The Fractal and The Recurrence Equations Concerning The Integer Partitions

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem

On a question of Demailly-Peternell-Schneider

This note aims to give an affirmative answer to an open question posed by Demailly-Peternell-Schneider [DPS] in 2001 and recently by Peternell [P] again. Let $f:X\mapsto Y$ be a surjective morphism from a log canonical pair (X,D) onto a ${\mathbb Q}$-Gorenstein variety $Y$. If $-(K_X+D)$ is nef, we show that $-K_Y$ is pseudo-effective.Comment: J. Eur. Math. Soc. (to appear), minor corrections to some misleading misprint

Analytical solution for the lattice Boltzmann model beyond Naviers-Stokes

To understand lattice Boltzmann model capability for capturing nonequilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer

Joint Secure Beamforming for Cognitive Radio Networks with Untrusted Secondary Users

In this paper, we consider simultaneous wireless information and power transfer (SWIPT) in orthogonal frequency division multiple access (OFDMA) systems with the coexistence of information receivers (IRs) and energy receivers (ERs). The IRs are served with best-effort secrecy data and the ERs harvest energy with minimum required harvested power. To enhance physical-layer security and yet satisfy energy harvesting requirements, we introduce a new frequency-domain artificial noise based approach. We study the optimal resource allocation for the weighted sum secrecy rate maximization via transmit power and subcarrier allocation. The considered problem is non-convex, while we propose an efficient algorithm for solving it based on Lagrange duality method. Simulation results illustrate the effectiveness of the proposed algorithm as compared against other heuristic schemes.Comment: To appear in Globecom 201