Book reviews

Please forward books for review to the book review editor: Magdolna Hargittai, Structural Chemistry Research Group of the Hungarian Academy of Sciences, Eötvös University, H-1431 Budapest, Pf. 117, Hungary     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

Quantum Riemann surfaces I. The unit disc

We construct a non-commutative ^*-algebra which is a quantum deformation of the algebra of continuous functions on the closed unit disc . is generated by the Toeplitz operators on a suitable Hilbert space of holomorphic functions onU.Supported in part by the National Science Foundation under grant DMS/PHY 88-16214     

D-bar Operators on Quantum Domains

We study the index problem for the d-bar operators subject to Atiyah- Patodi-Singer boundary conditions on noncommutative disk and annulus.     

The blogosphere as an excitable social medium: Richter’s and Omori’s Law in media coverage

We study the dynamics of public media attention by monitoring the content of online blogs. Social and media events can be traced by the propagation of word frequencies of related keywords. Media events are classified as exogenous–where blogging activity is triggered by an external news item–or endogenous where word frequencies build up within a blogging community without external influences. We show that word occurrences exhibit statistical similarities to earthquakes. Moreover the size distribution of events scales with a similar exponent as found in the Gutenberg–Richter law. The dynamics of media events before and after the main event can be satisfactorily modeled as a type of process which has been used to understand fore–and aftershock rate distributions in earthquakes–the Omori law. We present empirical evidence that for media events of endogenous origin the overall public reception of the event is correlated with the behavior of word frequencies at the beginning of the event, and is to a certain degree predictable. These results imply that the process of opinion formation in a human society might be related to effects known from excitable media.     

Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Composite Julia sets generated by infinite polynomial arrays

A definition of a generalized filled-in Julia set generated by an infinite array of proper polynomial mappings in  is introduced. It is shown that such Julia sets depend analytically on the defining polynomial mappings.     

Fractional sequential mechanics — models with symmetric fractional derivative

The symmetric fractional derivative is introduced and its properties are studied. The Euler-Lagrange equations for models depending on sequential derivatives of type are derived using minimal action principle. The Hamiltonian for such systems is introduced following methods of classical generalized mechanics and the Hamilton’s equations are obtained. It is explicitly shown that models of fractional sequential mechanics are non-conservative. The limiting procedure recovers classical generalized mechanics of systems depending on higher order derivatives. The method is applied to fractional deformation of harmonic oscillator and to the case of classical frictional force proportional to velocity. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

Do­decyl 2‐nitro­phenyl disulphide

Do­decyl 2‐nitro­phenyl disulphide, C₁₈H₂₉NO₂S₂, contains an intramolecular S?O contact of 2.623 (3) Å. The angle between the planes of the NO₂ group and the attached phenyl ring is 4.2 (3)°. The thermal vibrations of the atoms increase along the paraffinic chain. The nitro­so O atom not involved in the S?O intramolecular contact also has high thermal motion. Attempts to create disordered models to allow for the thermal motions were unsuccessful.