‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We introduce the notion of a nonlinear splitting on fibre bundle as generalization an Ehresmann connection. present its basic properties and we pay attention to special cases affine, homogeneous principal splittings. explain where splittings appear in context Lagrangian systems Finsler geometry show their relation Routh symmetry reduction, submersive second-order differential equations unreduct...

In this work, we describe a simple and efficient construction of a large subset S of Fp , where p is a prime, such that the set A(S) for any non-identity affine map A over Fp has small intersection with S . Such sets, called affine-evasive sets, were defined and constructed in [ADL14] as the central step in the construction of non-malleable codes against affine tampering over Fp , for a prime p...

In this paper, we propose an image encryption algorithm based on the chaos, substitution boxes, nonlinear transformation in galois field GF(2 8 ) and Latin square. Initially, the dynamic S-boxes are generated using Fisher-Yates shuffle method and piece-wise linear chaotic map. The algorithm utilizes advantages of keyed Latin square and affine-power-affine transformation to substitute highly cor...

0. Introduction. Let Kn denote the «-dimensional torus. Let 7 be an affine transformation of Kn onto Kn and S an affine transformation of Km onto Km for which there exists a continuous map h of Kn onto Km satisfying hT= Sh. R. L. Adler and R. Palais have proved that, in the special cases when m = n and 7 and S are ergodic automorphisms of Kn, all homeomorphism g of Kn, satisfying gT= Sg, are af...

Counting the models of a propositional formula is a key issue for a number of AI problems, but few propositional languages offer the possibility to count models efficiently. In order to fill the gap, we introduce the language EADT of (extended) affine decision trees. An extended affine decision tree simply is a tree with affine decision nodes and some specific decomposable conjunction or disjun...

In this paper, we consider the problem of constructing abstractions of affine control systems that preserve reachability properties, and, in particular, local accessibility. In this framework, showing local accessibility of the higher level, abstracted model is equivalent to showing local accessibility of the, more detailed, lower level model. Given an affine control system and a smooth surject...

A class of linear positive, trace preserving maps in Mn is given in terms of affine maps in R n 2 −1 which map the closed unit ball into itself.

We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of the uncertainty s...

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...