A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN

Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk： ｜z1｜^2＋ ｜｜z2｜｜2^p2＋ … ＋ ｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1） ＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.

An optimized numerical method to pre-researching the performance of solid-phase oxygen control in a non-isothermal lead–bismuth eutectic loop

In the present work,a new transient calculation method for parameters that can be used to evaluate the ability of oxygen control in a non-isothermal lead-bismuth eutectic(LBE)loop with solid-phase oxygen control was proposed.It incorporates the dissolution process of PbO particles and the oxygen mass transfer process,and an optimized method was used for finding out the optimized oxygen mass transfer coefficient.In numerical terms,three mass transfer models were simultaneously applied,and comparisons of calculated and experimental results from the CRAFT loop indicated that the optimized calculation method and these new oxygen mass transfer models were correct and applicable to other LBE loops.Through this calculation method,we aimed to optimize prediction of the distribution of oxygen and iron concentrations,time taken to establish the steady state of oxygen,and maximum dissolution/precipitation rates of corrosion products and corrosion depth across the entire LBE loop.We hope that this work will provide a potential reference for designing a more intelligent oxygen control system in the future.

Assessing the operational design domain of lane support system for automated vehicles in different weather and road conditions

With the growing rate of automated vehicles(AVs)at the lower level of automation,the experimental tests are also in progress with vehicles at higher levels.In the absence of extended digital infrastructures and deployment of level 5 full automated vehicles,the physical infrastructure is required to maintain a fundamental role to enable their introduction in public roads.This paper focuses on lane support system(LSS)whose operational design domain(ODD)is strongly connected to the road characteristics and conditions.An experimental test was carried out with a state of the art,and LSS and advanced technologies were used for road monitoring on different roads under various environmental conditions including dry,wet pavements and rain.We applied the generalized estimation equation for logistic regression to account within-cluster homogeneity which is induced by repeated measures on the same road sections.Statistical models allow the identification of variables that are significant for the LSS fault probability among various effects of road features including marking,pavement distress,weather conditions,horizontal curvature,and cross section.Results pointed out the relevance of the wet retro-reflection of marking(RLw)and the horizontal curvature in the definition of ODD for LSS.Threshold values have been proposed for the tested LSS.Wet pavement doesn’t affect the LSS performance when compared to the dry condition.Rain was shown to be critical even with very good road characteristics.

Singular integral operators on product domains along twisted surfaces

We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.

SOTIF risk mitigation based on unified ODD monitoring for autonomous vehicles

Purpose–The purpose of this paper is to design a unified operational design domain(ODD)monitoring framework for mitigating Safety of the Intended Functionality(SOTIF)risks triggered by vehicles exceeding ODD boundaries in complex traffic scenarios.Design/methodology/approach–A unified model of ODD monitoring is constructed,which consists of three modules:weather condition monitoring for unusual weather conditions,such as rain,snow and fog;vehicle behavior monitoring for abnormal vehicle behavior,such as traffic rule violations;and road condition monitoring for abnormal road conditions,such as road defects,unexpected obstacles and slippery roads.Additionally,the applications of the proposed unified ODD monitoring framework are demonstrated.The practicability and effectiveness of the proposed unified ODD monitoring framework for mitigating SOTIF risk are verified in the applications.Findings–First,the application of weather condition monitoring demonstrates that the autonomous vehicle can make a safe decision based on the performance degradation of Lidar on rainy days using the proposed monitoring framework.Second,the application of vehicle behavior monitoring demonstrates that the autonomous vehicle can properly adhere to traffic rules using the proposed monitoring framework.Third,the application of road condition monitoring demonstrates that the proposed unified ODD monitoring framework enables the ego vehicle to successfully monitor and avoid road defects.Originality/value–The value of this paper is that the proposed unified ODD monitoring framework establishes a new foundation for monitoring and mitigating SOTIF risks in complex traffic environments.