An X-Ray Detection Possibility of Star-Formation-Bursting Proto-Elliptical Galaxies

A possibility to detect X-rays from star-formation burst activities in proto-elliptical galaxies is considered. The X-ray flux of an emission due to inverse Compton scattering of the cosmic microwave background (CMB) by high energy electrons accelerated in SNRs is shown to increase as z increases far beyond unity, since the local CMB flux largely increases in association with a z-increase. The flux is estimated for the case of a very high rate of type II supernovae at an initial star formation burst of a proto-elliptical galaxy and is found to be detectable with a future large X-ray telescope such as intended in the XEUS mission.Comment: 4 pages, 1 figure, will appear in PAS

Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painlev\'e equations, using expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page

Confluent primary fields in the conformal field theory

For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric functions of confluent type, as expectation values of products of generalized primary fields. In the case of sl(2), these integral representations coincide with solutions to confluent KZ equations. Computing the operator product expansion of the energy-momentum tensor and the generalized primary field, new differential operators appear in the result. In the case of sl(2), these differential operators are the same as those of the confluent KZ equations.Comment: 15 pages. Corrected typos. Proposition 3.1 rewritten. Other minor changes, title change

Resonant growth of stellar oscillations by incident gravitational waves

Stellar oscillation under the combined influences of incident gravitational wave and radiation loss is studied in a simple toy model. The star is approximated as a uniform density ellipsoid in the Newtonian gravity including radiation damping through quadrupole formula. The time evolution of the oscillation is significantly controlled by the incident wave amplitude $h$, frequency $\nu$ and damping time $\tau$. If a combination $h \nu \tau$ exceeds a threshold value, which depends on the resonance mode, the resonant growth is realized.Comment: 11 pages, 6 figures, Accepted for the publication in Classical and Quantum Gravit

Systematic Errors in the Hubble Constant Measurement from the Sunyaev-Zel'dovich effect

The Hubble constant estimated from the combined analysis of the Sunyaev-Zel'dovich effect and X-ray observations of galaxy clusters is systematically lower than those from other methods by 10-15 percent. We examine the origin of the systematic underestimate using an analytic model of the intracluster medium (ICM), and compare the prediction with idealistic triaxial models and with clusters extracted from cosmological hydrodynamical simulations. We identify three important sources for the systematic errors; density and temperature inhomogeneities in the ICM, departures from isothermality, and asphericity. In particular, the combination of the first two leads to the systematic underestimate of the ICM spectroscopic temperature relative to its emission-weighed one. We find that these three systematics well reproduce both the observed bias and the intrinsic dispersions of the Hubble constant estimated from the Sunyaev-Zel'dovich effect.Comment: 26 pages, 7 figures, accepted for publication in ApJ, Minor change

Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels

The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.Comment: REVTeX4, 4 page

Financial Assessment Considered Weighting Factor Scenarios for the Optimal Combination of Power Plants on the Power System Operation

This paper presents an application of the novel evolutionary algorithm for assessing financially an economic power system operation throughout a combined economic and emission dispatch problem required by various technical limitations. In detail, this problem considers two dispatches for fuel and environmental aspects as a constrained objective function associated with weighting factor scenarios. Running out simulations show that minimum costs are depended on weighting factors, which implemented on the combination of the problem. Reducing the total fuel cost focused on the dispatching priority and the pollutant target based on the emission production have difference implications as its contribution to the economic operation, the increasing load demand leads to generated powers, costs and emission discharges associated with its parameters and power schedules