Certain subdirect sums of finite prime fields

Subdirect Sums of Rings

Structure of finite wavelet frames over prime fields

‎This article presents a systematic study for structure of finite wavelet frames‎ ‎over prime fields‎. ‎Let $p$ be a positive prime integer and $mathbb{W}_p$‎ ‎be the finite wavelet group over the prime field $mathbb{Z}_p$‎. ‎We study theoretical frame aspects of finite wavelet systems generated by‎ ‎subgroups of the finite wavelet group $mathbb{W}_p$.

Character Sums in Finite Fields

Let F q be a finite field of order q with q = p n , where p is a prime. A multiplicative character χ is a homomorphism from the multiplicative group F * q , ·· to the unit circle. In this note we will mostly give a survey of work on bounds for the character sum x χ(x) over a subset of F q. In Section 5 we give a nontrivial estimate of character sums over subspaces of finite fields. §1. Burgess'...

On eigenvalues and eigenvectors of subdirect sums

Some new properties of the eigenvalues of the subdirect sums are presented for the particular case of 1-subdirect sums. In particular, it is shown that if an eigenvalue λ is associated with certain blocks of matrix A or matrix B then λ is also an eigenvalue associated with the 1-subdirect sum A ⊕1 B. Some results concerning eigenvectors of the k-subdirect sum A⊕k B for an arbitrary positive int...

Subdirect sums of doubly diagonally dominant matrices

The problem of when the k-subdirect sum of a doubly diagonally dominant matrix (DDD matrix) is also a DDD matrix is studied. Some sufficient conditions are given. The same situation is analyzed for diagonally dominant matrices and strictly diagonally dominant matrices. Additionally, some conditions are also derived when card(S)>card(S1) which was not studied by Bru, Pedroche and Szyld [Electron...