Smoothing of bump functions

Let X be a separable Banach space with a Schauder basis, admitting a continuous bump which depends locally on finitely many coordinates. Then X admits also a C^∞-smooth bump which depends locally on finitely many coordinates.     

The Toda system and multiple-end solutions of autonomous planar elliptic problems

We prove the existence of a new class of entire, positive solutions for the classical elliptic problem Δu−u+up=0 in R², when p>2. The solutions we construct are obtained by perturbing the function

     

Weighted Bartholdi zeta functions of graph coverings

We define the weighted Bartholdi zeta function and a weighted L-function of a graph G, and give determinant expressions of them. Furthermore, we present a decomposition formula for the weighted Bartholdi zeta function of a regular covering of G by weighted L-functions of G.     

Folded bump diagrams for partitions of classical types

We introduce folded bump diagrams for $B_n$, $C_n$ and $D_n$ partitions. They allow us to use the type A methods to handle all other classical types simultaneously. As applications, we give uniform interpretations for two families of bijections between noncrossing and nonnesting partitions, where the first family preserves openers and closers, while the second family preserves the statistics a and μ. Here a is the increasing sequence of the minimal elements of the blocks, and μ is the sizes of these blocks. We also extend the results of Chen, Deng, Du, Stanley and Yan (2007) [5] and Kasraoui and Zeng (2006) [10] concerning the symmetry of partitions of type A to other classical types uniformly.     

Direct numerical simulation of the two-dimensional speed bump flow at increasing Reynolds numbers

The Speed Bump flow model was designed by Boeing to provide a mildly three-dimensional flow with separation from a very smooth surface, strongly controlled by the turbulence. Experiments are conducted by several teams, as are simulations, over a range of Reynolds numbers. Direct Numerical Simulations (DNS) are not possible for the full 3D geometry of width L, leading several groups to conduct DNS over a two-dimensional geometry, in other words the cross-section of the full geometry, with periodic lateral conditions and a typical domain width of 0.04L. This does not allow precise comparisons with experiment, but code-to-code comparison is instructive. A shallow separation bubble is present, as intended. The domain width becomes marginal after reattachment, where the boundary layer is much thicker. The Reynolds number based on L has been 10⁶, so far in the literature, which causes partial relaminarization and tends to defeat the purpose of testing turbulence models. Flow visualisation is clear on this. Here, we present results at the Reynolds number 10⁶ and 1.4 × 10⁶, and the higher value essentially eliminates relaminarization. Detailed results are shown, including studies of domain width, grid resolution, and numerical dissipation. The turbulence models give inaccurate results for skin friction, already in the intense favourable pressure gradient, which causes the formation of an internal boundary layer; the separation prediction on the other hand is reasonable. The wall curvature seems to play a role. The present results also provide trustworthy data to test Large-Eddy Simulation (LES), especially if using a Wall Model (WMLES). The comparisons will have a preliminary character until the results of the ongoing detailed experiments and of DNS at even higher Reynolds number and with a wider domain are available and carefully compared.     

Plasmonic coupler based on the nanoslit with bump

In this paper, we propose a plasmonic coupler which is composed of a nanoslit with a bump. The slit is used to generate surface plasmon polariton (SPP), and the bump is employed as a SPP reflector. It is found that the phase difference between the SPP propagating the opposite direction to the bump and the one reflected by the bump can be periodically adjusted by the distance between the center of slit and the bump. When the constructive interference between the two SPPs occurs, the proposed structure can be regarded as a undirectional plasmonic coupler. Moreover, we also find that the propagation of the interfering SPPs is influenced by the width and length of bump. It is expected that our results may be utilized to control the electromagnetic wave in subwavelength optics.     

Vibration analysis of automobile tire due to bump impact

The improvement of car driving comfort is requested according to development of automobile manufacturing technology. Therefore, many experts have been studying automotive vibration of normally driving cars to improve automotive driving comfort. In this paper, vibration characteristics of an automobile tire that passes a cleat are analyzed. The model for automobile tire is verified through numerical analysis and experimental method. The automobile tire is assumed to 7-degree of freedom system, and the effect on the proposed tire design factor is considered. This analysis result proved that the proposed tire design factor reduced tire and wheel vibration energy.     

半序集的碰撞数与分层深度贪婪算法

设Ｐ＝（Ｘ，≤）是一个半序集，本文在关于碰撞数的深度贪婪算法的基础上，直接证明了对任意的Ｐ存在一个最优的ＤＬＧ扩张，给出了ＤＬＧ半序集的定义，并证明了半序集Ｐ是ＤＬＧ半序集的一个充分条件，最后给出了ＤＬＧ扩张算法。     

The Bumpy Road to the Mode Forest

Abstract

The mode tree of Minnotte and Scott provides a valuable method of investigating features such as modes and bumps in a unknown density. By examining kernel density estimates for a range of bandwidths, we can learn a lot about the structure of a data set. Unfortunately, the basic mode tree can be strongly affected by small changes in the data, and gives no way to differentiate between important modes and those caused, for example, by outliers. The mode forest overcomes these difficulties by looking simultaneously at a large collection of mode trees, all based on some variation of the original data, by means such as resampling or jittering. The resulting graphic tool is both visually appealing and informative.     

On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds

We show that the number of solutions of a nonlinear elliptic problem on a Riemannian manifold depends on the topological properties of the manifold. In particular we consider the Lusternik-Schnirelmann category and the Poincaré polynomial of the manifold.