We present some techniques to obtain smooth derivations of concurrent programs that address both safety and progress in a formal manner. Our techniques form an extension to the calculational method of Feijen and van Gasteren using a UNITY style progress logic. We stress the role of stable guards, and we illustrate the derivation techniques on some examples in which progress plays an essential r...

We must mention that the assumption that we are dealing with a Cartan matrix of finite type and a root of unity appears only at the very end (see Chapter 4). We need these assumptions in order to compare our representations with the conventional definition of the category C. All previous results are valid in more general assumptions. In particular a Cartan matrix could be arbitrary and a deform...

Unity: Unity is a widely-used cross-platform game develop system. It consists of a game engine and an integrated development environment (IDE). It can be used to develop games for many different platforms, including PCs, consoles, mobile devices, and deployment on the Web. In this lecture, we will present the basic elements of Unity. However, this is a complex system, and we will not have time ...

A novel idea to construct flat-top partition of unity functions in a closed form on a general (structured or unstructured) finite element mesh is presented. An efficient and practical construction method of a flat-top partition of unity function is important in the generalized finite element method (GFEM). Details on how to construct flat-top partition of unity functions on a provided mesh are ...

The notion that science is unified in one way or another dates back at least to Aristotle, though unity claims since then have been diverse and variously motivated. By way of introduction to the modern discussion of unity, disunity, and integration, in this first section we examine five historical attempts to unify knowledge: Aristotle’s metaphysical and hierarchical unity; the Enlightenment pr...

Let p ≡ 1 (mod 4) be a prime number and let ζ = e be a primitive root of unity. Then there exists a unique biquadratic extension eld Q(y)/Q that is a sub eld of Q(ζ). The aim of this work is to construct an algorithm for nding such y explicitly. Finally we state a general conjecture about the y we found.

Recently, the authors introduced two new second-order single-resistance-controlled oscillators (SRCO) employing four/three unity-gain cells (unity-gain voltage followers and unity-gain current followers). In this communication, a novel family of SRCOs has been presented which employ a reduced number of (only two) unity-gain cells as active elements. The workability of the new circuits has been ...

The partition of unity is an essential ingredient for meshless methods named by GFEM, PUFEM (partition of unity FEM), XFEM(extended FEM), RKPM(reproducing kernel particle method), RPPM(reproducing polynomial particle method), the method of clouds in the literature. There are two popular choices for partition of unity: a piecewise linear FEM mesh and the Shepard-type partition of unity. However,...

7 Periodic Series and Functions 128 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 128 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 130 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 131 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 133 7.5 The Exponential of a Complex Number . . . . . . . . . . . . . 133 7.6...