Existence of u‐Representation of Graphs

Recently, Jones et al. (Electron J Comb 22(2) (2015), #P2.53) introduced the study of u‐representable graphs, where u is a word over containing at least one 1. The notion of a u‐representable graph is a far‐reaching generalization of the notion of a word‐representable graph studied in the literature in a series of papers. Jones et al. have shown that any graph is 11???1‐representable assuming that the number of 1s is at least three, while the class of 12‐representable graphs is properly contained in the class of comparability graphs, which, in turn, is properly contained in the class of word‐representable graphs corresponding to 11‐representable graphs. Further studies in this direction were conducted by Nabawanda (M.Sc. thesis, 2015), who has shown, in particular, that the class of 112‐representable graphs is not included in the class of word‐representable graphs. Jones et al. raised a question on classification of u‐representable graphs at least for small values of u . In this article, we show that if u is of length at least 3 then any graph is u‐representable. This rather unexpected result shows that from existence of representation point of view there are only two interesting nonequivalent cases in the theory of u‐representable graphs, namely, those of and .     

新型综合船桥系统

综合船桥系统是实施船舶导航和控制的集成系统,它通过相互连接以集中使用来自工作站的传感器信息、命令或控制以提高操作人员管理船舶的安全性和效率.文中分析了综合船桥系统设备配置,研究了综合船桥系统的关键技术,基于综合船桥系统的体系结构和信息流程开发了综合船桥系统,并进行了系统测试与联调.试验结果表明,综合船桥系统具有导航、驾驶、航行监测、避碰和报警等功能,通过系统集成对船舶周围的航行态势进行监控,保证了船舶的航行安全.     

Efficient and reliable hierarchical error estimates for an elliptic obstacle problem

We present and analyze novel hierarchical a posteriori error estimates for a self-adjoint elliptic obstacle problem. Under a suitable saturation assumption, we prove the efficiency and reliability of our hierarchical estimates. The proof is based upon some new observations on the efficiency of some hierarchical error indicators. These new observations allow us to remove an additional regularity condition on the underlying grid required in the previous analysis. Numerical computations confirm our theoretical findings.     

影响接受移动支付业务决定因素的实证研究

From a global perspective, the development of 3G services in China is quite different from other countries. The factors that influence user's adoption of mobile payment are worth exploring. This study employs the Technology Acceptance Model (TAM) to examine determinant factors affecting consumer's acceptance intentions of mobile payment. We adopt Hofstede's cultural dimensions as moderators to extend the TAM model for exploring the impact of uncertainty avoidance on mobile payment acceptance. Based on the data from China and United State, we conduct a confirmatory factor analysis and the results show an adequate level of reliability and validity, with Cronbach's Alpha value, Composite Reliability (CR) value and Average Variance Extracted (AVE) value greater than 0.850, 0.823 and 0.519 separately. The model and the relationship between the variables are confirmed based on SEM. Multi-Group Analysis is used to test the moderating effect and it shows that the moderating effects of Uncertainty Avoidance on PR---> BI, PU---> BI and SN---> BI are significant at 0.049, 0. 032 and 0. 000 significance level. Results support that Uncertainty Avoidance has a profound moderating effect on user's behavior intention to use mobile payment.     

Perception for collision avoidance and autonomous driving

The Navlab group at Carnegie Mellon University has a long history of development of automated vehicles and intelligent systems for driver assistance. The earlier work of the group concentrated on road following, cross-country driving, and obstacle detection. The new focus is on short-range sensing, to look all around the vehicle for safe driving. The current system uses video sensing, laser rangefinders, a novel light-stripe rangefinder, software to process each sensor individually, a map-based fusion system, and a probability based predictive model. The complete system has been demonstrated on the Navlab 11 vehicle for monitoring the environment of a vehicle driving through a cluttered urban environment, detecting and tracking fixed objects, moving objects, pedestrians, curbs, and roads.     

A Hopf-Bifurcation Theorem for the Vorticity Formulation of the Navier–Stokes Equations in ℝ3

We prove a Hopf-bifurcation theorem for the vorticity formulation of the Navier–Stokes equations in ?³ in case of spatially localized external forcing. The difficulties are due to essential spectrum up to the imaginary axis for all values of the bifurcation parameter which a priori no longer allows to reduce the problem to a finite dimensional one.     

一种基于Dijkstra算法的机器人避障问题路径规划

移动机器人的避障问题是移动机器人控制领域的研究热点.针对给定的移动机器人避障问题,探讨了最短路径及最短时间路径的路径规划问题.对于最短路径问题,建立了简化的路径网格模型,将其抽象为由节点及边构成的两维图,再使用经典的Dijkstra算法获得可行的最短路径.对于最短时间路径问题,通过分析移动机器人弯道运行的速度曲线,基于几何方法得出了移动时间与过渡圆弧圆心之间严格的数学关系,此后借助MATLAB优化函数获得最佳的移动路径.算法可为类似机器人避障问题的解决提供借鉴.     

Inversion polynomials for 321-avoiding permutations

We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formula for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin paths, polyominoes, and continued fractions.     

Increasing Powers in a Degenerate Parabolic Logistic Equation

The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$\partial _t u - \Delta u = au - b\left( x \right)u^p in \Omega \times \mathbb{R}^ + , u(0) = u_0 , \left. {u(t)} \right|_{\partial \Omega } = 0,$$ as p → + ∞, where Ω is a bounded domain, and b(x) is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.