Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

A possible role of tachykinin-related peptide on an immune system activity of mealworm beetle, Tenebrio molitor L.

Tachykinin-related peptides (TRPs) are important neuropeptides. Here we show that they affect the insect immune system, especially the cellular response. We also identify and predict the sequence and structure of the tachykinin-related peptide receptor (TRPR) and confirm the presence of expression of gene encoding TRPR on Tenebrio molitor haemocytes. After application of the Tenmo-TRP-7 in T. molitor the number of circulating haemocytes increased and the number of haemocytes participating in phagocytosis of latex beads decreased in a dose- and time-dependent fashion. Also, Tenmo-TRP-7 affects the adhesion ability of haemocytes. Six hours after injection of TenmoTRP-7, a decrease of haemocyte surface area was observed under both tested Tenmo-TRP-7 concentrations (10-7 and 10-5 M). The opposite effect was reported 24 h after injection, which indicates that the influence of Tenmo-TRP-7 on modulation of haemocyte behaviour differs at different stages of stress response. Tenmo-TRP-7 application also resulted in increased phenoloxidase activity 6 and 24 h after injection. The assessment of DNA integrity of haemocytes showed that the injection of Tenmo-TRP-7 at 10-7 M led to a decrease in DNA damage compared to control individuals. This effect was only visible 6 h after Tenmo-TRP-7 application. After 24 h, Tenmo-TRP-7 injection increased DNA damage. We also confirmed the expression of immune-related genes in nervous tissue of T. molitor. Transcripts for genes encoding receptors participating in pathogen recognition processes and antimicrobial peptides were detected in T. molitor brain, retrocerebral complex and ventral nerve cord. These results may indicate a role of the insect nervous system in pathogen recognition and modulation of immune response similar to vertebrates. Taken together, our results support the notion that tachykinin-related peptides probably play an important role in the regulation of the insect immune system. Moreover, some resemblances with action of tachykininrelated peptides and substance P showed that insects can be potential model organisms for analysis of hormonal regulation of conserved innate immune mechanisms

Rigidity of escaping dynamics for transcendental entire functions

We prove an analog of Boettcher's theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are *quasiconformally equivalent* in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points which remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane. We also prove that this conjugacy is essentially unique. In particular, we show that an Eremenko-Lyubich class function f has no invariant line fields on its escaping set. Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f and g which belong to the same parameter space are conjugate on their sets of escaping points.Comment: 28 pages; 2 figures. Final version (October 2008). Various modificiations were made, including the introduction of Proposition 3.6, which was not formally stated previously, and the inclusion of a new figure. No major changes otherwis

The Schroedinger operator as a generalized Laplacian

The Schroedinger operators on the Newtonian space-time are defined in a way which make them independent on the class of inertial observers. In this picture the Schroedinger operators act not on functions on the space-time but on sections of certain one-dimensional complex vector bundle -- the Schroedinger line bundle. This line bundle has trivializations indexed by inertial observers and is associated with an U(1)-principal bundle with an analogous list of trivializations -- the Schroedinger principal bundle. For the Schroedinger principal bundle a natural differential calculus for `wave forms' is developed that leads to a natural generalization of the concept of Laplace-Beltrami operator associated with a pseudo-Riemannian metric. The free Schroedinger operator turns out to be the Laplace-Beltrami operator associated with a naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger principal bundle. The presented framework is proven to be strictly related to the frame-independent formulation of analytical Newtonian mechanics and Hamilton-Jacobi equations, that makes a bridge between the classical and quantum theory.Comment: 19 pages, a remark, an example and references added - the version to appear in J. Phys. A: Math. and Theo

Measurements, Models, Systems and Design

531 s.

Thermodynamic formalism for contracting Lorenz flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure