Dielectric studies of the paracetamol-lenticular tissue interactions

This paper reports on the effect of paracetamol on the dielectric behavior of the rabbit lens. Measurements were performed over the frequency range of 100 Hz-100 kHz in air and at the temperature of 35°C. The frequency dependencies of the relative permittivity and dielectric loss for the control and paracetamol-control lenses are described in terms of a power-low, Debye and Cole-Cole relations. The effect of paracetamol on the dielectric properties of the lens is visible in the lower values of the relative permittivity than those for the control sample at the same frequency. In addition, the relaxations around 18 and 46 kHz for the paracetamol-control lens are shifted to lower frequencies compared with the control lens. The results of this work indicate that the present method is useful in detection of the lens toxicity elicited by overdoses of paracetamol in animal.     

A large set containing few orbits of measure preserving transformations

Summary There exists a Borel set C of product Lebesgue measure one in the Hilbert cube having the property that, for every measure preserving transformationT of the unit interval, allT-orbits contained inC originate from a zero set. This settles an infinite dimensional version of a problem raised by Th. M. Rassias.     

Piecewise Absolutely Continuous Cocycles Over Irrational Rotations

For an irrational rotation of the circle group T=R/Z and apiecewise absolutely continuous function f:TR, the unitary operatorVh(x)=e^2if(x)h(x+) on L²(T) is studied. It is shown that iff has a single discontinuity with non-integer jump then V is-weakly mixing for some with 0<||<1. In particular Vhas continuous singular spectrum. The property of -weak mixing(with possible change of the value of , 0<||<1) holdsfor all irrational rotations and, given , is stable under perturbationsof f by functions with sufficiently small O(1/n)-norm. On theother hand, there exists a piecewise linear function f withtwo non-integer jumps such that the spectrum of V is continuoussingular for one value of and Lebesgue for another.     

Code length between Markov processes

LetX ₁ andX ₂ be two mixing Markov shifts over finite alphabet. If the entropy ofX ₁ is strictly larger than the entropy ofX ₂, then there exists a finitary homomorphism ϕ:X ₁→X ₂ such that the code length is anL ^p random variable for allp<4/3. In particular, the expected length of the code ϕ is finite. Research supported by KBN grant 2 P03A 039 15 1998–2001.     

Absolutely continuous cocycles over irrational rotations

For homeomorphisms $$\left( {z,w} \right)\mathop \to \limits^{T\varphi } \left( {z . e^{2xi\alpha } ,\varphi \left( z \right)w} \right)$$ (z, w ∈S ¹,α is irrational,?:S ¹→S ¹) of the torusS ¹×S ¹ it is proved thatT? has countable Lebesgue spectrum in the orthocomplement of the eigenfunctions whenever? is absolutely continuous with nonzero topological degree and the derivative of? is of bounded variation. Some other cocycles with bounded variation are studied and generalizations of the above result to certain distal homeomorphisms on finite dimensional tori are presented.     

Anzai Skew Products with Lebesgue Component of Infinite Multiplicity

Let f be a 1-periodic C¹-function whose Fourier coefficientssatisfy the condition _n|n|³|f(n|² < . For every R\Q andm Z\{0}, we consider the Anzai skew product T(x, y) = (x +, y + mx + f(x)) acting on the 2-torus. It is shown that T hasinfinite Lebesgue spectrum on the orthocomplement L²(dx) ofthe space of functions depending only on the first variable.This extends some earlier results of Kushnirenko, Choe, Lemaczyk,Rudolph, and the author. 1991 Mathematics Subject Classification28D05.