Weak External Bisection of Some Graphs

Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V1 ∪ V2 and V1 ∩ V2 = ∅. If a bipartition satisfies ∥V1∣ - ∣V2∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V1, V2) such that ∀v ∈ V1, at least half minuses one of the neighbors of v are in the V2;∀v ∈ V2, at least half minuses one of the neighbors of v are in the V1. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.

A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.

KNOT POINT PLANNING FOR CARTESIAN TRAJECTORY GENERATION BASED ON INHERITANCE BISECTION ALGORITHM

The computation algorithm of knot point planning for Cartesian trajectorygeneration of manipulator is investigated, A novel inheritance bisection algorithm (IBA) based onconventional bisection algorithm (B A) is proposed. IBA has two steps. The first step is the 1 stknot point planning under lower set position accuracy; the second step is the 2nd knot pointplanning that inherits the results of the 1st planning under higher set position accuracy. Thesimulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA isdecreased compared with BA. IBA is more efficient to plan knot points.

n-transitivity of Bisection Groups of a Lie Groupoid

The notion of n-transitivity can be carried over from groups of diffeomorphisms on a manifold M to groups of bisections of a Lie groupoid over M. The main theorem states that the n-transitivity is fulfilled for all n ∈N by an arbitrary group of Cr-bisections of a Lie groupoid F of class Cr, where 1 ≤ r ≤ ω, under mild conditions. For instance, the group of all bisections of any Lie groupoid and the group of all Lagrangian bisections of any symplectic groupoid are n-transitive in the sense of this theorem. In particular, if F is source connected for any arrow γ∈ Г, there is a bisection passing through γ.

A COARSENING ALGORITHM ON ADAPTIVE GRIDS BY NEWEST VERTEX BISECTION AND ITS APPLICATIONS

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimemsions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

On the Existence of Global Bisections of Lie Groupoids

We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of bisections through more than one prescribed point is also discussed. We give some interesting applications of these results.

The Chern-Ricci flow and holomorphic bisectional curvature

In this note, we show that on Hopf manifold S^(2n-1)×S^1, the non-negativity of the holomorphic bisectional curvature is not preserved along the Chern-Ricci flow.

Bisection technique for designing synchronous parallel algorithms

A basic technique for designing synchronous parallel algorithms, the so-called bisection technique, is proposed. The basic pattern of designing parallel algorithms is described. The relationship between the designing idea and I Ching (principles of change) is discussed.

Judicious Bisection of Hypergraphs

Judicious bisection of hypergraphs asks for a balanced bipartition of the vertex set that optimizes several quantities simultaneously. In this paper, we prove that if G is a hypergraph with n vertices and ni edges of size i for i = 1, 2,…, k, then G admits a bisection in which each vertex class spans at mostm1/2＋1/4m2＋…＋（1/2^k）mk＋o（m1＋…＋mk）edges, where G is dense enough or △（G） =o（n） but has no isolated vertex, which turns out to be a bisection version of a conjecture proposed by Bollobas and Scott.

The Khler-Ricci Flow on Khler Manifolds with 2-Non-negative Traceless Bisectional Curvature Operator

The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kahler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kahler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corol- lary, the Kahler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kahler-Ricci soliton in the sense of Cheeger-Cromov-Hausdorff topology if complex dimension n ≥ 3.

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

页岩气开采中的压力变化与气液传质规律

根据页岩气的赋存及流动机理,建立考虑页岩渗吸与吸附、渗流与扩散的流动方程,采用线段源叠加解等效为压裂产生的压力分布作为方程的初始条件,使用非结构PEBI(perpendicular bisection)网格对水平井多段压裂井进行网格划分,有限体积法进行离散。利用高频压力监测的闷井压力数据验证了算法程序的可靠性。研究得出以下结果:(1)发现页岩气开发的压力双漏斗及气液双向传质流动规律;(2)依据这一规律给出页岩气压最佳闷井时间和最优排采制度。

Video Summarization Approach Based on Binary Robust Invariant Scalable Keypoints and Bisecting K-Means

Due to the exponential growth of video data,aided by rapid advancements in multimedia technologies.It became difficult for the user to obtain information from a large video series.The process of providing an abstract of the entire video that includes the most representative frames is known as static video summarization.This method resulted in rapid exploration,indexing,and retrieval of massive video libraries.We propose a framework for static video summary based on a Binary Robust Invariant Scalable Keypoint(BRISK)and bisecting K-means clustering algorithm.The current method effectively recognizes relevant frames using BRISK by extracting keypoints and the descriptors from video sequences.The video frames’BRISK features are clustered using a bisecting K-means,and the keyframe is determined by selecting the frame that is most near the cluster center.Without applying any clustering parameters,the appropriate clusters number is determined using the silhouette coefficient.Experiments were carried out on a publicly available open video project(OVP)dataset that contained videos of different genres.The proposed method’s effectiveness is compared to existing methods using a variety of evaluation metrics,and the proposed method achieves a trade-off between computational cost and quality.

Maximum Correntropy Criterion-Based UKF for Loosely Coupling INS and UWB in Indoor Localization

Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy criterion(MCC)instead of the minimummean square error criterion(MMSE).This innovative approach is applied to the loose coupling of the Inertial Navigation System(INS)and Ultra-Wideband(UWB).By introducing the maximum correntropy criterion,the MCCUKF algorithm dynamically adjusts the covariance matrices of the system noise and the measurement noise,thus enhancing its adaptability to diverse environmental localization requirements.Particularly in the presence of non-Gaussian noise,especially heavy-tailed noise,the MCCUKF exhibits superior accuracy and robustness compared to the traditional UKF.The method initially generates an estimate of the predicted state and covariance matrix through the unscented transform(UT)and then recharacterizes the measurement information using a nonlinear regression method at the cost of theMCC.Subsequently,the state and covariance matrices of the filter are updated by employing the unscented transformation on the measurement equations.Moreover,to mitigate the influence of non-line-of-sight(NLOS)errors positioning accuracy,this paper proposes a k-medoid clustering algorithm based on bisection k-means(Bikmeans).This algorithm preprocesses the UWB distance measurements to yield a more precise position estimation.Simulation results demonstrate that MCCUKF is robust to the uncertainty of UWB and realizes stable integration of INS and UWB systems.

Steady State Analysis of Towed Marine Cables

Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems,the steady state problem can be resolved into two-point boundary-value problem,or initial value problem in some special cases where the initial values are available directly.A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency.First,the boundary conditions are transformed into a set of nonlinear governing equations about the initial values,then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method.In common sense,non-uniform (sheared) current is assumed,which varies in magnitude and direction with depth.The schemes are validated through the DE Zoysa's example,then several numerical examples are also presented to illustrate the numerical schemes.

基于iForest+Biscting K-means的驾驶风格辨识方法研究

提出了一种基于iForest+Biscting K-means模型的客运驾驶员驾驶风格辨识方法。该方法针对在Bisceting Kmeans模型中,聚类质心严重影响聚类结果问题,采用iForest模型训练聚类中心候选集作为聚类质心集的方法加以改进。通过考察某城际客运线路30位客车职业驾驶员,在直线道路行驶工况下,90余天约400万条客车行驶数据开展模型验证。试验表明:在加速度标准差和超速倾向系数作为聚类指标的情况下,客运驾驶员驾驶风格聚类为谨慎型、普通型和激进型3类,其中谨慎型11人,普通型19人,激进型0人。

ON A KHLER VERSION OF CHEEGER-GROMOLL-PERELMAN'S SOUL THEOREM

In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.

Stewart formula and some inequalities for a simplex

Problems on Stewart formula and inequalities for the areas of the bisection planes of the dihedral angles of a simplex are studied with the theory and method of distance geometry. Stewart formula and some inequalities for the areas of the bisection planes of the dihedral angles of a simplex in nE are established.

VOLUME GROWTH ESTIMATES OF MANIFOLDS WITH NONNEGATIVE CURVATURE OUTSIDE A COMPACT SET

In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau＇s theorem.

VANISHING THEOREMS FOR ACH KHLER MANIFOLDS AND HARMONIC MAPS

We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.