zhou studied a ...

Calculating portions of eigenvalues and eigenvectors of matrices or matrix pencils has many applications. An approach to this calculation for Hermitian problems based on a density matrix has been proposed in 2009 and a software package called FEAST has been developed. The density-matrix approach allows FEAST’s implementation to exploit a key strength of modern computer architectures, namely, mu...

We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we ide...

in terms of the Langlands parametrization of Irr(G). More precisely, the Gan-Gross-Prasad triples come from certain pairs W ⊂ V of quadratic spaces or hermitian spaces (over a fixed quadratic extension E/F ). We will denote uniformly by h the underlying quadratic or hermitian form on these spaces. To get a GGP triple, you need the following two conditions to be satisfied : – W⊥ (the orthogonal ...