Linear transformations have been routinely applied in various field applications since they permit a straightforward geometric relationship between different coordinate systems. The most general form of linear transformations which is also referred to as the affine model allows coordinate transformations between non-uniformly dilated systems. This particular model is intrinsically useful for da...

When two shapes that differ in orientation or size have to be compared or objects have to be recognized from different viewpoints, the response time and error rate are systematically affected by the size of the geometric difference. In this report, we argue that these effects are not necessarily solid evidence for the use of mental transformations and against the use of invariants by the visual...

Image enhancement is an important stage in the image-processing domain. The most known image enhancement method is the histogram equalization. This method is an automated one, and realizes a simultaneous modification for brightness and contrast in the case of monochrome images and for brightness, contrast, saturation and hue in the case of color images. Simple and efficient methods can be obtai...

The aim of this paper is to reduce the number of operations in Cantor’s algorithm for the Jacobian group of hyperelliptic curves for genus 4 in projective coordinates. Specifically, we developed explicit doubling and addition formulas for genus 4 hyperelliptic curves over binary fields with h(x) = 1. For these curves, we can perform a divisor doubling in 63M + 19S, while the explicit adding for...

In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of “affine-invariant” codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes form a natural abstraction of algebraic properties such as li...

An ind-variety is an inductive limit of closed embeddings algebraic varieties and ind-group a group object in the category ind-varieties. These notions were first introduced by Shafarevich study automorphism affine spaces have been studied many authors afterwards. ind-torus obtained as tori that are also homomorphisms. In this paper, we introduce natural definition toric ind-varieties having op...

self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. they belong to the general category of patch-based methods. particularly, each self-affine map is defined by one pair of patches in the image domain. by minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. almost all image process...

We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification smooth scri $\mathscr{I^+}$. Metrics are written in Bondi-Sachs coordinates and expanded into inverse powers affine distance $r$. Unlike case $\Lambda=0$ all free data located on scri. There linear differential constraints Bondi mass angular momentum aspects. All other...

The paper gives a definition of exponential arcs in the manifold non-degenerate density matrices and uses it as starting point to develop parameter-free version non-commutative Information Geometry finite-dimensional case. Given Bogoliubov metric m- e-connections are each other dual. Convex potentials introduced. They allow introduce dual charts. Affine coordinates introduced at end make connec...