Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Strongly interacting matter from holographic QCD model

We introduce the 5-dimension dynamical holographic QCD model, which is constructed in the graviton-dilaton-scalar framework with the dilaton background field $\Phi$ and the scalar field $X$ responsible for the gluodynamics and chiral dynamics, respectively. We review our results on the hadron spectra including the glueball and light meson spectra, QCD phase transitions and transport properties in the framework of the dynamical holographic QCD model.Comment: 8 pages, 8 figures, proceedings for QCD@Work2016, June 27-30,2014, Martina Franca, Italy. arXiv admin note: text overlap with arXiv:1409.843

Transmit design for MIMO wiretap channel with a malicious jammer

In this paper, we consider the transmit design for multi-input multi-output (MIMO) wiretap channel including a malicious jammer. We first transform the system model into the traditional three-node wiretap channel by whitening the interference at the legitimate user. Additionally, the eavesdropper channel state information (ECSI) may be fully or statistically known, even unknown to the transmitter. Hence, some strategies are proposed in terms of different levels of ECSI available to the transmitter in our paper. For the case of unknown ECSI, a target rate for the legitimate user is first specified. And then an inverse water-filling algorithm is put forward to find the optimal power allocation for each information symbol, with a stepwise search being used to adjust the spatial dimension allocated to artificial noise (AN) such that the target rate is achievable. As for the case of statistical ECSI, several simulated channels are randomly generated according to the distribution of ECSI. We show that the ergodic secrecy capacity can be approximated as the average secrecy capacity of these simulated channels. Through maximizing this average secrecy capacity, we can obtain a feasible power and spatial dimension allocation scheme by using one dimension search. Finally, numerical results reveal the effectiveness and computational efficiency of our algorithms.Comment: 2015 IEEE 81st Vehicular Technology Conference (VTC Spring

Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model with $SU_L(N_f)\times SU_R(N_f)$ symmetry, especially for $N_f=2,3$ and $N_f=2+1$. It is shown that in quark mass plane($m_{u/d}-m_s$) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents $\beta$ and $\delta$, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values $\beta=\frac{1}{2}, \delta=3$ and $\beta=\frac{1}{3}, \delta=3$ for $N_f=2$ and $N_f=3$ respectively. For $N_f=2+1$, in small strange quark mass($m_s$) region, the phase transitions for strange quark and $u/d$ quarks are strongly coupled, and the critical exponents are $\beta=\frac{1}{3},\delta=3$; when $m_s$ is larger than $m_{s,t}=0.290\rm{GeV}$, the dynamics of light flavors($u,d$) and strange quarks decoupled and the critical exponents for $\bar{u}u$ and $\bar{d}d$ becomes $\beta=\frac{1}{2},\delta=3$, exactly the same as $N_f=2$ result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at $m_{s,t}=0.290\rm{GeV}$, at which $\beta=0.250,\delta=4.975$. In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.Comment: 32 pages, 11 figures, regular articl