In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X = M = K conjecture. It is proved for tensor products of the “symmetric power” Kirillov-Reshetikhin modules for all nonexceptio...

Finite affine groups are given by groups of translations and di- lations on finite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters ...

The classical Nullstellensatz asserts that a reduced affine variety is known by its closed points; algebraically, a prime ideal in an affine ring is the intersection of the maximal ideals containing it. A leading special case of our theorem says that any affine scheme can be distinguished from its subschemes by its closed points with a bounded index of nilpotency; algebraically, an ideal I in a...

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finitedimensional or pappian. Mathematics Subject Classification...

Nonlinear multichannel filters have successfully been applied to biomedical signals, multichannel images as well as processing of vector fields. In multichannel signals, component variances and correlations among components may be unequal and time-varying. Such changes can be expressed as an affine transformation of the input signal. In this paper, we investigate how the performance and statist...

This paper describes a correlation based image registration method which is able to register images related by a single global affine transformation or by a transformation field which is approximately piecewise affine. The method has two key elements: an affine estimator, which derives estimates of the six affine parameters relating two image regions by aligning their Fourier spectra prior to c...

This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image of a fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine t...

In this paper, asymptotic stability of uncalibrated eye-in-hand visual servoing is proved in an affine invariance approach. After a brief retrospection on the uncalibrated eye-inhand visual servoing, the affine invariance framework is introduced with discussion in depth. Then the visual servoing algorithm is reconstructed in an affine invariance framework, or more precisely as an affine contrav...

Recognition of planar objects from their images taken from different viewpoints requires affine invariants calculated from the object boundaries. The equivalence between affine transformation and the source mixture model simplifies the recognition problem. The rotation, scaling, skewing, and translation effects of the affine transformation can be undone by using blind source separation (BSS) te...