Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton–Jacobi–Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton–Jacobi–Bellman equation.     

Influence of the type of light polarization on photoinduced processes

We investigate the influence of the type of light polarization (linear or circular) on the efficiency of non-linear optical processes in photoanisotropic materials. A theoretical model of photoprocesses in materials in which optical non-linearity is related to absorbing centres with intrinsic linear anisotropy is constructed. Theoretical calculations show that the photostationary concentration of the photoproducts (and the mean values of the non-linear changes in optical constants) in these materials is higher if the exciting light is circularly polarized. Experimental results on non-linear processes in samples of fluorescein incorporated in orthoboric acid and in azodye/polymer layers are in good agreement with the theory. This revised version was published online in November 2006 with corrections to the Cover Date.     

Observation of alignment of the ground state of NO<Subscript>2</Subscript> under laser excitation

A Hanle signal is observed in the absorption of a cell filled with nitrogen dioxide NO₂ at room temperature. The excitation was performed by an Ar⁺ laser at a wavelength of 476.4 nm.     

Purcell enhancement of spontaneous emission from quantum cascades inside mirror-grating metal cavities at THz frequencies

Quantum cascade devices processed into double metal cavities with subwavelength thickness and a grating on top are studied at terahertz frequencies. The power extracted from the devices as a function of the device thickness and the grating period is analyzed owing to electrodynamical modeling of dipole emission based on a modal method in multilayer systems. The experimental data thus reveal a strong Purcell enhancement, with Purcell factors up to approximately 50.     

Thermoelectrics from abundant chemical elements: high-performance nanostructured PbSe-PbS

We report promising thermoelectric properties of the rock salt PbSe-PbS system which consists of chemical elements with high natural abundance. Doping with PbCl(2), excess Pb, and Bi gives n-type behavior without significantly perturbing the cation sublattice. Thus, despite the great extent of dissolution of PbS in PbSe, the transport properties in this system, such as carrier mobilities and power factors, are remarkably similar to those of pristine n-type PbSe in fractions as high as 16%. The unexpected finding is the presence of precipitates ~2-5 nm in size, revealed by transmission electron microscopy, that increase in density with increasing PbS concentration, in contrast to previous reports of the occurrence of a complete solid solution in this system. We report a marked impact of the observed nanostructuring on the lattice thermal conductivity, as highlighted by contrasting the experimental values (~1.3 W/mK) to those predicted by Klemens-Drabble theory at room temperature (~1.6 W/mK). Our thermal conductivity results show that, unlike in PbTe, optical phonon excitations in PbSe-PbS systems contribute to heat transport at all temperatures. We show that figures of merit reaching as high as ~1.2-1.3 at 900 K can be obtained, suggesting that large-scale applications with good conversion efficiencies are possible from systems based on abundant, inexpensive chemical elements.     

The ubiquity of generalized cluster categories

Associated with a finite-dimensional algebra of global dimension at most 2, a generalized cluster category was introduced in Amiot (2009) [1]. It was shown to be triangulated, and 2-Calabi–Yau when it is Hom-finite. By definition, the cluster categories of Buan et al. (2006) [4] are a special case. In this paper we show that a large class of 2-Calabi–Yau triangulated categories, including those associated with elements in Coxeter groups from Buan et al. (2009) [7], are triangle equivalent to generalized cluster categories. This was already shown for some special elements in Amiot (2009) [1].     

Dynamical systems with Lipschitz inverse shadowing properties

In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Mañé analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.     

The effect of pressure on halothane binding to hydrated DMPC bilayers

Halothane binding to hydrated dimyristoylphosphatidylcholine (DMPC) bilayer membranes has been examined over a wide range of pressures from 10⁵ to 4?×?10⁸?Pa. We show that the solvation of halothane by the membrane and bulk water are both pressure dependent, with an increased pressure driving halothane into the membrane. Analysis of these results shows that this pressure dependence is not the cause of pressure reversal, the process whereby general anaesthetics lose their efficacy at pressures of about 8?×?10⁶ to about 2.5?×?10⁷?Pa.