Feynman Path Integral Using Operator Integration in Banach Space

Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.

Study on Path Selection and Implementation Effect of Counselors in College Students’Career Planning Education

Under the background of a severe job market and fierce talent competition,the career planning education of college students is of great importance.In this study,a combination of quantitative and qualitative research methods was used;500 students in Shenzhen Polytechnic of Information Technology were surveyed by questionnaire,and 40 counselors were interviewed in depth to comprehensively analyze the role and practical effect of counselors in career planning education.The research showed that the role positioning of counselors includes the guide of students’career development,emotional support,and job-hunting strategy,and the specific path selection involves the strengthening of professional knowledge,the construction of interpersonal relationship networks,and personalized counseling.Based on the survey and interview data,this paper constructed a model for enhancing the role of counselors in career planning education and put forward a set of targeted work paths.

The Path Dependence of Enterprise Strategic Adjustment and Its Transcendence Analysis

The world today is in a period of great development and integration of economy,information,and technology,especially the high-tech industries represented by big data,cloud computing,and artificial intelligence.It is promoting the rapid increase of human productivity and leading the changes in various industries.Enterprises are facing more and more uncertain external environments.The previous organizational strategy,personnel structure,and operating strategies have been unable to adapt to the turbulent external environment,and innovation has become the norm.Therefore,how to find an innovative breakthrough point on the original strategic road on which to survive has become a matter of life and death.From the perspective of path dependence theory,this paper analyzes the characteristics of path dependence and transcendence path dependence during the adjustment of corporate strategy,and analyzes the internal causes and mechanisms of its generation with the help of the PEST model.Based on this,the negative impact of path dependence on the adjustment of the strategy was found.Furthermore,it was found above that the degree of transcendence path dependence in corporate strategic adjustment is determined by two factors:its ability to drive independent innovation in a dynamic environment and its ability to transform strategically.Finally,according to the research conclusions,it proposes countermeasures to overcome the path dependence of enterprises when adjusting their strategies,and provides suggestions for companies to find breakthrough points in disruptive innovation.

The Path Dependence of Enterprise Strategic Adjustment and Its Transcendence Analysis

The world today is in a period of great development and integration of economy,information,and technology,especially the high-tech industries represented by big data,cloud computing,and artificial intelligence.It is promoting the rapid increase of human productivity and leading the changes in various industries.Enterprises are facing more and more uncertain external environments.The previous organizational strategy,personnel structure,and operating strategies have been unable to adapt to the turbulent external environment,and innovation has become the norm.Therefore,how to find an innovative breakthrough point on the original strategic road on which to survive has become a matter of life and death.From the perspective of path dependence theory,this paper analyzes the characteristics of path dependence and transcendence path dependence during the adjustment of corporate strategy,and analyzes the internal causes and mechanisms of its generation with the help of the PEST model.Based on this,the negative impact of path dependence on the adjustment of the strategy was found.Furthermore,it was found above that the degree of transcendence path dependence in corporate strategic adjustment is determined by two factors:its ability to drive independent innovation in a dynamic environment and its ability to transform strategically.Finally,according to the research conclusions,it proposes countermeasures to overcome the path dependence of enterprises when adjusting their strategies,and provides suggestions for companies to find breakthrough points in disruptive innovation.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact（CC） point,while not considering the smoothness and continuity of a whole tool path.When the surface curvature varies significantly,a local abrupt change of tool paths will happen.The abrupt change has a great influence on surface machining quality.In order to keep generated tool paths smooth and continuous,a five-axis tool positioning algorithm based on smooth tool paths is presented.Firstly,the inclination angle,the tilt angle and offset distance of the tool at a CC point are used as design variables,and the machining strip width is used as an objective function,an optimization model of a local tool positioning algorithm is thus established.Then,a vector equation of tool path is derived by using the above optimization model.By analyzing the equation,the main factors affecting the tool path quality are obtained.Finally,a new tool position optimization model is established,and the detailed process of tool position optimization is also given.An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine,and the machined blade surface is measured with a coordinate measuring machine（CMM）.Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous,improve the tool path quality,avoid the local abrupt change of tool paths,and enhance machining quality and machining efficiency of sculptured surfaces.

Hybrid Navigation System Based Autonomous Positioning and Path Planning for Mobile Robots

Positioning and navigation technology is a new trend of research in mobile robot area.Existing researches focus on the indoor industrial problems,while many application fields are in the outdoor environment,which put forward higher requirements for sensor selection and navigation scheme.In this paper,a complete hybrid navigation system for a class of mobile robots with load tasks and docking tasks is presented.The work can realize large-range autonomous positioning and path planning for mobile robots in unstructured scenarios.The autonomous positioning is achieved by adopting suitable guidance methods to meet different application requirements and accuracy requirements in conditions of different distances.Based on the Bezier curve,a path planning scheme is proposed and a motion controller is designed to make the mobile robot follow the target path.The Kalman filter is established to process the guidance signals and control outputs of the motion controller.Finally,the autonomous positioning and docking experiment are carried out.The results of the research verify the effectiveness of the hybrid navigation,which can be used in autonomous warehousing logistics and multi-mobile robot system.

On the Strategic Paths of the Going Global Strategy of Chinese Literature

The going global strategy of Chinese literature is a vital part of the going global strategy of Chinese culture. In recent years,the Chinese government has launched and strongly supported a series of activities and projects to promote this strategy,but little effect has been produced. Starting from analyzing the predicament and reasons of the current strategy,the essay suggests four strategic paths: enhancing the overall strength of the country to promote the international influence of Chinese culture,strengthening cultural awareness and cultural introspection,integrating the nationality and cosmopolitan of literature and establishing a market-oriented literary translation mechanism.

Chinese Childrenswear Brand Development Path Based on Differentiated Positioning

Sorting and collecting the data by questionnaire survey and literature analysis,the childrenswear brand elemental analysis is completed.The development goal of differentiated positioning of Chinese childrenswear brands is decided.Four modules which influence the brand differentiated development were extracted to establish the hierarchical analysis framework for the differentiated positioning development of Chinese childrenswear brand.Judgment matrix diagram is constructed by using the analytic hierarchy process(AHP).According to the data analysis and judgment,the core elements,basic elements and auxiliary elements are identified which support the development of differentiated positioning of Chinese childrenswear brands.The clear development path of differentiated positioning of Chinese childrenswear brands is formed,namely to enhance the core essential factors as the key point,to grasp the elements’spirit exactly in differentiated positioning of brand style,childrenswear color feature,green and security of products quality and retail prices which influence the brand differentiated development.The Chinese existing technical advantages was given full play by providing the basic support for the differentiated development of childrenswear brands.Auxiliary elements were heleped to grow by making auxiliary elements play a greater role.The goal was achieved to improve the market competitiveness by development of differentiated positioning of Chinese childrenswear brands.

Research on the Generation Path of Heuristic Teaching Language Based on Positive Psychology Theory

As the essence of traditional Chinese educational thought,heuristic teaching has gradually enriched and devel-oped its ideas through the continuous efforts of educational researchers of the past dynasties.In front-line teach-ing,heuristic teaching,as a teaching principle that can help teachers and students to interact and learn,undoubtedly plays an important role in students’acquisition of knowledge and scientific thinking activities.But teachers’understanding of heuristic teaching is not the same.In actual teaching,there are obvious gaps in language ability among different teachers.This research aims to enrich the heuristic teaching theory based on the perspective of psychology,and provide a certain theoretical basis for teacher training.Through the research and analysis of the generation path of the heuristic teaching language,this paper helps more teachers realize the advantages of the heuristic teaching language,improve their own heuristic teaching language level,and provide reference for the scientific teaching evaluation standard.We apply the heuristic instruction language approach proposed in this study and apply it to real classrooms.In the application,it can be clearly found that the students’thinking and participation have been strengthened,and the teaching effect has been significantly improved com-pared with the past,which indicates that the heuristic teaching language generation path in this study has certain practical application value.

Robust Fingerprint Construction Based on Multiple Path Loss Model (M-PLM) for Indoor Localization

A robust radio map is essential in implementing a fingerprint-based indoor positioning system(IPS).However,the offline site survey to manually construct the radio map is time-consuming and labour-intensive.Various interpolation techniques have been proposed to infer the virtual fingerprints to reduce the time and effort required for offline site surveys.This paper presents a novel fingerprint interpolator using a multi-path loss model(MPLM)to create the virtual fingerprints from the collected sample data based on different signal paths from different access points(APs).Based on the historical signal data,the poor signal paths are identified using their standard deviations.The proposed method reduces the positioning errors by smoothing out the wireless signal fluctuations and stabilizing the signals for those poor signal paths.By consideringmultipath signal propagations from different APs,the inherent noise from these signal paths can be alleviated.Firstly,locations of the signal data with standard deviations higher than the threshold are identified.The new fingerprints are then generated at these locations based on the proposed M-PLM interpolation function to replace the old fingerprints.The proposed technique interpolates virtual fingerprints based on good signal paths with more stable signals to improve the positioning performance.Experimental results show that the proposed scheme enhances the positioning accuracy by up to 44%compared to the conventional interpolation techniques such as the Inverse DistanceWeighting,Kriging,and single Path LossModel.As a result,we can overcome the site survey problems for IPS by building an accurate radio map with more reliable signals to improve indoor positioning performance.

Short Baseline Positioning with an Improved Time Reversal Technique in a Multi-path Channel

在水下面的一条多路径隧道的存在极大地减少放系统的短基线的精确性。在这份报纸，到放系统的短基线的一面时间颠倒镜子的申请被调查。时间颠倒镜子技术允许声学的信号更好集中在未知环境，它有效地减少了多路径的扩大声学的信号象一样改进了集中的信号。时间颠倒操作员的 signal-to-noise 比率(SNR ) 极大地增加了并且能被 ensonifying 获得水。这种技术被环境并且因此少些影响对复杂的浅水环境更适用。数字模拟和水池实验被用来表明这种技术的效率。

Kinematics and Path Following Control of an Articulated Drum Roller

Automatic navigation of an articulated drum roller, which is an articulated steering type vehicle widely used in the construction industry, is highly expected for operation cost reduction and improvement of work effi- ciency. In order to achieve the path following control, considering that its steering system is articulated steering and two frames are articulated by an active revolute joint, a kinematic model and an error dynamic state-space equation of an articulated drum roller are proposed. Besides, a state- feedback control law based on Lyapunov stability theory is also designed, which can be proved to achieve the purpose of control by the analysis of stability. What＇s more, to evaluate the performance of the proposed method, simu- lation under the MATLAB/Simulink and experiments using positioning algorithm and errors correction at the uneven construction site are performed, with initial dis- placement error （-1.5 m）, heading error （-0.11 tad） and steering angle （-0.19 rad）. Finally, simulation and exper- imental results show that the errors and steering angle can decrease gradually, and converge to zero with time. Meanwhile, the control input is not saturated. An articu- lated drum roller can lock into a desired path with the proposed method in uneven fields.

Optimal gear shift control strategy for positive independent mechanical split path transmission with automatic shift system

An improvement strategy which controls the shift effort and the power summing planetary gear set of steering clutches and brakes have been proposed based on the dynamic model of synchroniser in order to decrease the wear of synchroniser inserts, make gear shift easy and reduce the shock noise for a positive independent mechanical split path transmission which attached an auto- matic shift system when shifting. A kinetics model for the process of synchroniser engagement is built and analyzed in the paper. Thus for optimizing the gear shift process which is divided into three phases a model reference fuzzy self-adaption system is adopted. Through a 6 000 km road experiment, the control strategy has proved feasible and dependable.

Indoor Radio Propagation Model Based on Dominant Path

When there are bigger obstacles in the indoor environment such as elevator, the radio waves basically can not penetrate it. The contribution of received signal strength by transmission and reflection will be greatly reduced, and most of the time, the radio waves will reach the user by bypass diffraction. Therefore, the traditional path loss model is no longer applicable, and the improved model should be proposed. In this paper, we firstly proposed an indoor radio propagation model based on dominant path in which the received signal strength has nothing to do with the direct distance between user and access point, but is related to the length of dominant path. Then on the basis of dominant path model, the NLOS influence is considered in order to further improve the accuracy of dominant path model. Experimental results demonstrated that the proposed dominant path model can improve the accuracy of traditional path loss model remarkably.

Analysis of the Concept and Connotation of the New Economy and Reconstruction of Its Development Path:A Study Based on Chengdu’s Practices

In order to promote the transformation and development of China’s economy and cope with the realistic challenges posed by the global economic recession and slowing domestic economic growth,the Fourth Session of the 12 th National People’s Congress adopted a strategic resolution on developing the "new economy" and fostering new drivers of growth.Chengdu,capital of Sichuan province,is one of the cities in China which firstly begin to carry out the layout of the new economy development.While achieving results,it also faces many troubles due to its insufficient cognition of the connotation,definition,and path of the "new economy." The paper is based on a theoretical study in combination with the new economic development of Chengdu’s five new paths,to analyze the concept and connotation of the "new economy." It also analyzes from the perspective of higher dimensional reconstruction and new strategic path of economic development,in order to add some insights to the theorectical study and to promote better strategic value of the new economy.

The Path-Positive Property on the Products of Graphs

本文所讨论的积图是图的笛卡尔积，图的张量积，图的逻辑积和图的强直积四种积图．证明了：①如果Ｇ１和Ｇ２都是连通图，则积图中笛卡尔积，逻辑积和强直积都是道路正图．②图的张量积是道路正图的是图Ｇ１和Ｇ２是一个连通图，Ｇ１［或Ｇ２］有一个奇圈，且ｍａｘ｛λ１μ１，λｎμｍ｝≥２。

Path planning of the robot assembly based on Voronoi diagram

Based on the concepts of Voronoi diagram that describes geometry information of the robot assembly in C space, the position vector path parameter equation of the assembly movement between the step shaft and two-sided bearing bracket was given. And the path planning strategy of the component initiative assembly was put forward as well. Theoretical analysis proves that using the Voronoi diagram to do the geometry reasoning on the assembly space can evaluate the feasibility of the component assembly, and can present the reference position vector path of the component movement from the initial configuration to the objective configuration, therefore improves the flexibility of the robot initiative assembly.