Perturbational Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the perturbational method to construct the non-radially symmetric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitutional method and the separation method to construct a new class of analytical solutions for that system. In fact, we perturb the linear velocity: u=c(t)x+b(t), and substitute it into the system. Then, by comparing the coefficients of the polynomial, we can deduce the functional differential equations involving $(c(t),b(t),\rho^{2}(0,t)).$ Additionally, we could apply the Hubble's transformation c(t)={\dot{a}(3t)}/{a(3t)}, to simplify the ordinary differential system involving $(a(3t),b(t),\rho ^{2}(0,t))$. After proving the global or local existences of the corresponding dynamical system, a new class of analytical solutions is shown. And the corresponding solutions in radial symmetry are also given. To determine that the solutions exist globally or blow up, we just use the qualitative properties about the well-known Emden equation: {array} [c]{c} {d^{2}/{dt^{2}}}a(3t)= {\xi}{a^{1/3}(3t)}, a(0)=a_{0}>0 ,\dot{a}(0)=a_{1} {array} . Our solutions obtained by the perturbational method, fully cover the previous known results in "M.W. Yuen, \textit{Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations,}J. Math. Phys., \textbf{51} (2010) 093524, 14pp." by the separation method.Comment: 12 page

On the Security of Y-00 under Fast Correlation and Other Attacks on the Key

The potential weakness of the Y-00 direct encryption protocol when the encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In this paper, we show how this weakness can be eliminated with a proper design of ENC. In particular, we present a Y-00 configuration that is more secure than AES under known-plaintext attack. It is also shown that under any ciphertext-only attack, full information-theoretic security on the Y-00 seed key is obtained for any ENC when proper deliberate signal randomization is employed

Capacity-Achieving Iterative LMMSE Detection for MIMO-NOMA Systems

This paper considers a iterative Linear Minimum Mean Square Error (LMMSE) detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO) systems with Non-Orthogonal Multiple Access (NOMA). The iterative LMMSE detection greatly reduces the system computational complexity by departing the overall processing into many low-complexity distributed calculations. However, it is generally considered to be sub-optimal and achieves relatively poor performance. In this paper, we firstly present the matching conditions and area theorems for the iterative detection of the MIMO-NOMA systems. Based on the proposed matching conditions and area theorems, the achievable rate region of the iterative LMMSE detection is analysed. We prove that by properly design the iterative LMMSE detection, it can achieve (i) the optimal sum capacity of MU-MIMO systems, (ii) all the maximal extreme points in the capacity region of MU-MIMO system, and (iii) the whole capacity region of two-user MIMO systems.Comment: 6pages, 5 figures, accepted by IEEE ICC 2016, 23-27 May 2016, Kuala Lumpur, Malaysi

Optimal dynamic reinsurance with dependent risks: variance premium principle

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the variance premium principle, we adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model. From the numerical examples, we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model. The former depends not only on the safety loading, time, and the interest rate, but also on the claim size distributions and the claim number processes, while the latter depends only on the safety loading, time, and the interest rate.postprin