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).

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.

“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.

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.

Lithium nitrate regulated carbonate electrolytes for practical Li-metal batteries: Mechanisms, principles and strategies

Li-metal batteries(LMBs)regain research prominence owing to the ever-increasing high-energy requirements.Commercially available carbonate electrolytes exhibit unfavourable parasitic reactions with Limetal anode(LMA),leading to the formation of unstable solid electrolyte interphase(SEI)and the breed of Li dendrites/dead Li.Significantly,lithium nitrate(LiNO_(3)),an excellent film-forming additive,proves crucial to construct a robust Li_(3)N/Li_(2)O/Li_(x)NO_(y)-rich SEI after combining with ether-based electrolytes.Thus,the given challenge leads to natural ideas which suggest the incorporation of LiNO_(3) into commercial carbonate for practical LMBs.Regrettably,LiNO_(3) demonstrates limited solubility(~800 ppm)in commercial carbonate electrolytes.Thence,developing stable SEI and dendrite-free LMA with the incorporation of LiNO_(3) into carbonate electrolytes is an efficacious strategy to realize robust LMBs via a scalable and cost-effective route.Therefore,this review unravels the grievances between LMA,LiNO_(3)and carbonate electrolytes,and enables a comprehensive analysis of LMA stabilizing mechanism with LiNO_(3),dissolution principle of LiNO_(3) in carbonate electrolytes,and LiNO_(3) introduction strategies.This review converges attention on a point that the LiNO_(3)-introduction into commercial carbonate electrolytes is an imperious choice to realize practical LMBs with commercial 4 V layered cathode.

Single-atom electrocatalysts for lithium-sulfur chemistry:Design principle,mechanism,and outlook

Lithium-sulfur batteries(LSBs)have been regarded as one of the promising candidates for the next-generation“lithium-ion battery beyond”owing to their high energy density and due to the low cost of sulfur.However,the main obstacles encountered in the commercial implementation of LSBs are the notorious shuttle effect,retarded sulfur redox kinetics,and uncontrolled dendrite growth.Accordingly,single-atom catalysts(SACs),which have ultrahigh catalytic efficiency,tunable coordination configuration,and light weight,have shown huge potential in the field of LSBs to date.This review summarizes the recent research progress of SACs applied as multifunctional components in LSBs.The design principles and typical synthetic strategies of SACs toward effective Li–S chemistry as well as the working mechanism promoting sulfur conversion reactions,inhibiting the lithium polysulfide shuttle effect,and regulating Li+nucleation are comprehensively illustrated.Potential future directions in terms of research on SACs for the realization of commercially viable LSBs are also outlined.

Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems

This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.

How to improve machine learning models for lithofacies identification by practical and novel ensemble strategy and principles

Typically, relationship between well logs and lithofacies is complex, which leads to low accuracy of lithofacies identification. Machine learning (ML) methods are often applied to identify lithofacies using logs labelled by rock cores. However, these methods have accuracy limits to some extent. To further improve their accuracies, practical and novel ensemble learning strategy and principles are proposed in this work, which allows geologists not familiar with ML to establish a good ML lithofacies identification model and help geologists familiar with ML further improve accuracy of lithofacies identification. The ensemble learning strategy combines ML methods as sub-classifiers to generate a comprehensive lithofacies identification model, which aims to reduce the variance errors in prediction. Each sub-classifier is trained by randomly sampled labelled data with random features. The novelty of this work lies in the ensemble principles making sub-classifiers just overfitting by algorithm parameter setting and sub-dataset sampling. The principles can help reduce the bias errors in the prediction. Two issues are discussed, videlicet (1) whether only a relatively simple single-classifier method can be as sub-classifiers and how to select proper ML methods as sub-classifiers;(2) whether different kinds of ML methods can be combined as sub-classifiers. If yes, how to determine a proper combination. In order to test the effectiveness of the ensemble strategy and principles for lithofacies identification, different kinds of machine learning algorithms are selected as sub-classifiers, including regular classifiers (LDA, NB, KNN, ID3 tree and CART), kernel method (SVM), and ensemble learning algorithms (RF, AdaBoost, XGBoost and LightGBM). In this work, the experiments used a published dataset of lithofacies from Daniudi gas field (DGF) in Ordes Basin, China. Based on a series of comparisons between ML algorithms and their corresponding ensemble models using the ensemble strategy and principles, conclusions are drawn: (1) not only decision tree but also other single-classifiers and ensemble-learning-classifiers can be used as sub-classifiers of homogeneous ensemble learning and the ensemble can improve the accuracy of the original classifiers;(2) the ensemble principles for the introduced homogeneous and heterogeneous ensemble strategy are effective in promoting ML in lithofacies identification;(3) in practice, heterogeneous ensemble is more suitable for building a more powerful lithofacies identification model, though it is complex.

Experimental Study and Simulation Principles of An Oil-Gas Multiphase Transportation System

Presented is an experimental study on the performance of an oil-gas multiphase transportation system, especially on the multiphase flow patterns, multiphase pumping and multiphase metering of the system. A dynamic simulation analysis is conducted to deduce simulation parameters of the system and similarity criteria under simplified conditions are obtained. The reliability and feasibility of two-phase flow experiment with oil and natural gas simulated by water and air are discussed by using the similarity criteria.

A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

Solutions for Schrodinger-Poisson system involving nonlocal term and critical exponent

In this paper,we consider the following Kirchhoff-Schrodinger-Poisson system:{−(a+b∫_(R^(3))|∇u|^(2))△u+u+ϕu=μQ(x)|u|^(q-2)u+K(x)|u|^(4)u,in R^(3),−△ϕ=u^(2) the nonlinear growth of|u|^(4)u reaches the Sobolev critical exponent.By combining the variational method with the concentration-compactness principle of Lions,we establish the existence of a positive solution and a positive radial solution to this problem under some suitable conditions.The nonlinear term includes the nonlinearity f(u)~|u|^(q-2)u for the well-studied case q∈[4,6),and the less-studied case q∈(2,3),we adopt two different strategies to handle these cases.Our result improves and extends some related works in the literature.

THE VARIATIONAL PRINCIPLE FOR THE PACKING ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

Let(X,φ) be a nonautonomous dynamical system.In this paper,we introduce the notions of packing topological entropy and measure-theoretical upper entropy for nonautonomous dynamical systems.Moreover,we establish the variational principle between the packing topological entropy and the measure-theoretical upper entropy.

Systematic analysis of corporate environmental responsibility:elements,structure,function,and principles

Corporate Environmental Responsibility(CER) is the subsystem of Corporate Social Responsibility(CSR),which continues to increase prominence in the global economy.Nowadays,CER becomes more important in corporate sustainable development.Based on Carroll's pyramid mode of CSR,this article explores the systematic feature of CER.From a systematic perspective,it sorts out its elements,structure,function,and principles of CER.And the four levels of economic,legal,ethical,and charitable structure are emphasized.With these considerations interpreted into practice,success will be achieved in potential cost savings,technological innovation,increased public acceptance,and better relations with governments.

Global Existence and Stability of Solutions to River Flow System

In this short note,we are concerned with the global existence and stability of solutions to the river flow system.We introduce a new technique to set up a relation between the Riemann invariants and the finite mass to obtain a time-independent,bounded solution for any adiabatic exponent.The global existence of solutions was known long ago[Klingenberg and Lu in Commun.Math.Phys.187:327-340,1997].However,since the uncertainty of the function b(x),which corresponds physically to the slope of the topography,the L∞estimates growed larger with respect to the time variable.As a result,it does not guarantee the stability of solutions.By employing a suitable mathematical transformation to control the slope of the topography by the friction and the finite mass,we prove the uniformly bounded estimate with respect to the time variable.This means that our solutions are stable.

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler Lagrange equations and Hamilton＇s canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.

Analysis on the formation principle and present situation of nano phase state of multi-component self-assembly of traditional Chinese compound medicine decoction

Traditional Chinese medicine decoction is a complex polydispersed phase system containing real solution,colloid solution,emulsion and suspension.The compound decoction of traditional Chinese medicine has complex components,including saponins,alkaloids,polysaccharides,flavonoids,amino acids and so on,which can be self-assembled to form gels,fibers,micelles,vesicles and so on.The self-assembled nano-phase not only neutralizes the single drug and reduces the toxicity and side effects,but also has its own pharmacological effects,which complement each other to achieve synergistic effect,so as to achieve the role of drug supplement,which is of research significance.The formation principle,solubilization and synergism principle and characterization method of multi-component self-assembly of traditional Chinese medicine compound decoction are discussed in this paper.

A Single-Ended Protection Principle for LCC-VSC-MTDC System with High Resistance Fault Tolerance

Line-commutated converter-voltage source converter(LCC-VSC)power transmission technology does not have the problem of communication failure very usually.It therefore can support the long-distance,long-capacity transmission of electric energy.However,factors such as topology,control strategy,and short-circuit capacities make the traditional protection principles not fully applicable to LCC-VSC hybrid transmission systems.To enhance the reliability of hybrid DC systems,a single-ended principle based on transmission coefficients is proposed and produced.First,the equivalent circuit of the LCC-VSC hybrid DC system is analyzed and the expression of the first traveling wave is deduced accordingly.Then,the concept of multi-frequency transmission coefficients is proposed by analyzing the amplitude-frequency,and the characteristics of each element.Finally,the LCC-VSCDC system model is built to verify the reliability and superiority of the principle itself.Theoretical analysis and experimental verification show that the principle has strong interference resistance.

Hamiltonian Systems in Elasticity and Their Variational Principles

As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system inelasticity and its variational principle are derived from the basic equations of elasticity.

DYNAMIC PRINCIPLE FOR INTERACTION BETWEEN HEART AND ARTERIAL SYSTEM

Various steady models for interaction between heart and arterial system have been given in liter- ature,In our recent study,a dynamic principle,i.e.the principle of least cardiac work is proposed,and a dy- namic model for interaction of heart and arterial system is established.Preliminary results of our experiments show that both the principle and the model are consistent with the physiological phenomena.It reveals that the pres- ent analysis may offer a new measure for the study of dynamic process of interaction between heart and arterial system.