Spatial strategies of firms under Stackelberg competention

The paper explores a spatial duopoly of firms under Stackelberg competition, when one of the firms is a leader in term of product volume. The equilibrium spatial strategies of firms are found. In the process of the analysis of equilibrium stability, it is proved that the transport tariff is a bifurcation parameter for firms. It was found that the change in the central agglomeration strategy to the differentiation strategy occurs at the point of transcritical bifurcation. The conditions for full coverage of the markets for both strategies are defined. It is obtained that the information asymmetry leads to asymmetry of equilibrium locations of firms. It is established that under differentiation strategy, the follower can due to the space factor overcome information asymmetry in the nearest markets and get a profit more than the leader.В работе исследована пространственная дуополия фирм в условиях конкуренции Штакельберга, когда одна из фирм является лидером по объему продукции. Найдены равновесные пространственные стратегии фирм. В ходе анализа устойчивости равновесия доказано, что транспортный тариф является бифуркационным параметром для фирм. Найдено, что изменение стратегии центральной агломерации на стратегию дифференциации происходит в точке транскритической бифуркации. Определены условия полного покрытия рынка для обеих стратегий. Получено, что информационная асимметрия приводит к асимметрии равновесного расположения фирм. Установлено, что при дифференциации последователь может на прилегающих рынках преодолеть информационную асимметрию за счет фактора пространства и получить прибыль больше, чем у лидера

Friedmann universe with dust and scalar field

We study a spatially flat Friedmann model containing a pressureless perfect fluid (dust) and a scalar field with an unbounded from below potential of the form V(\fii)=W_0 - V_0\sinh(\sqrt{3/2}\kappa\fii), where the parameters $W_0$ and $V_0$ are arbitrary and $\kappa=\sqrt{8\pi G_N}=M_p^{-1}$. The model is integrable and all exact solutions describe the recollapsing universe. The behavior of the model near both initial and final points of evolution is analyzed. The model is consistent with the observational parameters. We single out the exact solution with the present-day values of acceleration parameter $q_0=0.5$ and dark matter density parameter $\Omega_{\rho 0}=0.3$ describing the evolution within the time approximately equal to $2H_0^{-1}$.Comment: 11 pages, 10 figure

Measuring sigma(e^+e^- \to hadrons) using tagged photon

We propose to use events with radiated photons in e^+e^- collisions to measure the total cross section of e^+ e^- \to hadrons as a function of the center of mass energy. The Monte Carlo simulation for the collider DAPHNE shows that a competitive accuracy can be achieved with this method.Comment: revtex, 13 page

Towards topological quantum computer

One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice, however, is at hand: it is provided by the quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, distinguished from the points of view of group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Observables in this case are (square modules of) the knot polynomials, and their pronounced integrality properties could provide a key to error correction. We suggest to use R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, to build a topological version of quantum computing.Comment: 14 page