LIMIT OF ITERATES FOR BERNSTEIN POLYNOMIALS DEFINED ON A TRIANGLE

Let f ∈ C[0,1] , and Bn(f,x) be the n-th Bernstein polynomial associated with function f. In 1967, the limit of iterates for Bn(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and generalized this result. But anyway, all these discussions are only for univariate case. In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely.

CONVERGENCE RATE FOR ITERATES OF q-BERNSTEIN POLYNOMIALS

Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn（., qn）} when n → ∞ and convergence rate of Bn（f,q;x） when f ∈ C^n-1 [0, 1], q → ∞ are also presented.

On the Approximation by the Iterates of Stancu Operators and Its Modified Operators

This paper discusses the approximation of the class of function W2 and W2Lp(1<p<∞) by the iterates of Stancu operators and its modified operators and obtains some theorems which extend the results of paper [3].

Toroidal torques due to n=1 magnetic perturbations in ITER baseline scenario

Toroidal torques,generated by the resonant magnetic perturbation(RMP)and acting on the plasma column,are numerically systematically investigated for an ITER baseline scenario.The neoclassical toroidal viscosity(NTV),in particular the resonant portion,is found to provide the dominant contribution to the total toroidal torque under the slow plasma flow regime in ITER.While the electromagnetic torque always opposes the plasma flow,the toroidal torque associated with the Reynolds stress enhances the plasma flow independent of the flow direction.A peculiar double-peak structure for the net NTV torque is robustly computed for ITER,as the toroidal rotation frequency is scanned near the zero value.This structure is found to be ultimately due to a non-monotonic behavior of the wave-particle resonance integral(over the particle pitch angle)in the superbanana plateau NTV regime in ITER.These findings are qualitatively insensitive to variations of a range of factors including the wall resistivity,the plasma pedestal flow and the assumed frequency of the rotating RMP field.

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and suppose that there exists ε 】 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.

On Iterates of Holomorphic Maps in Strongly Pseudoconvex Domains

The theory of iterates of holomorphic maps is a very active topic in recent years. The well-known Denjoy-Wolff theorem characterized the asymptotic behavior of the iterate sequences of holomorphic self-maps in the unit disc △C. Subsequent authors extended this theorem to some special domains of C^n(n】1). Briefly speaking, the research

316LN不锈钢真空电子束焊接工艺试验

本文对30mm的316LN不锈钢进行了真空电子束焊试验。随后对典型工艺参数下焊缝组织在常温及77K低温下焊接接头的力学性能进行了研究。微观组织SEM观察的结果表明,316LN的电子束焊接接头均不同程度地出现了气孔。力学性能测试结果表明,77K下接头的强度系数为83%,室温下接头的强度系数则达87%。此外,显微维氏硬度测试结果表明,接头区硬度约为母材的80%。

托卡马克高约束稳态物理的探路者——东方超环

人类已经在实验室通过托卡马克装置实现了10MW量级的可控氘氚核聚变反应,磁约束聚变研究进入到了实验堆时代。托卡马克高约束稳态运行成为开发商用聚变能的关键。中国全超导托卡马克装置(东方超环,EAST)瞄准国际热核聚变实验堆(ITER)和未来聚变堆稳态运行的需求,在前沿稳态物理研究中获得重要进展,率先演示了托卡马克高约束稳态模式的长脉冲运行,为ITER运行和未来聚变堆设计提供了重要参考。

An improved particle filter indoor fusion positioning approach based on Wi-Fi/PDR/geomagnetic field

The existing indoor fusion positioning methods based on Pedestrian Dead Reckoning(PDR)and geomagnetic technology have the problems of large initial position error,low sensor accuracy,and geomagnetic mismatch.In this study,a novel indoor fusion positioning approach based on the improved particle filter algorithm by geomagnetic iterative matching is proposed,where Wi-Fi,PDR,and geomagnetic signals are integrated to improve indoor positioning performances.One important contribution is that geomagnetic iterative matching is firstly proposed based on the particle filter algorithm.During the positioning process,an iterative window and a constraint window are introduced to limit the particle generation range and the geomagnetic matching range respectively.The position is corrected several times based on geomagnetic iterative matching in the location correction stage when the pedestrian movement is detected,which made up for the shortage of only one time of geomagnetic correction in the existing particle filter algorithm.In addition,this study also proposes a real-time step detection algorithm based on multi-threshold constraints to judge whether pedestrians are moving,which satisfies the real-time requirement of our fusion positioning approach.Through experimental verification,the average positioning accuracy of the proposed approach reaches 1.59 m,which improves 33.2%compared with the existing particle filter fusion positioning algorithms.

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.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

全钨ITER朗缪尔探针的高热负荷测试及损伤行为

本文研究了全钨ITER朗缪尔探针在高热负荷条件下的耐热性能、绝缘性能和损伤行为。利用核工业西南物理研究院的60 kW电子束测试平台,对探针在10 MW/m^(2)稳态热负荷、20 MW/m^(2)瞬态热负荷及15 MW/m^(2)高参数稳态热负荷下进行模拟测试。实验结果表明,全钨朗缪尔探针能够承受10 MW/m^(2)热负荷100分钟、20 MW/m^(2)热负荷300次循环以及15 MW/m^(2)热负荷3000次循环。在15 MW/m^(2)条件下,探针表面在前1000次循环中无明显损伤,但在3000次循环后出现裂纹,且部分探针表面发生再结晶现象。研究表明,现有全钨朗缪尔探针的设计能够满足当前ITER装置的服役条件,但面对未来DEMO堆更加苛刻的条件可能还需要进一步优化。

西物院ITER项目强矩阵管理模式探索与成效

ITER计划是目前全球规模最大、影响最深远的国际大科学工程,由欧盟、中国、美国、日本、俄罗斯、韩国、印度等七方共35个国家参与,也是我国参与的最大的国际合作项目,我国承担任务在所有七方中完成最好,多次受到ITER总干事的表扬。文章主要针对西物院ITER项目强矩阵管理模式探索进行了总结,希望为未来参与大科学工程项目提供借鉴。

Data-Driven Active Disturbance Rejection Control of Plant-Protection Unmanned Ground Vehicle Prototype: A Fuzzy Indirect Iterative Learning Approach

Dear Editor,This letter proposes a fuzzy indirect iterative learning(FIIL)active disturbance rejection control(ADRC)scheme to address the impact of uncertain factors of plant-protection unmanned ground vehicle(UGV),in which ADRC is a data-driven model-free control algorithm that only relies on the input and output data of the system.Based on the established nonlinear time-varying dynamic model including dynamic load(medicine box),the FIIL technology is adopted to turn the bandwidth and control channel gain online,in which the fuzzy logic system is used to update the gain parameters of iterative learning in real time.Simulation and experiment show the FIIL-ADRC scheme has better control performance.

MAUN:Memory-Augmented Deep Unfolding Network for Hyperspectral Image Reconstruction

Spectral compressive imaging has emerged as a powerful technique to collect the 3D spectral information as 2D measurements.The algorithm for restoring the original 3D hyperspectral images(HSIs)from compressive measurements is pivotal in the imaging process.Early approaches painstakingly designed networks to directly map compressive measurements to HSIs,resulting in the lack of interpretability without exploiting the imaging priors.While some recent works have introduced the deep unfolding framework for explainable reconstruction,the performance of these methods is still limited by the weak information transmission between iterative stages.In this paper,we propose a Memory-Augmented deep Unfolding Network,termed MAUN,for explainable and accurate HSI reconstruction.Specifically,MAUN implements a novel CNN scheme to facilitate a better extrapolation step of the fast iterative shrinkage-thresholding algorithm,introducing an extra momentum incorporation step for each iteration to alleviate the information loss.Moreover,to exploit the high correlation of intermediate images from neighboring iterations,we customize a cross-stage transformer(CSFormer)as the deep denoiser to simultaneously capture self-similarity from both in-stage and cross-stage features,which is the first attempt to model the long-distance dependencies between iteration stages.Extensive experiments demonstrate that the proposed MAUN is superior to other state-of-the-art methods both visually and metrically.Our code is publicly available at https://github.com/HuQ1an/MAUN.

Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.

Gyrokinetic simulations of the kinetic electron effects on the electrostatic instabilities on the ITER baseline scenario

The linear and nonlinear simulations are carried out using the gyrokinetic code NLT for the electrostatic instabilities in the core region of a deuterium plasma based on the International Thermonuclear Experimental Reactor(ITER)baseline scenario.The kinetic electron effects on the linear frequency and nonlinear transport are studied by adopting the adiabatic electron model and the fully drift-kinetic electron model in the NLT code,respectively.The linear simulations focus on the dependence of linear frequency on the plasma parameters,such as the ion and electron temperature gradientsκ_(Ti,e)≡R=L_(Ti,e),the density gradientκ_(n)≡R/L_(n)and the ion-electron temperature ratioτ=T_(e)=T_(i).Here,is the major radius,and T_(e)and T_(i)denote the electron and ion temperatures,respectively.L_(A)=-(δ_(r)lnA)^(-1)is the gradient scale length,with denoting the density,the ion and electron temperatures,respectively.In the kinetic electron model,the ion temperature gradient(ITG)instability and the trapped electron mode(TEM)dominate in the small and large k_(θ)region,respectively,wherek_(θ)is the poloidal wavenumber.The TEMdominant region becomes wider by increasing(decreasing)κ_(T_(e))(κ_(T_(i)))or by decreasingκ_(n).For the nominal parameters of the ITER baseline scenario,the maximum growth rate of dominant ITG instability in the kinetic electron model is about three times larger than that in the adiabatic electron model.The normalized linear frequency depends on the value ofτ,rather than the value of T_(e)or T_(i),in both the adiabatic and kinetic electron models.The nonlinear simulation results show that the ion heat diffusivity in the kinetic electron model is quite a lot larger than that in the adiabatic electron model,the radial structure is finer and the time oscillation is more rapid.In addition,the magnitude of the fluctuated potential at the saturated stage peaks in the ITGdominated region,and contributions from the TEM(dominating in the higher k_(θ)region)to the nonlinear transport can be neglected.In the adiabatic electron model,the zonal radial electric field is found to be mainly driven by the turbulent energy flux,and the contribution of turbulent poloidal Reynolds stress is quite small due to the toroidal shielding effect.However,in the kinetic electron model,the turbulent energy flux is not strong enough to drive the zonal radial electric field in the nonlinear saturated stage.The kinetic electron effects on the mechanism of the turbulence-driven zonal radial electric field should be further investigated.

Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating representation.Finally, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.

Development of an Engineered Sugar Aminotransferase with Simultaneously Improved Stability and Non-Natural Substrate Activity to Synthesize the Glucosidase Inhibitor Valienamine

Sugar aminotransferases(SATs)catalyze the installation of chiral amines onto specific keto sugars,pro-ducing bioactive amino sugars.Their activity has been utilized in artificial reactions,such as using the SAT WecE to transform valienone into the valuable a-glucosidase inhibitor valienamine.However,the low thermostability and limited activity on non-natural substrates have hindered their applications.Simultaneously improving stability and enzyme activity is particularly challenging owing to the acknowledged inherent trade-off between stability and activity.A customized combinatorial active-site saturation test-iterative saturation mutagenesis(CAST-ISM)strategy was used to simultaneously enhance the stability and activity of WecE toward valienone.Fourteen hotspots related to improving the stability-\activity trade-off were identified based on evolutionary conservation and the average mutation folding energy assessment of 57 residues in the active site of WecE.Positive mutagenesis and combinatorial mutations of these specific residues were accomplished via site-directed saturation mutagenesis(SSM)and iterative evolution cycles.Compared with those of the wild-type(WT)WecE,the quadruple mutant M4(Y321F/K209F/V318R/F319V)displayed a 641.49-fold increase in half-life(t_(1/2))at 40℃ and a 31.37-fold increase in activity toward the non-natural substrate valienone.The tri-ple mutant M3(Y321F/K209F/V318R)demonstrated an 83.04-fold increase in(t_(1/2))at 40℃and a 37.77-fold increase in activity toward valienone.The underlying mechanism was dependent on the strengthened interface interactions and shortened transamination reaction catalytic distance,compared with those of the WT,which improved the stability and activity of the obtained mutants.Thus,we accomplished a general target-oriented strategy for obtaining stable and highly active SATs for artificial amino-sugar biosynthesis applications.

Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.