Let G be a compact affine definable C group and let r be∞ or ω. We prove that the representative definable C functions on G is dense in the space of continuous functions on G. Moreover we compare the category of compact affine definable C groups D with that of compact real algebraic groups A.

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...

This paper introduces a new way of extracting affine invariant features from image functions. The presented approach is based on combining affine moment invariants (AMI) with multiscale invariants, in particular multiscale autoconvolution (MSA) and spatial multiscale affine invariants (SMA). Our approach includes all of these invariants as special cases, but also makes it possible to construct ...

This paper introduces a new way of extracting affine invariant features from image functions. The presented approach is based on combining affine moment invariants (AMI) with multiscale invariants, in particular multiscale autoconvolution (MSA) and spatial multiscale affine invariants (SMA). Our approach includes all of these invariants as special cases, but also makes it possible to construct ...

We give a formalization of affine forms [1, 2] as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic. Moreover we give a verified im...

In this paper, we obtain the cross-correlation spectrum of generalized bent Boolean functions in a subclass of MaioranaMcFarland class (GMMF). An affine transformation which preserve the cross-correlation spectrum of two generalized Boolean functions, in absolute value is also presented. A construction of generalized bent Boolean functions in (n+ 2) variables from four generalized Boolean funct...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya–Szegö symmetrization principle for functions on R. Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which is stronger than its classical Euclidean counterpart.

We study certain nearby cycles sheaves on an affine flag manifold which arise naturally in the Beilinson-Gaitsgory deformation of the affine flag manifold to the affine Grassmannian. We study the multiplicity functions we introduced in an earlier paper, which encode the data of the Jordan-Hoelder series. We prove the multiplicity functions are polynomials in q, and we give a sharp bound for the...

This paper presents an efficient approach for classification of the affine equivalence classes of cosets of the first order Reed-Muller code with respect to cryptographic properties such as correlationimmunity, resiliency and propagation characteristics. First, we apply the method to completely classify all the 48 classes into which the general affine group AGL(2, 5) partitions the cosets of RM...