Best possible densities of Dickson m-tuples, as a consequence of Zhang-Maynard-Tao

We determine for what proportion of integers $h$ one now knows that there are infinitely many prime pairs $p,\ p+h$ as a consequence of the Zhang-Maynard-Tao theorem. We consider the natural generalization of this to $k$-tuples of integers, and we determine the limit of what can be deduced assuming only the Zhang-Maynard-Tao theorem.Comment: 9 pages. Final version. Some minor changes, Analytic Number Theory - In Honor of Helmut Maier's 60th Birthday, Springer, 201

Problems of Clustering of Radiogalaxies

We present the preliminary analysis of clustering of a sample of 1157 radio-identified galaxies from Machalski & Condon (1999). We found that for separations $2-15 h^{-1}$Mpc their redshift space autocorrelation function $\xi(s)$ can be approximated by the power law with the correlation length $\sim 3.75h^{-1}$Mpc and slope $\gamma \sim 1.8$. The correlation length for radiogalaxies is found to be lower and the slope steeper than the corresponding parameters of the control sample of optically observed galaxies. Analysis the projected correlation function $\Xi(r)$ displays possible differences in the clustering properties between active galactic nuclei (AGN) and starburst (SB) galaxies.Comment: Submitted: Proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez & S. N. Zhang (eds.

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.Comment: 22 pages, 3 figure

On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e

For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved

Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems

The evolution of local spin polarization in finite systems involves interference phenomena that give rise to {\bf quantum dynamical echoes }and non-ergodic behavior. We predict the conditions to observe these echoes by exploiting the NMR sequences devised by Zhang et al. [Phys. Rev. Lett. {\bf % 69}, 2149 (1992)], which uses a rare $^{13}$C as {\bf local probe }for a dipolar coupled $^1$H spin system. The non-ideality of this probe when testing mesoscopic systems is carefully analyzed revealing the origin of various striking experimental features.Comment: 4 pages, Revtex, 3 Figures available upon reques

Theory of Four-dimensional Fractional Quantum Hall States

We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges $+(-)1/m^3$ in the total configuration space CP$^3$. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.Comment: 4 page

The price Asian venture capitalists pay to work in Silicon Valley

They pay higher valuations due to their lower social status rather than social network disadvantages, write Jing Zhang, Poh-Kam Wong and Yuen-Ping H