We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as encryption process. To hide such encryption (graph and walk on it) we will use two affine transfor...

Trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques. Well known systems theoretic concepts such as differential flatness or more recent ones such as simulation and bisimulation can be also understood through the trajectory lifting maps they define. In this paper we initiate a study of trajectory preserving and lifting maps...

These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems. Stanley symmetric functions are a family {Fw | w ∈ Sn} of symmetric functions indexed by permutations. They were invented by Stanley [Sta] to enume...

In this article, we prove the following interpolation problem: if composition of a function and regular map between affine varieties is function, then there exists global target variety that coincide with on image provided factorial almost surjective. We also discuss few applications problem.Communicated by Daniel Erman

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension. In this paper we are interested in the following question. Question. Classify all smooth affine surfaces X/C which admit a proper morphism f : X → X with degree f > 1. In [5] and [18], a classification of smooth projective surfaces with a self-map of degree > 1 has been given. Th...

We study the real Monge-Ampère equation in two and three dimensions, both from the point of view of the SYZ conjecture, where solutions give rise to semi-flat Calabi-Yau’s and in affine differential geometry, where solutions yield parabolic affine sphere hypersurfaces. We find explicit examples, connect the holomorphic function representation to Hitchin’s description of special Lagrangian modul...

We evaluate performances of different implementations of affine transform in motion compensation architecture based on a hierarchical adaptive structured mesh. The architecture predicts the next video frame using the reference frame, mesh code and mesh node motion vectors. It achieves significant reduction in describing the mesh topology by coding the splitting in recursive triangulation of the...

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .