Quantized chaotic dynamics and non-commutative KS entropy

We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of "cat maps" on a two dimensional torus, and the dynamics of baker's maps. Each of these dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non- commutative generalization of the Kolmogorov-Sinai entropy, namely the Connes-Stormer entropy, of the generator of this group, and find that its value is equal to the classical value. This can be interpreted as a sign of persistence of chaotic behavior in a dynamical system under quantization.Comment: a number of misprints corrected, new references and a new section added. 21 pages, plain Te

Matrix Cartan superdomains, super Toeplitz operators, and quantization

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck's constant tends to zero.Comment: 52

Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.Comment: 24

Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency

We formulate three famous, descriptive essays of C.N. Parkinson on bureaucratic inefficiency in a quantifiable and dynamical socio-physical framework. In the first model we show how the use of recent opinion formation models for small groups can be used to understand Parkinson's observation that decision making bodies such as cabinets or boards become highly inefficient once their size exceeds a critical 'Coefficient of Inefficiency', typically around 20. A second observation of Parkinson - which is sometimes referred to as Parkinson's Law - is that the growth of bureaucratic or administrative bodies usually goes hand in hand with a drastic decrease of its overall efficiency. In our second model we view a bureaucratic body as a system of a flow of workers, which enter, become promoted to various internal levels within the system over time, and leave the system after having served for a certain time. Promotion usually is associated with an increase of subordinates. Within the proposed model it becomes possible to work out the phase diagram under which conditions bureaucratic growth can be confined. In our last model we assign individual efficiency curves to workers throughout their life in administration, and compute the optimum time to send them to old age pension, in order to ensure a maximum of efficiency within the body - in Parkinson's words we compute the 'Pension Point'.Comment: 15 pages, 5 figure

Mixing fuel particles for space combustion research using acoustics

Part of the microgravity science to be conducted aboard the Shuttle (STS) involves combustion using solids, particles, and liquid droplets. The central experimental facts needed for characterization of premixed quiescent particle cloud flames cannot be adequately established by normal gravity studies alone. The experimental results to date of acoustically mixing a prototypical particulate, lycopodium, in a 5 cm diameter by 75 cm long flame tube aboard a Learjet aircraft flying a 20 sec low gravity trajectory are described. Photographic and light detector instrumentation combine to measure and characterize particle cloud uniformity

The monitoring of ultrasonic shear mechanical energy absorbed by film-forming systems

The purpose of this thesis is to describe the principles of the recording impedometer, to demonstrate its potential, and to interpret the physical and chemical information which it is capable of yielding

Fractional variational calculus of variable order

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.Comment: Submitted 26-Sept-2011; accepted 18-Oct-2011; withdrawn by the authors 21-Dec-2011; resubmitted 27-Dec-2011; revised 20-March-2012; accepted 13-April-2012; to 'Advances in Harmonic Analysis and Operator Theory', The Stefan Samko Anniversary Volume (Eds: A. Almeida, L. Castro, F.-O. Speck), Operator Theory: Advances and Applications, Birkh\"auser Verlag (http://www.springer.com/series/4850

Classical limit of the d-bar operators on quantum domains

We study one parameter families $D_t$, $0<t<1$ of non-commutative analogs of the d-bar operator D_0 = \frac{\d}{\d\bar{z}} on disks and annuli in complex plane and show that, under suitable conditions, they converge in the classical limit to their commutative counterpart. More precisely, we endow the corresponding families of Hilbert spaces with the structures of continuous fields over the interval $[0,1)$ and we show that the inverses of the operators $D_t$ subject to APS boundary conditions form morphisms of those continuous fields of Hilbert spaces

Effect of Gibberellic Acid (GA3) Inflorescence Application on Content of Bioactive Compounds and Antioxidant Potential of Grape (Vitis L.) ‘Einset Seedless’ Berries

Gibberellic acid (GA3) is a plant growth regulator widely used in the cultivation of seedless grape varieties to increase their yield. Hormonisation treatment has beneficial effects on yield size and quality, yet its influence on the level of biologically active compounds and grape antioxidant activity has not yet been studied extensively yet. Clusters of 11-year-old ‘Einset Seedless’ grapevines trained according to the singleGuyot pruning style were sprayed with GA3 at 100, 200 or 300 mg/L dose once, twice or three times.  Fruit harvested on 25 September were immediately examined for acidity, extract content, biologically active substances and antioxidant capacity using the DPPH test. In addition, correlations occurring between some parameters measured were calculated. Hormonisation had a negative effect on the content of extract, flavonoids and ascorbic acid, while it had no effect on the anthocyanin level. The antioxidant activity determined by the DPPH assay depended on dose and the number of treatments, and the analysed parameters were shown to decrease significantly with increasing application number. Gibberellic acid at 100 and 300 mg/L application rates had a significantly increased DPPH level compared to the control and 200 mg/L dose. The single GA3 treatment, and when applied three times, and application rates at 100 and 200 mg/L were shown to have a significant influence on phenolic acid content. The level of tannins after a single GA3 treatment and a 300 mg/L dose increased significantly