Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^{\alpha} and w^{\alpha}

This is the third and last part of a series of 3 papers. Using the same method and the same coordinates as in parts 1 and 2, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity $u^{\alpha}$ and rotation $w^{\alpha}$ at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given.Comment: One missing piece, signaled after eq. (10.7), is added after (10.21). List of corrections: In (3.7) wrong subscript in vorticity; In (3.10) wrong subscript in last term of g_{23}; In (4.23) wrong formulae for g_{12} and g_{22}; In (7.17) missing factor in velocity; In (7.18) one wrong factor in g_{22}; In (10.9) factor in vorticity; In (10.15) - (10.20) y_0 = 0; In (10.20) wrong second term in y. The rewriting typos did not influence result

On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which they are first-order asymptotically equivalent. Second, under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for "most" alternatives. This result further implies that empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities.Empirical likelihood, Large deviations, Hoeffding optimality, Moment restrictions

Phytohaemagglutinin on maternal and umbilical leukocytes

Almost all the umbilical lymphocytes showed more extensive blast cell formation than that of their mother's lymphocytes with PHA. Pathological conditions of mother in pregnancy and labor such as anemia, gestational toxicosis, difficult labor and asphyxia of babies, inhibited the normal response of both maternal and umbilical lymphocytes to PHA.</p

CubeHarmonic: A new interface from a magnetic 3D motion tracking system to music performance

We developed a new musical interface, CubeHarmonic, with the magnetic 3D motion tracking system IM3D. This sys- tem precisely tracks positions of tiny, wireless, battery-less, and identifiable markers (LC coils) in real time. The Cube- Harmonic is a musical application of the Rubik’s cube, with notes on each little piece. Scrambling the cube, we get dif- ferent chords and chord sequences. Positions of the pieces which contain LC coils are detected through IM3D, and transmitted to the computer to recognize the status of the Rubik’s cube, that plays sounds. The central position of the cube is also measured by the LC coils located into the corners of Rubik’s cube, and, depending on the position, we can manipulate overall loudness and pitch changes, as in theremin playing. This new instrument, whose first idea comes from mathematical theory of music, can be used as a teaching tool both for math (group theory) and music (music theory, mathematical music theory), as well as a composition device, a new instrument for avant-garde per- formances, and a recreational tool

High Angular Resolution, Sensitive CS J=2-1 and J=3-2 Imaging of the Protostar L1551 NE: Evidence for Outflow-Triggered Star Formation ?

High angular resolution and sensitive aperture synthesis observations of CS ($J=2-1$) and CS ($J=3-2$) emissions toward L1551 NE, the second brightest protostar in the Taurus Molecular Cloud, made with the Nobeyama Millimeter Array are presented. L1551 NE is categorized as a class 0 object deeply embedded in the red-shifted outflow lobe of L1551 IRS 5. Previous studies of the L1551 NE region in CS emission revealed the presence of shell-like components open toward L1551 IRS 5, which seem to trace low-velocity shocks in the swept-up shell driven by the outflow from L1551 IRS 5. In this study, significant CS emission around L1551 NE was detected at the eastern tip of the swept-up shell from $V_{\rm{lsr}}$ = 5.3 km s$^{-1}$ to 10.1 km s$^{-1}$, and the total mass of the dense gas is estimated to be 0.18 $\pm$ 0.02 $M_\odot$. Additionally, the following new structures were successfully revealed: a compact disklike component with a size of $\approx$ 1000 AU just at L1551 NE, an arc-shaped structure around L1551 NE, open toward L1551 NE, with a size of $\sim 5000$ AU, i.e., a bow shock, and a distinct velocity gradient of the dense gas, i.e., deceleration along the outflow axis of L1551 IRS 5. These features suggest that the CS emission traces the post-shocked region where the dense gas associated with L1551 NE and the swept-up shell of the outflow from L1551 IRS 5 interact. Since the age of L1551 NE is comparable to the timescale of the interaction, it is plausible that the formation of L1551 NE was induced by the outflow impact. The compact structure of L1551 NE with a tiny envelope was also revealed, suggesting that the outer envelope of L1551 NE has been blown off by the outflow from L1551 IRS 5.Comment: 29 pages, 12 figures, Accepted for Publication in the Astrophysical Journa

Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction

We study electron molecules in realistic vertically coupled quantum dots in a strong magnetic field. Computing the energy spectrum, pair correlation functions, and dynamical form factor as a function of inter-dot coupling via diagonalization of the many-body Hamiltonian, we identify structural transitions between different phases, some of which do not have a classical counterpart. The calculated Raman cross section shows how such phases can be experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e, Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter

Decision-Analysis under Extreme Uncertainties- Evaluating Unusual Weathers Caused by Global Warming

In this paper we propose a new methodology of decision analysis under extreme uncertainties which could analyze the preference of various type of persons from pessimistic ones to optimistic ones. For this purpose we revise a previous axiom of dominance for constructing a measurable value function (utility function) under uncertainty based on Dempster-Shafer theory of probability. The previous axiom of dominance has dealt with only the best and the worst results in the set element. Here, we propose a new axiom of dominance after defining the value of the set element taking into account the average of the value of all the results included in the set element. It is shown that we can construct a measurable value function under uncertainty for a pessimistic, an ordinary or an optimistic person, based on this new axiom of dominance. An example of evaluating the alternative policies to decrease the emission of carbon dioxide for avoiding global warming is included