A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

Construction of Generalized Diffusion Processes: the Resolvent Approach

In this paper, we define the generalized diffusion operator ■ for two suitable measures on the line, which includes the generators of the birth-death processes, the one-dimensional diffusion and the gap diffusion among others. Via the standard resolvent approach, the associated generalized diffusion processes are constructed.     

Comparison of implicit and explicit AUSM‐family schemes for compressible multiphase flows

This paper makes the first attempt of extending implicit AUSM‐family schemes to multiphase flow simulations. Water faucet, air–water shock tube and oscillating manometer problems are used as benchmark tests with the generic four‐equation two‐fluid model. For solving the equations implicitly, Newton's method along with a sparse matrix solver (UMFPACK solver) is employed, and the numerical Jacobian matrix is calculated. Comparison between implicit and explicit AUSM‐family schemes is presented, indicating that similarly accurate results are obtained with both schemes. Furthermore, the water faucet problem is solved using both staggered and collocated grids. This investigation helps integrate high‐resolution schemes into staggered‐grid‐based computational algorithms. The influence of the interface pressure correction on the simulation results is also examined. Results show that the interfacial pressure correction introduces numerical dissipation. However, this dissipation cannot eliminate the overshoots because of the incompatibility of numerical discretization of the conservative and non‐conservative terms in the governing equations. The comparison of CPU time between implicit and explicit schemes is also studied, indicating that the implicit scheme is capable of improving the computational efficiency over its explicit counterpart. Copyright © 2014 John Wiley & Sons, Ltd.     

Approximations of spectra of Schrödinger operators with complex potentials on ℝd

We study spectral approximations of Schrödinger operators T = ?Δ+Q with complex potentials on Ω = ?^d, or exterior domains Ω??^d, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains Ω_n, and of boundary conditions on ?Ω_n such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators T_n without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d = 1,2,3, illustrate our results.     

可修复人机系统的指数稳定性

研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.     

Blow‐up for the b‐family of equations

In this paper, we consider the b‐family of equations on the torus u _t ?u _{t x x} +(b + 1)u u _x =b u _x u _{x x} +u u _{x x x} , which for appropriate values of b reduces to well‐known models, such as the Camassa–Holm equation or the Degasperis–Procesi equation. We establish a local‐in‐space blow‐up criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and exact controllability of fractional evolution inclusions with damping

The aim of this paper is to deal with the existence of mild solutions and exact controllability for a class of fractional evolution inclusions with damping (FEID, for short) in Banach spaces. Firstly, we provide the representation of mild solutions for FEID by applying the method of Laplace transform and the theory of (α,κ)‐regularized families of operators. Next, we are concerned with the existence and exact controllability of FEID under some suitable sufficient conditions by using the method of measure of noncompactness and an appropraite fixed point theorem. Finally, an application to nonlinear partial differential equations with temporal fractional derivatives is presented to illustrate the effectiveness of our main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Existence of μ−pseudo almost periodic solutions to some evolution equations

In this article, a new approach for pseudo almost periodic solution under the measure theory, under Acquistpace‐Terreni conditions. We make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of μ‐pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. For illustration, we propose some application to a nonautonomous heat equation. Copyright © 2017 John Wiley & Sons, Ltd.     

Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.