In this note, we give a proof to the equality in law of a skewed stable variable and a nonlinear transformation of two independent uniform and exponential variables. The lack of an explicit proof of this formula has led to some inaccuracies in the literature. The Chambers et al. (1976) method of computer generation of a skewed stable random variable is based on this equality.

We present a polynomial-time algorithm deciding bisimilarity between a normed BPA process and a normed BPP process. This improves the previously known exponential upper bound by Černá, Křet́ınský, Kučera (1999). The algorithm relies on a polynomial bound for the “finite-state core” of the transition system generated by the BPP process. The bound is derived from the “prime form” of the underlying...

The Büchi non-emptiness problem for timed automata concerns deciding if a given automaton has an infinite non-Zeno run satisfying the Büchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, we show that this simple transformation may sometimes result in an exponential blowup. We propose a method avoidin...

In this work we review a recently proposed transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field. The used methodology is illustrated with the help of the s...

We show that several system-theoretic properties are preserved under a bilinear transformation from a continuous-time linear system to a discrete-time one (and conversely). For example, strong stability, infinite-time admissibility of the control and observation operators and approximate controllability and observability are all preserved. On the other hand, exponential stability (stabilizabili...

Abstract. For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this paper, we present two balanced boolean functions which have low Walsh spectra and high nonlinearity. In the proof of the nonlinearity, a new metho...

Let M be a projective manifold, p : MG −→ M a regular covering over M with a free abelian transformation group G. We describe holomorphic functions on MG of an exponential growth with respect to the distance defined by a metric pulled back from M . As a corollary we obtain for such functions Cartwright and Liouville type theorems. Our approach brings together L2 cohomology technique for holomor...

Gregory S. Chirikjian Johns Hopkins University 2.1 Rotations in Three Dimensions Rules for Composing Rotations • Euler Angles • The Matrix Exponential 2.2 Full Rigid-Body Motion Composition of Motions • Screw Motions 2.3 Homogeneous Transforms and the Denavit-Hartenberg Parameters Homogeneous Transformation Matrices • The Denavit-Hartenberg Parameters in Robotics 2.4 Infinitesimal Motions and A...

In almost all image-model and model-model registration problems the question arises as to what optimal rigid body transformation applies to bring a physical 3-dimensional model in alignment with the observed one. Data may also be corrupted by noise. Here I will present the exponential and quaternion representations for the SO(3) group. I will present the technique of compounding derivatives and...