We consider the topological space of composition operators C(H2) on the Hardy space H2(D) of the unit disc D with operator norm topology. We prove a necessary condition for two composition operators to lie in the same path components and as a consequence we are able to determine path components of composition operators induced by analytic self-maps of the unit disc D which are analytic in a nei...

This paper presents a new digital servo architecture that reduces power consumption significantly. This paper shows an example of the low power digital servo architecture, which reduces its current almost by 83%, compared to that of conventional digital servo. This architecture applies to the compact disc (CD), Video-CD (VCD), digital versatile disc (DVD), CD-ROM, and DVD-ROM. Through this redu...

An accretion disc around a compact star in a close binary star system is an ubiquitous and essential object. Accretion discs play, for example, important roles in cataclysmic variables, nova and X-ray sources. The standard theory to explain the physics in accretion discs is the α-disc model proposed by Shakura and Sunyaev (1973). In this theory, the accretion disc is in some kind of turbulent s...

We present a compact design for a unitary photo detector and single-path combination optical pickup head (OPH) which can be used for Blu-ray Disc, digital versatile disc and compact disc systems. The number of components in the OPH design can be reduced by focusing three discrete wavelength laser beams on the photo detector. The three laser diode chips and a photo detector can be encapsulated w...

An analysis is presented of a numerical investigation of the dynamics and geometry of accretion discs in binary systems with mass ratios q = M2/M1 < 0.1, applicable to ultra-compact X-ray binaries, AM CVn stars and very short period cataclysmic variables. The steady-state geometry of the disc in the binary reference frame is found to be quite different from that expected at higher mass ratios. ...

We consider and study Blaschke inductive limit algebras A(b), defined as inductive limits of disc algebras A(D) linked by a sequence b = {Bk}k=1 of finite Blaschke products. It is well known that big G-disc algebras AG over compact abelian groups G with ordered duals Γ = Ĝ ⊂Q can be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b) is a maximal and Dirichl...

Aims. Bipolarity in proto-planetary and planetary nebulae is associated with events occurring in or around their cores. Past infrared observations have revealed the presence of dusty structures around the cores, many in the form of discs. Characterising those dusty discs provides invaluable constraints on the physical processes that govern the final mass expulsion of intermediate mass stars. We...

We characterize those analytic self-maps <p of the unit disc which generate bounded or compact composition operators Cv between given weighted Banach spaces H£° or H® of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v. 1991 Mathematics subject classification (Amer. Math. Soc): ...

The Heegaard genus of a compact orientable 3-manifold is an important invariant. The aim of this paper is to demonstrate that it is algorithmically computable, at least when the 3-manifold is simple and has non-empty boundary. Recall that a compact orientable 3-manifold is simple if it is irreducible and any properly embedded disc, incompressible annulus or incompressible torus is boundary para...

In 1857, Sylvester [16] posed the minimal enclosing disc problem, which asks for the smallest disc which covers a given finite point set in the Euclidean plane. A natural extension of this is obtained if one replaces the family of Euclidean discs by the family F of homothetic images of a given non-empty, convex, compact set B ⊂ R which is centrally symmetric with respect to its interior point 0...