Quasi-Affine Transformation in Higher Dimension

Quasi-Affine Transformation in 3-D: Theory and Algorithms

In many applications and in many fields, algorithms can considerably be speed up if the underlying arithmetical computations are considered carefully. In this article, we present a theoretical analysis of affine transformations in dimension 3. More precisely, we investigate the arithmetical paving induced by the transformation to design fast algorithms.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Characterizing Global Minimizers of the Difference of Two Positive Valued Affine Increasing and Co-radiant Functions

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

On Falconer’s Formula for the Generalized Rényi Dimension of a Self-affine Measure

We investigate a formula of Falconer which describes the typical value of the generalised Rényi dimension, or generalised q-dimension, of a self-affine measure in terms of the linear components of the affinities. We show that in contrast to a related formula for the Hausdorff dimension of a typical self-affine set, the value of the generalised q-dimension predicted by Falconer’s formula varies ...

Two-Dimension Chaotic-Multivariate Signature System

A novel hybrid cryptosystem which is resistant to quantum algorithm is developed. The system is combined with multivariate cryptosystem and chaotic system, two systems which are both secure under quantum attacks. The plaintexts are displaced by an affine transformation and encrypted by central map in multivariable cryptosystem. And then, the outputs of central map act as initial values in a two...