Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System

This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial traveling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and nonexistence of traveling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle

Study of Nonleptonic B(s)∗→M1M2B^{\ast}_{(s)}\to M_1 M_2 (M=D(M=D, DsD_s, π\pi, K)K) Weak Decays with Factorization Approach

Motivated by the experiments of heavy flavor physics at running LHC and upgrading SuperKEKB/Belle-II in the future, the nonleptonic $B^{\ast}_{(s)}\to M_1 M_2$ $(M=D$, $D_s$, $\pi$, $K)$ weak decays are studied in this paper. The amplitudes are calculated with factorization approach, and the transition form factors $A_0^{B^{\ast}_{(s)}\to M_1}(0)$ are evaluated within BSW model. With the reasonable approximation $\Gamma_{tot}(B^*_{(s)})\simeq \Gamma(B^*_{(s)}\to B_{(s)}\gamma)$, our predictions of branching fractions are presented. Numerically, the CKM-favored tree-dominated $\bar{B}^{*0} \to D^+D^-_s$ and $\bar{B}^{*0}_s \to D^+_sD^-_s$ decays have the largest branching fractions of the order $\sim{\cal O}(10^{-8})$, and hence will be firstly observed by forthcoming Belle-II experiment. However, most of the other decay modes have the branching fractions~$<{\cal O}(10^{-9})$ and thus are hardly to be observed soon. Besides, for the possible detectable $B^{\ast}_{(s)}$ decays with branching fractions $\gtrsim{\cal O}(10^{-9})$, some useful ratios, such as $R_D$ {\it et al.,} are presented and discussed in detail.Comment: 17 pages, 5 tables, the version published in International Journal of Modern Physics

Composite Learning Control With Application to Inverted Pendulums

Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However, the condition of persistent excitation (PE) still has to be satisfied to guarantee parameter convergence in CAC. This paper proposes a novel model reference composite learning control (MRCLC) strategy for a class of affine nonlinear systems with parametric uncertainties to guarantee parameter convergence without the PE condition. In the composite learning, an integral during a moving-time window is utilized to construct a prediction error, a linear filter is applied to alleviate the derivation of plant states, and both the tracking error and the prediction error are applied to update parametric estimates. It is proven that the closed-loop system achieves global exponential-like stability under interval excitation rather than PE of regression functions. The effectiveness of the proposed MRCLC has been verified by the application to an inverted pendulum control problem.Comment: 5 pages, 6 figures, conference submissio

Sound radiation characteristics of a box-type structure

The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies

Spectral statistics of large dimensional Spearman's rank correlation matrix and its application

Let $\mathbf{Q}=(Q_1,\ldots,Q_n)$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_1,\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_j$, $j=1,\ldots,n$. Assume that $\mathbf {X}_i,i=1,\ldots ,p$ are i.i.d. copies of $\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix with $\mathbf{X}_i$ as its $i$th row. Then $S_n=XX^*$ is called the $p\times n$ Spearman's rank correlation matrix which can be regarded as a high dimensional extension of the classical nonparametric statistic Spearman's rank correlation coefficient between two independent random variables. In this paper, we establish a CLT for the linear spectral statistics of this nonparametric random matrix model in the scenario of high dimension, namely, $p=p(n)$ and $p/n\to c\in(0,\infty)$ as $n\to\infty$. We propose a novel evaluation scheme to estimate the core quantity in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576] to bypass the so-called joint cumulant summability. In addition, we raise a two-step comparison approach to obtain the explicit formulae for the mean and covariance functions in the CLT. Relying on this CLT, we then construct a distribution-free statistic to test complete independence for components of random vectors. Owing to the nonparametric property, we can use this test on generally distributed random variables including the heavy-tailed ones.Comment: Published at http://dx.doi.org/10.1214/15-AOS1353 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org