Complete synchronization of Kuramoto oscillators with finite inertia

We present an approach based on Gronwall’s inequalities for the asymptotic complete phase-frequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phase-frequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall’s inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations.     

X-Y振镜扫描式舌诊高光谱采集系统

针对目前舌诊研究中在舌体信息全面获取方面存在严重不足,将高光谱技术用到舌诊的研究中来,提出了一种基于X-Y振镜扫描式舌诊高光谱采集系统.通过模拟实验,采集与舌体大小相似图片的高光谱信息,验证了该系统可以用于舌体高光谱信息采集,实验结果表明,与现有舌诊客观化研究相比,该系统可以获得更多的舌体信息,为舌诊客观化研究提供了一...     

Müntz-type theorems on the half-line with weights

We consider the linear span S   of the functions t^_ak$t^{a_k}$ (with some _ak>0$a_k>0$) in weighted L²$L^2$ spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comparisons are also made between the new results and those that can be deduced from older ones in the literature.     

Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions

In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl–Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results.     

On the generalized Weyl problem for flat metrics in the hyperbolic 3-space

The paper deals with the study of complete embedded flat surfaces in H³${\mathbb{H}}^3$ with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weyl?s problem of realizing isometrically any complete flat metric with Euclidean singularities in H³${\mathbb{H}}^3$ which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities.     

ON SOLVABLE COMPLETE LIE SUPERALGEBRAS

The authors discuss the properties of solvable complete Lie superalgebra, proving that solvable Lie superalgebras of maximal rank are complete.