General Optimal Trajectory Planning:Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning(GOTP)framework for autonomous vehicles(AVs)that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently.Firstly,we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline.Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve.Considering the road constraints and vehicle dynamics,limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system.Furthermore,in selecting the optimal trajectory,we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’behavior and summarizing their manipulation characteristics of“seeking benefits and avoiding losses.”Finally,by integrating the idea of receding-horizon optimization,the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility,optimality,and adaptability.Extensive simulations and experiments are performed,and the results demonstrate the framework’s feasibility and effectiveness,which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants.Moreover,we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’manipulation.

The Principle of Proportionality Toward Risk Prevention——Based on the Judgment Logic of European COVID-19 Derogation Measures

The COVID-19 pandemic has brought legal challenges to the containment measures adopted by European countries.During the outbreak and containment phase of the pandemic,most European countries adopted measures such as lockdowns and mandatory home quarantines based on the principle of risk prevention.However,Article 15 of the European Convention on Human Rights and judgments by the European Court of Human Rights require such measures to comply with the principle of proportionality.In view of this,this article examines the European Court of Justice’s loose judgments on the derogation measures during the pandemic,and the European Court of Human Rights’situational judgments in this regard.Based on the analysis of the legitimacy of the principle of risk prevention and the principle of proportionality in responding to public health emergencies,this article prudently examines and predicts the trend of applying the principle of proportionality of risk prevention for the European COVID-19 derogation measures from three perspectives of legitimacy,necessity,and feasibility.

Effect of the Principle of Activating Blood Circulation to Break Stasis on GMP-140 and D_2 Dimer in Patients with Acute Cerebral Infarction

Objective: To explore the clinical efficacy of the principle of activating blood circulation to break stasis (ABCBS) and its influence on platelet membranous protein particle (GMP-140) and D 2 dimer (D-dimer) before and after treatment. Methods: Eighty-eight patients with blood stasis syndrome (BSS) of acute cerebral infarction (ACI) were randomly divided into two groups, both of which were treated with conventional treatment, i.e. with western medicine (WM), with Salvia injection added through intravenously dripping.One of the two groups was used as the control and the other group as the treated group who had ABCBS herbs orally taken in addition. The duration of treatment course for both groups was 3 weeks. Results: There were changes in both groups over clinical symptoms, nerve function deficit scoring and GMP-140, D-dimer, but the treated group showed significantly better than that of the control group, ( P <0.05). Conclusion: ABCBS principle could serve as an important auxiliary treating method for BSS of ACI, as it can effectively alter the blood of ACI patients which was viscous, condense, coagulant and aggregating.

Variational Principle of Instability of Atmospheric Motions

Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapbunoff norm can still be obtained on the basis of variational consideration.

Attack on Optical Double Random Phase Encryption Based on the Principle of Ptychographical Imaging

The principle of ptychography is applied in known plain text attack on the double random phase encoding （DRPE） system. We find that with several pairs of plain texts and cipher texts, the model of attack on DRPE can be converted to the model of ptyehographical imaging. Owing to the inherent merits of the ptyehographical imaging, the DRPE system can be breached totally in a fast and nearly perfect way, which is unavailable for currently existing attack methods. Further, since the decryption keys can be seen as an object to be imaged from the perspective of imaging, the ptychographical technique may be a kind of new direction to further analysis of the security of other encryption systems based on double random keys.

Inverse Dynamics of Delta Robot Based on the Principle of Virtual Work

A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.

ANALYSIS MODEL ON GRADUAL CHANGE PRINCIPLE OF EFFECT ZONES OF LAYER FACE FOR ROLLED CONTROL CONCRETE DAM

The effect zones of layer face for RCC （rolled control concrete） dam have gradual change characteristics. Based on the analysis thought of complex material, a model was built to analyze above principle of RCC dam by use of series-wound and shunt-wound connection. Some methods were proposed to determine the instantaneous Young＇s modulus, delayed Young＇s modulus and viscosity coefficient of effect zones of layer face. Above models and methods were used to mine the principle of gradual change of key calculation parameters which can response the characteristics of effect zones. The principle of gradual change was described. A model was established to analyze the threedimensional viscoelastic problem of RCC dam. Above programs were developed. The examples show that the proposed models and methods to determine the key calculation parameters of effect zones can reflect the status of RCC dam accurately.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

The principle of minimization of the equivalent load for design of launching vertical shiplift

Launching vertical shiplift is a type of shiplifts which have the advantages in characteristics of dynamics and statics, safety and simplicity in operation. But their applications are limited as the scales of mechanical equipments are too large. This paper puts forward the principle of minimization of the equivalent load for the general layout design of launching vertical shiplifts, based on the analysis of the load probability of the main hoists and their key mechanical equipments. The principle aims at determining the optimal weight of counterweight so that the equivalent loads of the main hoists of shiplifls are minimized, and larger ships are permitted to pass through. The theory and method presented in this paper have been applied in the design of the first step and third step shiplifts of the Goupitan Hydro Power Station. This has resulted in the breakthrough of the design and manufacture of launching vertical shiplifts so that the ships with tonnage of 500 t can pass through hydro dams for this type of shiplifts, comparing with the largest launching shiplift in Yantan Hydro Power Station with the 250 t shiplift.

Tomographic Principle of Multiconjugate Correction in Adaptive Optics

A wavefront sensing and correction correction is proposed that would allow the field of view (FOV) of an adaptive optics spstem to be increased in size by a factor of several tens. This concept is based on the idea of placing multiple deformable mirrors (DMs) at locations that are conjugate to corresponding. layers of atmospheric turbulence. In order to control properly each DM, a tomographic method for determining the phase distortion contributed by each atmospheric layer has been developed and used in dealing with the circumstance of two layers.

A FINITE ELEMENT—MATHEMATICAL PROGRAMMING METHOD FOR ELASTOPLASTIC PROBLEMS BASED ON THE PRINCIPLE OF VIRTUAL WORK

By expanding the yielding function according toTaylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness oj solution for the method are also discussed and some useful conclusions are given.

Coma of Stroke Treated with Principle of Resuscitation to Restore Consciousness

The prevalence ofstroke is high nowadays.The patient sufferedfrom stroke can be divided into hemorrhagicstroke and ischemic infarction.Someone isconscious,and the otherunconscious.The latteris due to apoplexy involving Zang-Fu organs.Zang organ can store

Comments on Zeng's Paper “Variational Principle of Instability of Atmospheric Motions”

After my paper (Zeng, 1986b) was published and another (Zeng, 1989) was submitted to the journal, I found two papers written by Arnold (1966) and McIntyre et al. (1987) and received some reprints of Ripa’s papers (1983; 1984; 1987; 1988) in the same field. I thank Drs. Mu Mu and Pedro Ripa very much for showing and sending me these interesting papers.

A Commented Translation of Three Short Stories from Amber Sparks’s The Unfinished World Under the Guidance of the Principle of Three Aes-thetics by XU Yuanchong

Classical Chinese Poetry is known for its rich prosodies,paralleled forms and profound ambience.To better retain po⁃ems’aesthetic appeal for its readers,Xu Yuanchong proposed and applied his“Principle of Three Aesthetics”-aesthetic of proso⁃dy,forms and ambiance-into his translation.Western Literatures,to some extent,share the similarities with those of Chinese.In Western literatures,prosody is the musical side of language while the intertwining of sentence rhythm and metric rhythm in poetry yields strong empathy.When translating Amber Sparks’s The Unfinished World,I found it reasonable to apply Xu’s“Principle of Three Aesthetics”into my translation due to the fact that between the lines are full of musical rhythm,paralleled structures and del⁃icate ambience cultivated by author.

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)──BASIC EQUATIONS

This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four simultaneous basic equations, i. e., equation of interest rate and amount of circulating fond, equations of purchasing and selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate, have been established. Discussions mainly on the solution and its simple applications of the equation of interest rate and amount of circulating fond are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping, and the influence of amount of circulating fond with exponential attenuation due to the decreasing of banking interest rate.Keyworks: stock market; network model; differential equation; contraction mapping; elasticity; methodology

Stream Function Wave Derived by Unified Variational Principle of Water Gravity Wave

Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.

DISCUSSION OF CRITICAL LOAD IN NONLINEAR STABILITY ANALYSIS AND SUGGESTION OF VARIATIONAL PRINCIPLE OF SOLVING CRITICAL LOADS

In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.

Examples of Application of Principle of Superposition in the Design of Structural Systems and in Static Analyses

The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.

A Critique on the Application of the Principle of Subsidiarity Concerning Human Embryonic Stem Cell Research in South Africa

Researchers from all around the world emphasize on the enormous possible benefits that stem cells may have for the treatment of diseases. However, this technology is considered morally problematic when the source of the stem cell is from a human embryo. Nonetheless, there is a consensus that of all the types of stem cells, hESC （human embryonic stem ceils） are the most promising for particular and important research and therapies. Yet, there are controversial issues regarding the ＂killing＂ of the human embryo for stem cell derivation. There are two general ethical conditions that should govern the instrumental use of embryo. One of them, the principle of subsidiarity, which is defined as ＂a state we have that we have to choose the less contentious means of achieving the intended goal＂. Based on this principle, we ought only to use hESC when there are no other alternatives, which are less morally controversially. Subsidiarity is based on the assumption that there is something ethically unsound about the use ofhESC. However, this principle only makes sense if it is based on consistently upheld views of the moral status of embryo, moreover, the law should also not limit or prohibit hESC research based on this principle. In this paper, I argue---using the South African law for hESC technology--that criterion for deciding which type of stem cells to use should be based on their potential and suitability for advancing scientific knowledge and development of new therapies which will be greatly beneficial in alleviating human suffering.

The Application of Principle of Automatic Control in the site Management of Electric Power Construction Enterprise

It is need to establish site project department during the construction of electric power project.The head office should design and build the main structure,continually improve structure of project department,meantime,positively apply principle of automatic control to improve the site management of electric power construction.In this article,the application strategy of principle of automatic control is analyzed focusing on the site work of electric power construction.