A note on the reflection principle for the biharmonic equation and the Stokes system

In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

On integrating vertex singularities using extrapolation

A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.Dedicated to Carl-Erik Fröberg on the occasion of his 75th birthday.This work was supported by The Norwegian Research Council for Science and the Humanities.     

Dimension and entropy of a non-ergodic Markovian process and its relation to Rademacher Riesz Products

Given a Markov chain (not necessarily stationary or homogeneous) with finite state space and an initial distribution, we can construct a measure on the unit interval [0, 1]. In this work we examine the equality (up to a constant) of the Hausdorff dimension of and of a suitably defined entropy for the Markovian process. The results are applied to the so-called Rademacher-Riesz Products.     

Complexity of the decidability of the unquantified set theory with a rank operator

The unquantified set theory MLSR containing the symbols ∪, ∖, ≠, ∈,R (R(x) is interpreted as a rank ofx) is considered. It is proved that there exists an algorithm which for any formulaQ of the MLSR theory decides whetherQ is true or not using the spacec|Q|³ (|Q| is the length ofQ).     

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

激光雷达辅助驾驶道路参数计算方法研究

针对特定场景辅助驾驶的需求,构建道路场景车载激光雷达三维扫描系统,并设计基于三维激光点云的道路参数提取与计算方法,包括路面宽度、横杆或桥梁或隧道限高、拐弯半径等等,为辅助判断道路的可通过性提供决策依据。测试和对比实验表明,所设计算法效果稳定、精度良好,在效率和自动化程度上有一定优势,可为辅助驾驶提供非常有益的决策参数。     

G波段500 W带状注扩展互作用速调管设计研究

针对太赫兹频段实现高功率面临物理机制上的难题,设计了一个G波段带状注速调管,展示了基于非相对论带状电子注和扩展互作用技术所能达到的功率水平以及影响性能的物理因素。文中设计基于电压24.5 kV、电流0.6 A,1 mm×0.15 mm的椭圆电子注,以及与之相匹配的互作用系统,即横向过尺寸哑铃型多间隙谐振腔,可以实现高功率和高增益。三维PIC仿真结果显示,在考虑实际腔体损耗的情况下,能够获得超过500 W的功率,电子效率和增益分别达到3.65%和38.2 dB。研究发现,输出功率和效率的提升很大程度上受到多间隙腔模式稳定性以及电路欧姆损耗的制约;输出腔的欧姆损耗对输出功率影响尤为显著,工程设计需要特别考虑。本文的研究为高频段带状注扩展互作用器件的研发打下了良好的基础。