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The Galaxy rotation curve is usually assumed to be flat. However, some galaxies have rotation curves that are lower than the flat rotation curve. In our Galaxy the Keplerian rotation of interstellar clouds in the galactic longitude l=135 was observed. We use a kinematic approach to derive the rotational velocity of classical Cepheids. The rotational velocity was calculated from radial velocity and from proper motion. The derived rotational velocities of Cepheids are between Keplerian rotation and the flat one. We fit a Galaxy rotation model consisting of a black hole, bulge, disk and halo to the rotation curve. The density of dark matter halo is at least 60% less than the value obtained from the flat rotation curve.

We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to such a game, with the constraints defining the linear game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of more general XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lov\'{a}sz theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. Linear games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite linear game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions., Comment: 17 pages. Submitted to the NJP focus issue on Device-Independent QI

The ultraviolet and far--ultraviolet spectra of HD 147888 allows to access the v=0 as well as higher vibrational levels of the ground H2 electronic level. We have determined column densities of the H2 molecule on vibrational levels v=0-5 and rotational levels J=0-6. The ortho to para H2 ratio for the excited vibrational states equals to 1.2. For the lowest vibrational state v=0 and rotational level J=1 the ortho to para H2 ratio is only 0.16. The temperature of ortho-para thermodynamical equilibrium is T_OP=43+-3 K. The large number of H2 absorption lines in the HST spectra allows to determine column densities even from a noisy spectra. The measurements of H2 column densities on excited vibrational levels (from the HST spectra) leads to constrains of radiation field in photon-dominated regions (PDR) models of interstellar cloud towards HD 147888.

We present an analysis of interstellar H2 toward HD 37903, which is a hot, B 1.5 V star located in the NGC 2023 reflection nebula. Meyer et al. (2001) have used a rich spectrum of vibrationally excited H2 observed by the HST to calculate a model of the interstellar cloud toward HD 37903. We extend Mayer's analysis by including the v"=0 vibrational level observed by the FUSE satellite. The T01 temperature should not be interpreted as a rotational temperature, but rather as a temperature of thermal equilibrium between the ortho and para H2. The ortho to para H2 ratio is lower for collisionally populated levels than for the levels populated by fluorescence. The PDR model of the cloud located in front of HD 37903 points to a gas temperature Tkin=110-377 K, hydrogen density nH=1874-544 cm^-3 and the star-cloud distance of 0.45 pc.

We present a list of interstellar absorption lines in the direction of HD 37061 in the M 43 nebula. Some of the absorption lines arise from atomic excited levels that are uncommon in interstellar clouds. The excited levels of Fe II are populated by fluorescence. We found a large number of H2 molecular absorption lines arising from vibrationally excited levels. The ortho/para H2 ratio is equal to 2.7. The H2 rotational temperature of vibrational levels 1 - 5 exceeds 2000 K.

The local disc deuter is known to be depleted in comparison to the local bubble. We show, that the same lines of sight that are depleted in deuter, are enhanced in magnesium. Heavier elements - Si and Fe do not show any difference in the abundance between the local disc and the local bubble. This observation implicates that astration is responsible for both deuter depletion and magnesium enhancement.

Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "anti-bubbles" appear after a crash, when the prices decreases. Here, we propose the third type of log-periodic oscillations, where a exogenous crash initializes a log-periodic behavior of market, and the market is growing up. Such behavior has been identified on Polish stock market index between the "Russian crisis" (August 1998) and the "New Economy crash" in April 2000., Comment: 10 pages (6 figures): conference APFA4 (Warsaw, November 2003)

We show using a numerical approach that gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation., Comment: 5 pages

A time series that represents daily values of the WIG index (the main index of Warsaw Stock Exchange) over last 5 years is examined. Non-Gaussian features of distributions of fluctuations, namely returns, over a time scale are considered. Some general properties like exponents of the long range correlation estimated by averaged volatility and detrended fluctuations analysis (DFA) as well as exponents describing a decay of tails of the cumulative distributions are found. Closing, the Zipf analysis for the WIG index time series translated into three letter text is presented., Comment: 10 pages and 15 files with figures