- Journal Details
- Format
- Journal
- eISSN
- 2309-5377
- First Published
- 30 Dec 2013
- Publication timeframe
- 2 times per year
- Languages
- English

#### Search

- Open Access

Discrete Correlation of Order 2 of Generalized Rudin-Shapiro Sequences on Alphabets of Arbitrary Size

Page range: 1 - 26

#### Abstract

In 2009, Grant, Shallit, and Stoll [Acta Arith.

#### Keywords

- discrete correlation
- Rudin-Shapiro sequence
- difference matrix
- exponential sums

#### MSC 2010

- 11A63
- 11K31
- 68R15

- Open Access

On the (Vil_{B}_{2}; α ; γ )-Diaphony of the Nets of Type of Zaremba–Halton Constructed in Generalized Number System

_{B}

_{2};

Page range: 27 - 50

#### Abstract

In the present paper the so-called (Vil_{Bs}; α; γ)-diaphony as a quantitative measure for the distribution of sequences and nets is considered. A class of two-dimensional nets _{2}-adic system or Cantor system is introduced and the (Vil_{B2}; α; γ)-diaphony of these nets is studied. The influence of the vector α = (α_{1}, α_{2}) of exponential parameters to the exact order of the (Vil_{B2}; α; γ)-diaphony of the nets _{1} = α_{2}, then the following holds: if 1 < α_{2} < 2 the exact order is 𝒪 (_{2} = 2 the exact order is 𝒪 (_{2} > 2 the exact order is 𝒪 (_{1} > α_{2}, then the following holds: if 1 < α_{2} < 2 the exact order is 𝒪 (_{2} = 2 the exact order is 𝒪 (_{2} > 2 the exact order is 𝒪 (_{ν}, where B_{ν} denotes the number of the points of the nets

#### Keywords

- Diaphony
- Vilenkin function
- Walsh function
- nets of type of Zaremba-Halton
- van der Corput sequence

#### MSC 2010

- 11K06
- 11K31
- 11K36
- 65C05

- Open Access

A Class of Littlewood Polynomials that are Not L ^{α} -Flat

^{α}

Page range: 51 - 74

#### Abstract

We exhibit a class of Littlewood polynomials that are not ^{α}^{α}^{α}^{α}

#### Keywords

- Merit factor
- flat polynomials
- ultraflat polynomials
- Erd˝ os-Newman flatness problem
- Littlewood flatness problem
- digital transmission
- palindromic polynomial
- TurynGolay’s conjecture

#### MSC 2010

- Primary 42A05, 42A55
- Secondary 37A05, 37A30

- Open Access

Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II

Page range: 75 - 92

#### Abstract

Let ^{×}^{e}_{e}

#### Keywords

- Number field
- reduction
- multiplicative order
- arithmetic progression
- density

#### MSC 2010

- Primary: 11R44
- Secondary: 11R45,11R18, 11R21

- Open Access

Notes on the Distribution of Roots Modulo a Prime of a Polynomial III

Page range: 93 - 104

#### Abstract

Let _{1},..., _{n}_{1} ≤··· ≤ _{n} <p_{1}_{n}_{1}_{n}

#### Keywords

- Equidistribution
- polynomial
- roots modulo a prime

#### MSC 2010

- 11K

- Open Access

Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors

Page range: 105 - 142

#### Abstract

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.

#### Keywords

- Mixed distribution
- uniform distribution
- optimal sets
- quantization error
- quantization dimension
- quantization coefficient

#### MSC 2010

- 60Exx
- 94A34