Positivity and Kodaira embedding theorem

Kodaira embedding theorem provides an effective characterization of projectivity of a K\"ahler manifold in terms the second cohomology. Recently X. Yang [21] proved that any compact K\"ahler manifold with positive holomorphic sectional curvature must be projective. This gives a metric criterion of the projectivity in terms of its curvature. In this note, we prove that any compact K\"ahler manifold with positive 2nd scalar curvature (which is the average of holomorphic sectional curvature over 2-dimensional subspaces of the tangent space) must be projective. In view of generic 2-tori being non-abelian, this new curvature characterization is sharp in certain sense

Properties and Origin of Galaxy Velocity Bias in the Illustris Simulation

We use the hydrodynamical galaxy formation simulations from the Illustris suite to study the origin and properties of galaxy velocity bias, i.e., the difference between the velocity distributions of galaxies and dark matter inside halos. We find that galaxy velocity bias is a decreasing function of the ratio of galaxy stellar mass to host halo mass. In general, central galaxies are not at rest with respect to dark matter halos or the core of halos, with a velocity dispersion above 0.04 times that of the dark matter. The central galaxy velocity bias is found to be mostly caused by the close interactions between the central and satellite galaxies. For satellite galaxies, the velocity bias is related to their dynamical and tidal evolution history after being accreted onto the host halos. It depends on the time after the accretion and their distances from the halo centers, with massive satellites generally moving more slowly than the dark matter. The results are in broad agreements with those inferred from modeling small-scale redshift-space galaxy clustering data, and the study can help improve models of redshift-space galaxy clustering.Comment: 15 pages, 11 figures. Accepted for publication in Ap

Energy-Efficient Transmission Schedule for Delay-Limited Bursty Data Arrivals under Non-Ideal Circuit Power Consumption

This paper develops a novel approach to obtaining energy-efficient transmission schedules for delay-limited bursty data arrivals under non-ideal circuit power consumption. Assuming a-prior knowledge of packet arrivals, deadlines and channel realizations, we show that the problem can be formulated as a convex program. For both time-invariant and time-varying fading channels, it is revealed that the optimal transmission between any two consecutive channel or data state changing instants, termed epoch, can only take one of the three strategies: (i) no transmission, (ii) transmission with an energy-efficiency (EE) maximizing rate over part of the epoch, or (iii) transmission with a rate greater than the EE-maximizing rate over the whole epoch. Based on this specific structure, efficient algorithms are then developed to find the optimal policies that minimize the total energy consumption with a low computational complexity. The proposed approach can provide the optimal benchmarks for practical schemes designed for transmissions of delay-limited data arrivals, and can be employed to develop efficient online scheduling schemes which require only causal knowledge of data arrivals and deadline requirements.Comment: 30 pages, 7 figure

4-Cyano­pyridinium bromide

In the title compound, C6H5N2 +·Br−, the pyridine N atom is protonated and involved in an inter­molecular N—H⋯Br hydrogen bond which, together with weak C—H⋯N hydrogen bonds, results in the formation of a chain along the c axis. Weak inter­molecular C—H⋯Br inter­actions between pyridine H atoms and Br− anions connect these chains into a network parallel to the bc plane

Probing signatures of bounce inflation with current observations

The aim of this paper is to probe the features of the bouncing cosmology with the current observational data. Basing on bounce inflation model, with high derivative term, we propose a general parametrization of primordial power spectrum which includes the typical bouncing parameters, such as bouncing time-scale, and energy scale. By applying Markov Chain Monto Carlo analysis with current data combination of Planck 2015, BAO and JLA, we report the posterior probability distributions of the parameters. We find that, bouncing models can well explain CMB observations, especially the deficit and oscillation on large scale in TT power spectrum.Comment: 17 pages, 8 figure

Oxalic acid–pyridine-4-carbonitrile (1/2)

In the title compound, 2C6H4N2·C2H2O4, the oxalic acid mol­ecule lies about an inversion center. The pyridine ring of the pyridine-4-carbonitrile mol­ecule is almost planar, the largest deviation from the least-squares plane being 0.006 (1) Å; the nitrile N atom deviates from this plane by 0.114 (1) Å. In the crystal, the oxalic acid mol­ecules and the pyridine-4-carbonitrile mol­ecules form stacks. Neighboring mol­ecules within the stacks are related by translation in the a direction, with inter­planar distances of 3.183 (1) and 3.331 (2) Å, respectively. Each oxalic acid mol­ecule forms strong O—H⋯N hydrogen bonds with two mol­ecules of pyridine-4-carbonitrile. Besides this, there are also weak C—H⋯O inter­actions

1,1′-(Phenyl­methyl­ene)dinaphthalen-2-ol

In the title compound, C27H20O2, the phenyl ring is oriented with respect to the naphthalene ring systems at 57.87 (6) and 85.12 (6)°. The two naphthalene ring systems make a dihedral angle of 70.10 (4)°. In the mol­ecule, the hy­droxy groups are involved in a strong intra­molecular O—H⋯O hydrogen bond. In the crystal, inversion dimers linked by pairs of O—H⋯O hydrogen bonds occur. A weak C—H⋯π inter­action is also observed in the crystal