Resource Allocation for Secure Communications in Cooperative Cognitive Wireless Powered Communication Networks

We consider a cognitive wireless powered communication network (CWPCN) sharing the spectrum with a primary network who faces security threats from eavesdroppers (EAVs). We propose a new cooperative protocol for the wireless powered secondary users (SU) to cooperate with the primary user (PU). In the protocol, the SUs first harvest energy from the power signals transmitted by the cognitive hybrid access point during the wireless power transfer (WPT) phase, and then use the harvested energy to interfere with the EAVs and gain transmission opportunities at the same time during the wireless information transfer (WIT) phase. Taking the maximization of the SU ergodic rate as the design objective, resource allocation algorithms based on the dual optimization method and the block coordinate descent method are proposed for the cases of perfect channel state information (CSI) and collusive/non-collusive EAVs under the PU secrecy constraint. More PU favorable greedy algorithms aimed at minimizing the PU secrecy outage probability are also proposed. We furthermore consider the unknown EAVs' CSI case and propose an efficient algorithm to improve the PU security performance. Extensive simulations show that our proposed protocol and corresponding resource allocation algorithms can not only let the SU gain transmission opportunities but also improve the PU security performance even with unknown EAVs' CSI.Comment: Submitted to IEEE Systems Journal for possible publicatio

A Monge-Ampere Type Fully Nonlinear Equation on Hermitian Manifolds

We study a fully nonlinear equation of complex Monge-Ampere type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution

The Dirichlet Problem for a Complex Monge-Ampere Type Equation on Hermitian Manifolds

We are concerned with fully nonlinear elliptic equations on complex manifolds and search for technical tools to overcome difficulties in deriving a priori estimates which arise due to the nontrivial torsion and curvature, as well as the general (non-pseudoconvex) shape of the boundary. We present our methods, which work for more general equations, by considering a specific equation which resembles the complex Monge-Ampere equation in many ways but with crucial differences. Our work is motivated by recent increasing interests in fully nonlinear equations on complex manifolds from geometric problems.Comment: Revised version based on the referees' reports, we would like to thank them for their helpful comment

Complex Monge-Ampere equations and totally real submanifolds

We study the Dirichlet problem for complex Monge-Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in the flat case. We also consider the equation on compact manifolds without boundary, attempting to generalize Yau's theorems in the Kaehler case. As applications of the main result we study some connections between the homogeneous complex Monge-Ampere ({\em HCMA}) equation and totally real submanifolds, and a special Dirichlet problem for the HCMA equation related to Donaldson's conjecture on geodesics in the space of Kaehler metrics

Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions

We derive analytic formula for electric and magnetic fields produced by a moving charged particle in a conducting medium with the electric conductivity $\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We use the Green function method and assume that $\sigma_{\chi}$ is much smaller than $\sigma$. The compact algebraic expressions for electric and magnetic fields without any integrals are obtained. They recover the Lienard-Wiechert formula at vanishing conductivities. Exact numerical solutions are also found for any values of $\sigma$ and $\sigma_{\chi}$ and are compared to analytic results. Both numerical and analytic results agree very well for the scale of high energy heavy ion collisions. The space-time profiles of electromagnetic fields in non-central Au+Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.Comment: RevTex 4, 7 figures, 13 pages; section III-B has been re-written using dimensionful variables to improve readability; added references and one figur

Analytical Solution of Cross Polarization Dynamics

Cross polarization (CP) dynamics, which was remained unknown for five decades, has been derived analytically in the zero- and double-quantum spaces. The initial polarization in the double-quantum space is a constant of motion under strong pulse condition ($|\omega_{1I}+\omega_{1S}|\gg |d(t)|$), while the Hamiltonian in the zero-quantum space reduces to $d(t)\sigma_{z}^{\Delta}$ under the Hartmann-Hahn match condition ($\omega_{1I}=\omega_{1S}$). The time dependent Hamilontian ($d(t)\sigma_{z}^{\Delta}$) in the zero-quantum space can be expressed by average Hamiltonians. Since$[d(t')\sigma_{z}^{\Delta}, d(t")\sigma_{z}^{\Delta}]=0$, only zero order average Hamiltonian needs to be calculated, leading to an analytical solution of CP dynamics

Some LpL^p rigidity results for complete manifolds with harmonic curvature

Let $(M^n, g)(n\geq3)$ be an $n$-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by $R$ and $\mathring{Rm}$ the scalar curvature and the trace-free Riemannian curvature tensor of $M$, respectively. The main result of this paper states that $\mathring{Rm}$ goes to zero uniformly at infinity if for $p\geq \frac n2$, the $L^{p}$-norm of $\mathring{Rm}$ is finite. Moreover, If $R$ is positive, then $(M^n, g)$ is compact. As applications, we prove that $(M^n, g)$ is isometric to a spherical space form if for $p\geq \frac n2$, $R$ is positive and the $L^{p}$-norm of $\mathring{Rm}$ is pinched in $[0,C_1)$, where $C_1$ is an explicit positive constant depending only on $n, p$, $R$ and the Yamabe constant. In particular, we prove an $L^{p}(\frac n2\leq p<\frac{n-2}{2}(1+\sqrt{1-\frac4n}))$-norm of $\mathring{Ric}$ pinching theorem for complete, simply connected, locally conformally flat Riemannian $n(n\geq 6)$-manifolds with constant negative scalar curvature. We give an isolation theorem of the trace-free Ricci curvature tensor of compact locally conformally flat Riemannian $n$-manifolds with constant positive scalar curvature, which improves Thereom 1.1 and Corollary 1 of E. Hebey and M. Vaugon \cite{{HV}}. This rsult is sharped, and we can precisely characterize the case of equality.Comment: We revise the older version, and add some content

An example of compact K\"ahler manifold with nonnegative quadratic bisectional curvature

We construct a compact K\"ahler manifold of nonnegative quadratic bisectional curvature, which does not admit any K\"ahler metric of nonnegative orthogonal bisectional curvature. The manifold is a 7-dimensional K\"ahler C-space with second Betti number equal to 1, and its canonical metric is a K\"ahler-Einstein metric of positive scalar curvatureComment: 11 page

Rigidity Theorem for integral pinched shrinking Ricci solitons

We prove that an $n$-dimensional, $n\geq4$, compact gradient shrinking Ricci soliton satisfying a $L^{\frac n2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^n$, which improves the rigidity theorem given by G. Catino (arXiv:1509.07416vl).Comment: arXiv admin note: text overlap with arXiv:1509.07416 by other author

Transverse Energy Production at RHIC

We study the mechanism of transverse energy (E_T) production in Au+Au collisions at RHIC. The time evolution starting from the initial energy loss to the final E_T production is closely examined in transport models. The relationship between the experimentally measured E_T distribution and the maximum energy density achieved is discussed.Comment: 5 pages, 4 figure