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...

In this paper we study the dynamics of an impact oscillator with a modified reset law derived from considering a problem (the pin-ball machine) with an active impact. Typical studies of the impact oscillator consider impacts which are governed by Newton’s Law of Restitution where the velocity after impact is r times less than the incoming velocity. But in this paper we consider an active impact...

Let Φ be an irreducible crystallographic root system with Weyl group W , coroot lattice Q̌ and Coxeter number h. Recently the second named author defined a uniform W -isomorphism ζ between the finite torus Q̌/(mh + 1)Q̌ and the set of non-nesting parking functions Park(Φ). If Φ is of type An−1 and m = 1 this map is equivalent to a map defined on labelled Dyck paths that arises in the study of the ...

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call semimetals. The host band touching at finite energies, whose protection is inherited from squared Hamiltonian. Such a character also reflected emergence of boundary modes with energies. Specifically, focusing on properties Hamiltonian class AIII, reveal th...

Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement matrix into square root form. Such techniques ...

Square Root Palindromes ................................... 1 Sigma Quest .......................................................... 6 Decimal Fractions ................................................ 9 Designing Weavable Color Patterns ............... 12 Polygraphic Substitution .................................. 17 Programming Tips ............................................. 20 What’s Comi...

Three algorithm implementations for square root computation are considered in this paper. Newton-Raphson's, iterative, and binary search algorithm implementations are completely designed, verified and compared. The algorithms, entire system-on-chip realisations and their functioning are described.

Let Q0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0 = 0. Q0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q0(s, √ ) of the signed rationals in which every number has a unique square root.

Identify the domain and range of each. Then sketch the graph.