A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections

Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice. The second, closely related to the first, is used to prove in a short way the Knaster-Tarski’s fixed point theore

Implication of Barrier Fluctuations on the Rate of Weakly Adiabatic Electron Transfer

The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. Especially, for the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the non-adiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media.Comment: RevTeX 4, 14 pages, 3 figures. To be printed in IJMP C. References corrected and update

The model of cohesion development of metropolitan areas

Artykuł analizuje doświadczenia jednostek samorządu terytorialnego aglomeracji poznańskiej w rozwijaniu różnych form kooperacji. Szczególna uwaga została poświęcona rozpoznaniu i zaprezentowaniu instytucjonalnych form współdziałania na tworzących się metropolitalnych obszarach funkcjonalnych.Badania dotyczące rozwoju form spójności w aglomeracji poznańskiej przedstawiono na tle aktualnej europejskiej polityki ukierunkowanej terytorialnie, kładącej nacisk na wspieranie rozwoju obszarów funkcjonalnych. Specjalna wagę przykłada się w tej polityce do rozwiązywania wyzwań wynikających z narastania powiązań funkcjonalnych na obszarach metropolitalnych. Aktualne działania podejmowane w kształtujących się funkcjonalnych polskich obszarach metropolitalnych są omawiane także w świetle powstającej obecnie polskiej polityki ukierunkowanej terytorialnie. Szczególną uwagę poświęca ona wzmacnianiu współpracy międzysamorządowej oraz kooperacji z innymi sektorami na obszarach funkcjonalnych, ze szczególnym uwzględnieniem obszarów o charakterze metropolitalnym.Efektem badań prezentowanych w artykule jest propozycja modelu budowania spójności w obszarach metropolitalnych. Model uwzględnia zalecenia polityki europejskiej, polskiej i zmieniające się krajowe ramy legislacyjne oraz uwarunkowania i doświadczenia lokalne.he development of various forms of cooperation. Particular attention has been devoted to the recognition and presentation of institutional forms of cooperation in emerging metropolitan functional areas.The results of a research in the development of forms of cohesion in the Poznań agglomeration are shown in the context of the current European territorially oriented development policy that emphasizes supporting the development of functional areas. Special attention is paid to the policyto deal with the challenges arising from increasing functional connections in metropolitan areas. Current activities in the Polish emerging functional metropolitan areas are discussed in light of the currently emerging Polish territorial based policy. The paper draws special attention to the strengthening of cooperation between local authorities and cooperation with other sectors of the functional areas with special emphasis on metropolitan areas.The result of the research presented in the paper is the proposal to build a model of cohesion in metropolitan areas. The model takes into account the recommendations of European and Polish policy, the changing national legislative framework and local conditions and experience

Radiative transitions of DsJ∗(2317)D^*_{sJ}(2317) and DsJ(2460)D_{sJ}(2460)

We study radiative decays of $D^*_{sJ}(2317)$ and $D_{sJ}(2460)$ using light-cone QCD sum rules. In particular, we consider the decay modes $D^*_{sJ}(2317)\to D_s^* \gamma$ and $D_{sJ}(2460)\to D_s^{(*)} \gamma, D^*_{sJ}(2317) \gamma$ and evaluate the hadronic parameters in the transition amplitudes analyzing correlation functions of scalar, pseudoscalar, vector and axial-vector quark currents. In the case of $D^*_{sJ}(2317)\to D_s^* \gamma$ we also consider determinations based on two different correlation functions in HQET. The decay widths turn out to be different than previous estimates obtained by other methods; the results favour the interpretation of $D^*_{sJ}(2317)$ and $D_{sJ}(2460)$ as ordinary $\bar c s$ mesons.Comment: RevTex, 23 pages, 9 eps figure

Tuning of the spin-orbit interaction in a quantum dot by an in-plane magnetic field

Using an exact diagonalization approach we show that one- and two-electron InAs quantum dots exhibit avoided crossing in the energy spectra that are induced by the spin-orbit coupling in the presence of an in-plane external magnetic field. The width of the avoided crossings depends strongly on the orientation of the magnetic field which reveals the intrinsic anisotropy of the spin-orbit coupling interactions. We find that for specific orientations of the magnetic field avoided crossings vanish. Value of this orientation can be used to extract the ratio of the strength of Rashba and Dresselhaus interactions. The spin-orbit anisotropy effects for various geometries and orientations of the confinement potential are discussed. Our analysis explains the physics behind the recent measurements performed on a gated self-assembled quantum dot [S. Takahashi et al. Phys. Rev. Lett. 104, 246801 (2010)].Comment: Corrected according to referees comment

Coarse and uniform embeddings between Orlicz sequence spaces

We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. On the other hand, we present examples which show that sometimes the embeddability is not determined by the values of these indices.Comment: 12 pages. This is the final version. To appear in Mediterr. J. Mat

Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures

Detection of sodium in the atmosphere of WASP-69b

Transit spectroscopy is one of the most commonly used methods to characterize exoplanets atmospheres. From the ground, these observations are very challenging due to the terrestrial atmosphere and its intrinsic variations, but high-spectral resolution observations overcome this difficulty by resolving the spectral lines and taking advantage of the different Doppler velocities of the Earth, the host star and the exoplanet. We analyze the transmission spectrum around the Na I doublet at 589 nm of the exoplanet WASP-69b, a hot Jupiter orbiting a K-type star with a period of 3.868 days, and compare the analysis to that of the well-know hot Jupiter HD 189733b. We also present the analysis of the Rossiter-McLaughlin effect for WASP-69b. Two transits of WASP-69b were observed with the HARPS-North spectrograph (R = 115 000) at the TNG telescope. We perform a telluric contamination subtraction based on the comparison between the observed spectra and a telluric water model. Then, the common steps of the differential spectroscopy are followed to extract the transmission spectrum. The method is tested with archival transit data of the extensively studied exoplanet HD 189733b, obtained with the HARPS-South spectrograph at ESO 3.6m telescope, and then applied to WASP-69b data. For HD 189733b, we spectrally resolve the Na I doublet and measure line contrasts of $0.72\pm0.05\%$ (D2) and $0.51\pm0.05\%$ (D1), and FWHMs of $0.64\pm0.04${\AA} (D2) and $0.60\pm0.06${\AA} (D1), in agreement with previously published results. A net blueshift of ${\sim}0.04${\AA} is measured. For WASP-69b only the contrast of the D2 line is measured ($5.8\pm0.3\%$). Even if this corresponds to a detection at the $5\sigma$-level of excess absorption of $0.5\pm0.1\%$ in a passband of $1.5${\AA}, more transits are needed to fully characterize the lines profiles and retrieve accurate atmospheric properties.Comment: 15 pages, 14 figure

Direct Boundary Element Method for Dynamics in a Half-Space

An application of the direct boundary element method for solving the response of a linearly elastic half-space with a canyon cut into the surface is presented. This approach uses source solutions for an undamped half-space where the resulting singular integral equations are solved directly without adding any artificial damping. Solutions for the displacements on the canyon surface reveal an artificial resonance phenomenon when solving the exterior problem in the frequency domain. The use of an additional source loading in the boundary element method is shown to eliminate these resonances and yield accurate results. A method for solving the Rayleigh waves generated on the surface of the half-space caused by the canyon is shown