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The Compactness of Commutators on the heisenberg Group

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Acta Mathematica Sinica,English Series 2006年第2期22卷 425-430页

作者： he ping liu Xuan Yuan ZheNG LMAM School of Mathematical Sciences Peking University

We consider the commutators of the HSrmander multiplier with CMO-functions on the heisenberg group. The result of compactness on L^P spaces is proved.

关键词： heisenberg group Multiplier Commutator CMO Compactness

Littlewood Paley g-function on the heisenberg Group

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Acta Mathematica Sinica,English Series 2006年第1期22卷 95-100页

作者： he ping liu Rui Qin MA LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

We consider the g-function related to a class of radial functions which gives a characterization of the L^p-norm of a function on the heisenberg group.

关键词： heisenberg group g-function

An Analogue of Beurling's Theorem for the Jacobi Transform

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Acta Mathematica Sinica,English Series 2009年第1期25卷 85-94页

作者： Ji Zheng HUANG he ping liu Jian Ming liu LMAM School of Mathematical Sciences Peking University Beijing lO0871 P. R. China

In this paper, we prove Beurling＇s theorem for the Jacobi transform, from which we derive some other versions of uncertainty principles.

关键词： Jacobi transform uncertainty principle Beurling's theorem Abel transform

Oxidation Behavior of Fe-based Amorphous Ribbons

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Journal of Iron and Steel Research International 2016年第11期23卷 1219-1225页

作者： Shu-lan ZHANG he-ping liu Xiao-tong FU Central Iron and Steel Research Institute Beijing 100081China

The oxidation behavior of Fe-based amorphous ribbons was tested by annealing at 380℃ in air for different time with heat treatment furnace and analyzed by X-ray photoelectron spectroscopy （XPS） and scanning electron micros- copy （SEM）. The mechanism of oxides formation of the amorphous ribbons was discussed in detail. The results showed that the oxides were mostly B2O3 , SiO2 and Fe2O3 or FeO. With the increase of annealing time and holding temperature, the fraction of the oxides on the ribbon surface increased and the size of the oxides became larger due to the generation of new oxides and the coalescence of small oxides. The oxides have different shapes, such as round, rod and needle-shaped. Experimental results also showed that the oxides nucleated at fish scale, air pocket and impu-rities in priority, and the growth of the oxides was controlled by the diffusion of atoms. With the increase of the distance to the ribbon surface, the oxygen concentration decreased dramatically. Due to the low binding energy of B2O3 and the large diffusion coefficient of B atom, the B elemaent was oxidized firstly compared with other elements. More- over, the oxidation deoths of the B2O3 and SiO2 were larger than that of Fe2O3.

关键词： oxidation amorphous ribbon nucleation~ oxide growth

Numerical Simulation of Electromagnetic Field and Flow Pattern in a Continuous Slab Caster with In-roll Type Strand Electromagnetic Stirring

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Journal of Iron and Steel Research International 2015年第5期22卷 414-422页

作者： Jian GONG he-ping liu Xian-hui WANG Yan-ping BAO School of Metallurgical and Ecological Engineering University of Science and Technology Beijing Shougang Qian'an Iron & Steel Company Central Iron and Steel Research Institute

The electromagnetic field and flow analysis model were developed to simulate the electromagnetic field and the flow pattern in a vertical curved continuous slab caster with the in-roll type strand electromagnetic stirring. The transient electromagnetic field distribution and the induced electromagnetic force were numerically described. The effects of stirring current, stirring frequency, and different stirrer configurations on the electromagnetically driven flow field in the strand were investigated and the optimization of the stirring parameters was discussed by performing a relative comparison of numerical results. Results show that the in-roller type strand electromagnetic stirrer （S- EMS） pair generates the fluctuating magnetic fields, penetrating through the cast slab and periodically parallel shift- ing along the slab wide face w!th time evolution. The transient induced electromagnetic forces travels toward the magnetic flux shifting direction, Different stirring parameters （i. e. current and frequency） and stirrer configurations affect the stirring strength and the flow rbcirculation pattern in the strand, which are closely related to metallurgical performances of the stirrers. There is an optimum frequency to obtain the maximum stirring. The present model pro vides a relatively theoretical insight into the in-roll type strand electromagnetic stirring system for best operating.

关键词： strand electromagnetic stirrer continuous casting slab caster in roll type numerical simulation

Numerical simulation of 3D electromagnetic–thermal phenomena in an induction heated slab

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Journal of Iron and Steel Research International 2020年第4期27卷 420-432页

作者： he-ping liu Xian-hui Wang Liang-ying Si Jian Gong Central Iron and Steel Research Institute Beijing 100081China Shougang Zhixin Qian’an Electromagnetic Material Co. Ltd.Qian’an 064404HebeiChina

A mathematical model was developed to get an insight into 3D electromagnetic–thermal phenomena in an induction heated steel slab with a large width/thickness ratio by solving a fully coupled Maxwell equations and energy conservation *** spatial heat radiation between the slab surface and the refractory wall in an induction furnace was *** electromagnetic induction and temperature distribution features inside the slab with time evolution were *** effects of electromagnetic induction parameters,thermal conductivity of the material and process parameters on the induction heating process were theoretically *** results show that the spatial distribution of induction heat generation inside the slab is *** high work frequency and the low heat conductivity of slab increase the non-uniformity of slab induction heating *** radiative heat loss and heat transfer between the slab and the metal parts used for holding the slab have an important effect on the slab surface *** is necessary to separately control the current input in the multi-layer coil windings along the height direction of furnace and adopt the multi-step heating strategies with time evolution to improve the homogenization of the slab temperature.

关键词： Slab Electromagnetic feld Induction heating Numerical simulation

Longitudinal corner crack of chamfered slab and optimization of mould

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Journal of Iron and Steel Research International 2023年第2期30卷 259-266页

作者： Hong-biao Tao Hui Zhang he-ping liu Ming-lin Wang National Engineering&Research Center of Continuous Casting Technology CISRIBeijing100081China

Chamfered mould has gradually become a new technology equipment to eliminate transverse corner ***,longitudinal corner crack ratio of chamfered slab was very *** microstructure was detected in the area where the longitudinal corner crack *** of narrow face shape and taper distribution of mould copper plate on longitudinal corner crack was studied by industrial *** velocity distribution in the narrow copper plate was studied by numerical *** the premise of preventing cooling water from nuclear boiling,improvement measures of mould cooling process and water seam structure were put forward through heat transfer *** results showed that local taper of the meniscus region of mould should be increased to prevent generation of longitudinal corner *** slope length of narrow copper plate should be controlled within 55 mm,and chamfering angle should be controlled at about 30°.Average water velocity should be more than 7.0 m/*** flat and chamfering regions of narrow copper plate working face should be designed as double taper and funnel structure,*** water seam in the chamfering region should preferentially choose the combined cooling structure with two holes and one *** order to prevent the extension of longitudinal corner crack,chamfered narrow face foot roller should be used.

关键词： Chamfered mould Longitudinal corner crack Copper plate shape Mould water velocity Mould taper

Fault Tolerant Control for Networked Control Systems with Packet Loss and Time Delay

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International Journal of Automation and computing 2011年第2期8卷 244-253页

作者： Ming-Yue Zhao he-ping liu Zhi-Jun Li De-Hui Sun College of Automation University of Science and Technology Beijing Beijing 100083 PRC Department of Automation North China University of Technology Beijing 100144 PRC

In this paper,a fault tolerant control with the consideration of actuator fault for a networked control system （NCS） with packet loss is *** NCS with data packet loss can be described as a switched system *** loss dependent Lyapunov function is used and a fault tolerant controller is proposed respectively for arbitrary packet loss process and Markovian packet loss *** a controlled plant with external energy-bounded disturbance,a robust H ∞ fault tolerant controller is designed for the *** results are also expanded to the NCS with packet loss and networked-induced *** examples are given to illustrate the effectiveness of the proposed design method.

关键词： Fault tolerant control networked control system (NCS) packet loss actuator fault time delay.

The BMO_L Space and Riesz Transforms Associated with Schrdinger Operators

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Acta Mathematica Sinica,English Series 2010年第4期26卷 659-668页

作者： Jian Feng DONG he ping liu LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

Let L =△ ＋ V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Feffe... 详细信息

关键词： BMO space reverse HSlder class Schr5dinger operator Riesz transform