Strong invariance principle for a counterbalanced random walk

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

Design Principles and Mechanistic Understandings of Non-Noble-Metal Bifunctional Electrocatalysts for Zinc-Air Batteries

Zinc-air batteries(ZABs)are promising energy storage systems because of high theoretical energy density,safety,low cost,and abundance of zinc.However,the slow multi-step reaction of oxygen and heavy reliance on noble-metal catalysts hinder the practical applications of ZABs.Therefore,feasible and advanced non-noble-metal elec-trocatalysts for air cathodes need to be identified to promote the oxygen catalytic reaction.In this review,we initially introduced the advancement of ZABs in the past two decades and provided an overview of key developments in this field.Then,we discussed the work-ing mechanism and the design of bifunctional electrocatalysts from the perspective of morphology design,crystal structure tuning,interface strategy,and atomic engineering.We also included theoretical studies,machine learning,and advanced characterization technologies to provide a comprehensive understanding of the structure-performance relationship of electrocatalysts and the reaction pathways of the oxygen redox reactions.Finally,we discussed the challenges and prospects related to designing advanced non-noble-metal bifunctional electrocatalysts for ZABs.

Adaptive Optimal Discrete-Time Output-Feedback Using an Internal Model Principle and Adaptive Dynamic Programming

In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed method, termed as IMP-ADP, does not require complete state feedback-merely the measurement of input and output data. More specifically, based on the IMP, the output control problem can first be converted into a stabilization problem. We then design an observer to reproduce the full state of the system by measuring the inputs and outputs. Moreover, this technique includes both a policy iteration algorithm and a value iteration algorithm to determine the optimal feedback gain without using a dynamic system model. It is important that with this concept one does not need to solve the regulator equation. Finally, this control method was tested on an inverter system of grid-connected LCLs to demonstrate that the proposed method provides the desired performance in terms of both tracking and disturbance rejection.

Anisotropic etching mechanisms of 4H-SiC:Experimental and first-principles insights

Molten-alkali etching has been widely used to reveal dislocations in 4H silicon carbide(4H-SiC),which has promoted the identification and statistics of dislocation density in 4H-SiC single crystals.However,the etching mechanism of 4H-SiC is limited misunderstood.In this letter,we reveal the anisotropic etching mechanism of the Si face and C face of 4H-SiC by combining molten-KOH etching,X-ray photoelectron spectroscopy(XPS)and first-principles investigations.The activation energies for the molten-KOH etching of the C face and Si face of 4H-SiC are calculated to be 25.09 and 35.75 kcal/mol,respectively.The molten-KOH etching rate of the C face is higher than the Si face.Combining XPS analysis and first-principles calculations,we find that the molten-KOH etching of 4H-SiC is proceeded by the cycling of the oxidation of 4H-SiC by the dissolved oxygen and the removal of oxides by molten KOH.The faster etching rate of the C face is caused by the fact that the oxides on the C face are unstable,and easier to be removed with molten alkali,rather than the C face being easier to be oxidized.

Scientific principles for accelerating the Sustainable Development Goals

The Sustainable Development Goals(SDGs)are significantly off-course as we reach the midpoint of their 2030 deadline.From a scientific perspective,the critical challenge in achieving the SDGs lies in the need for more scientific principles to understand the complex socio-ecological systems(SES)and their interactions influencing the 17 SDGs.Here,we propose a scientific framework to clarify the common scientific principles and the rational treatment of diversity under these principles.The framework’s core is revealing the complex mechanisms underlying the achievement of each Sustainable Development Goal(SDG)and SDG interactions.Building upon the identified mechanisms,complex SES models can be established,and the implementation of SDGs can be formulated as a multi-objective optimization problem,seeking a compromise in competition between essential costs and desired benefits.Our framework can assist countries,and even the world in accelerating progress towards the SDGs.

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 Five Principles of Peaceful Coexistence:Connotations in International Law and Contemporary Relevance

The year 2024 marks the 70th anniversary of the Five Principles of Peaceful Coexistence initiated by China.As an anchor foreign policy of New China and its first contribution of public product for the international community,the Five Principles have made a historic contribution to the building of a new type of just and equitable international relations,advancing the purposes and principles of the Charter of the United Nations,and becoming universally applicable basic norms for international relations and key fundamental principles of international law.

Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

Sabatier principle guiding the design of cathode catalysts for Li-CO_(2) batteries

The Sabatier principle has been widely used for designing electrocatalysts for energy conversion applications,but it is rarely mentioned in the research of cathode catalyst of Li-CO_(2) batteries.In our work,the"volcanic"relationship between the catalytic activity and the adsorption energy of the catalyst to the intermediates is first demonstrated based on the first-principles calculation,which meets the Sabatier principle and can be used to design the cathode catalysts.The increases in the number of nitrogenvacancy in WN shift the d-band center and increase the interaction with the reactants.The catalytic activity increases first and then decreases with the increase of adsorption energy,which was proved in the experiment.The optimal catalyst for moderate adsorption of intermediate makes the thin LiaCO_(3) distribute evenly.It exhibits a median voltage difference of 0.68 V and an energy efficiency of 84.33%at20μA cm^(-2)with a limited capacity of 200μA h cm^(-2).

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Principles of Shiology——Revealing the Basic Rules of Human Shiance

The objective principles of shiology are mainly reflected in three fields as food acquisition, eaters' health and shiance order. Most of the objective principles in the field of food acquisition have been revealed by agronomy and foodstuff science. This research mainly focuses on 10 principles in the field of eaters' health and shiance order and in addition, there are also five lemmas that extend from the above principles. The 10 principles are the core theory of the shiology knowledge system, which play an important role in the objective principles revealed by human beings and constitute one of the basic principles of human civilization. Compared with the scientific principles of mathematics, physics, chemistry and economics, the principles of shiology have three characteristics as popularity, practicability and survivability. The principles of shiology in the field of eaters' health are all around us, and everyone can understand and master them. Using the principles of shiology can improve the healthy life span of 8 billion people. The principles of shiology in the field of shiance order is an important tool of social governance, which can reduce human social conflicts, reduce social involution, improve overall efficiency of social operation, and maintain the sustainable development of human beings.

An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

International law obligations for the disposal of Fukushima nuclear-contaminated water under the principles of nuclear safety

The disposal of contaminated water from Japan’s Fukushima nuclear power plant is a significant international nuclear safety issue with considerable cross-border implications.This matter requires compliance not only with the law of the sea but also with the principles of nuclear safety under international law.These principles serve as the overarching tenet of international and China’s domestic nuclear laws,applicable to nuclear facilities and activities.The principle of safety in nuclear activities is fully recognized in international and domestic laws,carrying broad legal binding force.Japan’s discharge of nuclear-contaminated water into the sea violates its obligations under the principle of safety in nuclear activities,including commitments to optimum protection,as low as reasonably practicable,and prevention.The Japanese government and the International Atomic Energy Agency(IAEA)have breached the obligation of optimum protection by restricting the scope of assessments,substituting core concepts,and shielding dissenting views.In the absence of clear radiation standards,they have acted unilaterally without fulfilling the obligation as low as reasonably practicable principle.The discharge of Fukushima nuclear-contaminated water poses an imminent and unpredictable risk to all countries worldwide,including Japanese residents.Japan and the IAEA should fulfill their obligations under international law regarding disposal,adhering to the principles of nuclear safety,including optimum protection,the obligation as low as reasonably practicable,and prevention through multilateral cooperation.Specifically,the obligation to provide optimum protection should be implemented by re-evaluating the most reliable disposal technologies and methods currently available and comprehensively assessing various options.The standard of the obligation as low as reasonably practicable requires that the minimization of negative impacts on human health,livelihoods,and the environment should not be subordinated to considerations of cutting costs and expenses.Multilateral cooperation should be promoted through the establishment of sound multilateral long-term monitoring mechanisms for the discharge of nuclear-contaminated water,notification and consultation obligations,and periodic assessments.These obligations under international law were fulfilled after the accidents at the Three Mile Island and Chernobyl nuclear power plants.The implications of the principles of nuclear safety align with the concept of building a community of shared future for nuclear safety advocated by China.In cases of violations of international law regarding the disposal of nuclear-contaminated water that jeopardize the concept of a community of a shared future for nuclear safety,China can also rely on its own strength to promote the implementation of due obligations through self-help.

Fundamental Principles behind Climate Change

The attribution of climate change is complex,and the current mainstream view is more inclined towards human activities and carbon dioxide emissions from fossil fuels.Any complex problem is composed of basic principles.This article elaborates on the basic logic behind climate change(a global hot topic)through basic principles such as reaction types,carbon thermal properties of biomass energy,greenhouse gas attribution,ecological basic theory,and energy cycle.

Four Dimensions of Integrating Chinese Culture Into College English Teaching From the Perspective of Tyler’s Basic Principles

Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.

Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

“Three Beauties”Principle in the English Versions of“Jing Ye Si”--Translations by Xu and Fletcher as Examples

“Jing Ye Si”is a classical poem with international influence by the Chinese poet Li Bai in the Tang Dynasty,which expresses the poet’s deep nostalgia.This paper compares and analyzes its two English versions translated by the Chinese translator Xu Yuanchong and the British translator W.J.B.Fletcher based on the“three beauties”principle(beauty in sense,beauty in sound,and beauty in form),and discovers that the English version of Xu basically achieves the unity of the“three beauties”,while the English version of Fletcher realizes the“beauty in sound and form”,but deviates from the“beauty in sense”mainly owing to the inaccurate comprehension of the moon as an image and other factors.This analysis may afford us with certain reference in poetry translation.

The Accelerated Expansion of the Universe in the Light of the Maximum Ordinality Principle

The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.

A Solution to the Cosmological Constant Problem Using the Holographic Principle (A Brief Note)

This paper integrates a quantum conception of the Planck epoch early universe with FSC model formulae and the holographic principle, to offer a reasonable explanation and solution of the cosmological constant problem. Such a solution does not appear to be achievable in cosmological models which do not integrate black hole formulae with quantum formulae such as the Stephan-Boltzmann law. As demonstrated herein, assuming a constant value of Lambda over the great span of cosmic time appears to have been a mistake. It appears that Einstein’s assumption of a constant, in terms of vacuum energy density, was not only a mistake for a statically-balanced universe, but also a mistake for a dynamically-expanding universe.

Research on Teaching Methods of Flight Control Principles

With the rapid development of China’s civil aviation industry,the teaching method of operating knowledge of flight principles has changed greatly,which creates a good implementation environment to improve the safety of civil aviation in our country.At present,the main training content of air route transport pilots in China is basic aviation theory,initial flight training,airline modification,etc.The principles of flight control are an important part of basic aviation theoretical knowledge training,which will involve a large number of flight technology training content,instructors will also be based on the pilot type.Teaching flight control theory and practical knowledge requires relatively high theoretical learning ability of students,and the learning effect of this part of theoretical knowledge will directly affect the quality of subsequent learning,but also directly affect the effectiveness of flight training.This paper focuses on the analysis of the basic concepts of flight control,studies the existing problems in the teaching of flight control principles,summarizes the teaching measures of flight control principles,aiming to provide a reference to teaching personnel.