Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of Affine Arithmetic called Revised Affine Arithmetic. We extend the range of functions presented in Revised Affi...

The problem of finding APN permutations ${\mathbb {F}}_{2^{n}}$ where n is even and > 6 has been called the Big Problem. Li, Helleseth Qu recently characterized functions defined on {F}}_{q^{2}}$ form f(x) = x3q + a1x2q+ 1 a2xq+ 2 a3x3, q 2m m ≥ 4. We will call this Kim-type because they generalize Kim function that was used to construct an permutation {F}}_{2^{6}}$ . prove with 4 (previously b...

The size-change principle devised by Lee, Jones and Ben-Amram, provides an effective method of determining program termination for recursive functions over well-founded types. Termination analysis using the principle involves the classification of functions either into size-change terminating ones, or ones which are not size-change terminating. Size-change graphs are constructed to represent th...

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...

Mixed f -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kull...

We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: • Pieri rules for the Schubert bases of H∗(Gr) and H∗(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. • A new combinatorial definition for k-Schur functions, which represent the Schubert ba...

We present a technique and an accompanying tool that learns guarded affine functions. In our setting, a teacher starts with a guarded affine function and the learner learns this function using equivalence queries only. In each round, the teacher examines the current hypothesis of the learner and gives a counter-example in terms of an input-output pair where the hypothesis differs from the targe...

The Sparse Polyhedral Framework (SPF) extends the Polyhedral Model by using the uninterpreted function call abstraction for the compile-time specification of run-time reordering transformations such as loop and data reordering and sparse tiling approaches that schedule irregular sets of iteration across loops. The Polyhedral Model represents sets of iteration points in imperfectly nested loops ...

In this paper, we consider certain affine similarity of refinable functions and establish certain connection between some local and global properties of refinable functions, such as local and global linear independence , local smoothness and B-spline, local and global Hölder continuity.