Affine Sessions

Realization of locally extended affine Lie algebras of type $A_1$

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...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

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 ne...

On Analytical Study of Self-Affine Maps

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...

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 ...

C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

application of affine gray-box neural models for nonlinear control of chemical processes