How fast can Maker win in fair biased games?

We study $(a:a)$ Maker–Breaker games played on the edge set of the complete graph on $n$ vertices. In the following four games — perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the least number of moves which Maker needs in order to win these games. Moreover, for all games except for the star factor game, we show how first player can win in the strong version of these games.     

Martingale–coboundary decomposition for families of dynamical systems

We prove statistical limit laws for sequences of Birkhoff sums of the type ${\sum }_{j=0}^{n?1}{v}_n°T_n^j$ where $T_n$ is a family of nonuniformly hyperbolic transformations.The key ingredient is a new martingale–coboundary decomposition for nonuniformly hyperbolic transformations which is useful already in the case when the family $T_n$ is replaced by a fixed transformation T, and which is particularly effective in the case when $T_n$ varies with n.In addition to uniformly expanding/hyperbolic dynamical systems, our results include cases where the family $T_n$ consists of intermittent maps, unimodal maps (along the Collet–Eckmann parameters), Viana maps, and externally forced dispersing billiards.As an application, we prove a homogenisation result for discrete fast–slow systems where the fast dynamics is generated by a family of nonuniformly hyperbolic transformations.     

Fast orthogonalization to the kernel of the discrete gradient operator with application to Stokes problem

We obtain a simple tensor representation of the kernel of the discrete d-dimensional gradient operator defined on tensor semi-staggered grids. We show that the dimension of the nullspace grows as O(n^d-2), where d is the dimension of the problem, and n is one-dimensional grid size. The tensor structure allows fast orthogonalization to the kernel. The usefulness of such procedure is demonstrated on three-dimensional Stokes problem, discretized by finite differences on semi-staggered grids, and it is shown by numerical experiments that the new method outperforms usually used stabilization approach.     

A fast and stable method for rotating spherical harmonic expansions

In this paper, we present a simple and efficient method for rotating a spherical harmonic expansion. This is a well-studied problem, arising in classical scattering theory, quantum mechanics and numerical analysis, usually addressed through the explicit construction of the Wigner rotation matrices. We show that rotation can be carried out easily and stably through “pseudospectral” projection, without ever constructing the matrix entries themselves. Existing fast algorithms, based on recurrence relations, are subject to a variety of instabilities, limiting the effectiveness of the approach for expansions of high degree.     

Fast sweeping method for the factored eikonal equation

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss–Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss–Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.     

The black-box fast multipole method

A new O(N)$O(N)$ fast multipole formulation is proposed for non-oscillatory kernels. This algorithm is applicable to kernels K(x,y)$K(x\text{,}y)$ which are only known numerically, that is their numerical value can be obtained for any (x,y)$(x\text{,}y)$. This is quite different from many fast multipole methods which depend on analytical expansions of the far-field behavior of K  , for |x-y|$|x-y|$ large. Other “black-box” or “kernel-independent” fast multipole methods have been devised. Our approach has the advantage of requiring a small pre-computation time even for very large systems, and uses the minimal number of coefficients to represent the far-field, for a given L²$L^2$ tolerance error in the approximation. This technique can be very useful for problems where the kernel is known analytically but is quite complicated, or for kernels which are defined purely numerically.     

Decay kinetics of the defect-based visible luminescence in ZnO

Photoluminescence spectra and decays under pulsed N₂ (337 nm) laser excitation were measured for hydrothermally grown bulk and liquid-phase epitaxy (LPE)-grown film ZnO samples within 9-300 K. Temperature dependence of integrated spectra over the exciton and visible spectral regions was evaluated using a model involving standard energy barrier processes. Decay curves measured within a broad time window (10 ns-1 ms) and with extreme signal/background ratio (five orders of magnitude) point to complex decay mechanism in which the exponential and inverse power-law processes can coexist. There is no straightforward interconnection between the observed temperature dependence of integrated visible photoluminescence intensity and its decay shape over the 9-300 K temperature interval.     

一种水声信道均衡器的混合算法

水声高速相干通信中使用自适应均衡对抗信道在接收信号中产生的码间串扰。目前,1/2分数间隔采样的判决反馈均衡器结构得到了广泛的应用。本文分析了几种自适应算法在此种均衡器结构下的性能,结合浅海水声信道的特点,提出了一种快速卡尔曼滤波和快速自优化最小均方的混合算法,模拟及海试结果表明,该混合算法在计算复杂度、收敛速度以及稳定性方面都有很好的性能,已经应用到了水声实时高速通信系统当中。     

含左手材料对称三层平板空气波导的模式特性

研究了左手材料作为衬底及覆盖层的对称三层平板空气波导的传输特性.快波和慢波都可以在这种波导中传播.快波不存在基模模式,只有0阶和1阶的TE或TM模才会出现慢波.当左手材料的相对介电常量和相对磁导率相等时,TE、TM模式完全简并,当其相异时简并消除.可以存在同阶模式的双传播模.     

Impact of selective excitation on carbon longitudinal relaxation: Towards fast solid-state NMR techniques

The effect of selective pulses on the apparent carbon longitudinal relaxation is investigated in three fully ¹³C-labeled systems, histidine as a model system and two proteins MerP and YajG. It is shown that the longitudinal relaxation of a selectively excited carbon spin is greatly enhanced, mainly because of fast spin-diffusion. This relaxation enhancement allows reducing the time necessary for polarization recovery between two experiments. This effect can be exploited either to improve the sensitivity of NMR experiments or to reduce the experimental time. Using selective carbon excitation combined with fast pulsing on fully ¹³C-labeled proteins, a sensitivity improvement of 20–45% over standard cross-polarization methods is predicted from the measured relaxation times.