Cephalopod life cycles: Patterns and exceptions

A holistic (life-cycle orientated) approach to ecological research and resource management of cephalopods is outlined. The first phase of such an approach involves the collection of basic life-cycle data; the second phaseinvolves developing predictive models of stock response to harvesting that incorporate information on the life history, the third is the implementation of management measures. The crucial data required are those on speciesdistribution (preferably on distribution of species concentrations) and on the basic life cycle itself. The survival strategy of cephalopods is spatially orientated (i.e. how and to what extent individuals are distributed is directlylinked to the success or failure of the next generation). The use of basic life-cycle parameters in management application is emphasized, and comparisons in this regard are drawn with the management of teleost stocks

Determination of the Wigner function from photon statistics

We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state.Comment: 4 pages LaTeX, contribution to proceedings of 6th central-european workshop on quantum optics; see also http://www.fuw.edu.pl/~kbanasz/QOLab/ExpWigner

On the constants in a Kato inequality for the Euler and Navier-Stokes equations

We continue an analysis, started in [10], of some issues related to the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d. More specifically, we consider the quadratic term in these equations; this arises from the bilinear map (v, w) -> v . D w, where v, w : T^d -> R^d are two velocity fields. We derive upper and lower bounds for the constants in some inequalities related to the above bilinear map; these bounds hold, in particular, for the sharp constants G_{n d} = G_n in the Kato inequality | < v . D w | w >_n | <= G_n || v ||_n || w ||^2_n, where n in (d/2 + 1, + infinity) and v, w are in the Sobolev spaces H^n, H^(n+1) of zero mean, divergence free vector fields of orders n and n+1, respectively. As examples, the numerical values of our upper and lower bounds are reported for d=3 and some values of n. When combined with the results of [10] on another inequality, the results of the present paper can be employed to set up fully quantitative error estimates for the approximate solutions of the Euler/NS equations, or to derive quantitative bounds on the time of existence of the exact solutions with specified initial data; a sketch of this program is given.Comment: LaTeX, 39 pages. arXiv admin note: text overlap with arXiv:1007.4412 by the same authors, not concerning the main result

Localized endomorphisms of graph algebras

Endomorphisms of graph C*-algebras are investigated. A combinatorial ap- proach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, proper endomor- phisms which restrict to automorphisms of the canonical diagonal MASA are analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found

SPECIAL ISSUE INTRODUCTION

“At the early stages of evolution, increasingly complex organisms developed powerful defense mechanisms against such adverse radiation effects as mutation and malignant change. These effects originate in the cell nucleus, where the DNA is their primary target. That evolution has apparently proceeded for so long is proof, in part, of the effectiveness of living things’ defenses against radiation.” Zbigniew Jaworowski 1999 “Chernobyl was indeed an historic event; it is the only nuclear power station disaster that ever resulted in an occupational death toll, albeit a comparatively small one. A vast environmental dispersion of radioactivity occurred that did not cause any scientifically confirmed fatalities in the general population. The worst harm to the population was caused not by radiation, and not to flesh, but to minds.” Zbigniew Jaworowski 201

The Weyl group of the Cuntz algebra

The Weyl group of the Cuntz algebra On is investigated. This is (isomorphic to) the group of polynomial automorphisms λu of On, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries Si and their adjoints. A necessary and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism λu restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of λu on the whole of On are also taken. A condition for verifying invertibility of a certain subclass of polynomial endomorphisms is given. First examples of polynomial automorphisms of On not inner related to permutative ones are exhibited, for every n≥2. In particular, the image of the Weyl group in the outer automorphism group of On is strictly larger than the image of the reduced Weyl group analyzed in previous papers. Results about the action of the Weyl group on the spectrum of the diagonal are also included

Coherence in laser-induced Compton scattering

The concept of the electron mass dressing by a powerful laser pulse is discussed. It is shown, by considering the coherent frequency combs generated out of the Compton radiation, how the electron dressed mass can be determined experimentally. This also opens a possibility to measure properties of extremely intense pulses for which the previously developed methods, working at moderate intensities, are not applicable. Namely, one can determine these properties from the properties of coherent Compton radiation

Coherence in laser-induced Compton scattering

The concept of the electron mass dressing by a powerful laser pulse is discussed. It is shown, by considering the coherent frequency combs generated out of the Compton radiation, how the electron dressed mass can be determined experimentally. This also opens a possibility to measure properties of extremely intense pulses for which the previously developed methods, working at moderate intensities, are not applicable. Namely, one can determine these properties from the properties of coherent Compton radiation