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Constructing a quasi-Legendre basis based on the C-Bézier basis

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Progress in Natural Science:Materials International 2005年第6期15卷 559-563页

作者： HUANG yu* and WANG Guozhao(department of mathematics, zhejiang university, hangzhou 310027, china) department of mathematics Zhejiang University Hangzhou 310027 China

In the space Γ_n=span｛sint,cost,1,t,t2,…,t n-2 ｝, a C-Bézier basis is constructed by an integral approach. However, the C-Bézier basis is not orthogonal. For some applications, we construct an orthogonal basis based on the C-Bézier basis, which has remarkable properties similar to that of the Legendre basis. Then we derive the transformation matrices that convert the C-Bézier basis and the orthogonal basis into each other. As an example of application, we apply this orthogonal basis to the degree reduction approximation of the C-Bézier curves.

关键词： C-Bézier basis orthogonal basis basis transformations degree reduction.

Estimation for nearly unit root processes with GARCH errors

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Applied mathematics(A Journal of Chinese Universities) 2010年第3期25卷 297-306页

作者： yuAN yu-ze ZHANG Rong-mao department of mathematics, zhejiang university, hangzhou 310027, china department of mathematics Zhejiang University Hangzhou China

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.

关键词： Nearly unit root GARCH error least square estimation Ornstein-Uhlenbeck process empirical likelihood.

Narrative review of latest research progress about robotic percutaneous coronary intervention

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Journal of Geriatric Cardiology 2024年第8期21卷 816-825页

作者： Zhen-yu LIU Guang-Yao zhai department of Clinical Medicine Beijing Luhe HospitalCapital Medical UniversityBeijingChina department of Cardiology Beijing Luhe HospitalCapital Medical UniversityBeijingChina

Robotic percutaneous coronary intervention(R-PCI)is a novel technology in which operators can manipulate guidewires and catheter devices in interventional *** approach provides great benefits to interventional cardiologists in terms of reducing both radiation exposure and orthopedic *** large,high-quality cohort studies have confirmed the short-term safety and high technical success rate of ***,randomized long-term data are still needed before adopting them as part of standard coronary ***,tele-stenting for complex coronary lesions has significant potential for *** need to overcome the present relevant challenges for its application such as inherent delays,bedside care for unstable patients from R-PCIs to manual PCIs(M-PCIs),incompatibility for a thrombus aspiration catheter and heavily calcified *** is a great future in laboratory workflow teams,3D-printed anatomical models and multiple joint collaborative control *** narrative review summarizes the latest developments in R-PCI,with a focus on developments in robotic technology,and discusses the current and future potential use of R-PCI in clinical practice globally.

关键词： coronary injuries unstable

Derivation of Martin-Hou Equation of State from Hard-particle Perturbation Theory

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Chemical Research in Chinese Universities 2000年第1期16卷 49-56页

作者： ZHANG Bing-jian (department of Chemistry, zhejiang university, hangzhou 310027, P. R. china) HOU yu-chun (department of Chemical Engineering, zhejiang university, hangzhou 310027, P. R. china) 浙江大学浙江杭州 310027

In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.

关键词： Perturbation theory Martin-Hou equation of state Theoretical expression P-V-T properties Molecular parameter

Programmable silicon-photonic quantum simulator based on a linear combination of unitaries

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Photonics Research 2024年第8期12卷 1760-1767页

作者： yuE yu yuLIN CHI CHONGHAO zhai JIESHAN HUANG QIHUANG GONG JIANWEI WANG State Key Laboratory for Mesoscopic Physics School of PhysicsPeking UniversityBeijing 100871China Frontiers Science Center for Nano-optoelectronics&Collaborative Innovation Center of Quantum Matter Peking UniversityBeijing 100871China Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China Yangtze Delta Institute of Optoelectronics Peking UniversityNantong 226010China Hefei National Laboratory Hefei 230088China department of Electrical and Computer Engineering University of WashingtonSeattleWashington 98195USA china Mobile Research Institute Beijing 100053China

Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many *** implementation of dynamics simulation requires efficient quantum *** Lie-Trotter-Suzuki approximation algorithm,also known as the Trotterization,is basic in Hamiltonian dynamics simulation.A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation ***,implementing such multiproduct Trotterization in quantum computers remains challenging due to the requirements of highly controllable and precise quantum entangling operations with high success ***,we report a programmable integrated-photonic quantum simulator based on a linear combination of unitaries,which can be tailored for implementing the linearly combined multiple Trotterizations,and on the simulator we benchmark quantum simulation of Hamiltonian *** modify the multi-product algorithm by integrating it with oblivious amplitude amplification to simultaneously reach high simulation precision and high success *** quantum simulator is devised and fabricated on a large-scale silicon-photonic quantum chip,which allows the initialization,manipulation,and measurement of arbitrary four-qubit states and linearly combined unitary *** an example,the quantum simulator is reprogrammed to emulate the dynamics of an electron spin and nuclear spin coupled *** work promises the practical dynamics simulations of real-world physical and molecular systems in future large-scale quantum computers.

关键词： quantum Hamiltonian linearly

Lp integrability of trigonometric series with special varying coefficients

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Applied mathematics:A Journal of Chinese Universities 2009年第4期24卷 402-410页

作者： WEI Bao-rong department of mathematics,hangzhou Normal university,zhejiang 310036,china department of mathematics Hangzhou Normal University Zhejiang China

Very recently,yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2 conditions,which are generalizations of the monotone *** applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric *** fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.

关键词： Lp integrability trigonometric series special varying coefficients

Bridging properties of the debonded interface with frictional sliding

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Progress in Natural Science:Materials International 2006年第2期16卷 153-162页

作者： LIU Pengfei, TAO Weiming, yu Xuezhong and GUO Yimu ( department of Engineering Mechanics, zhejiang university, hangzhou 310027, china Second Affiliated Hospital, zhejiang university, hangzhou 310009, china) department of Engineering Mechanics Zhejiang University Hangzhou 310027 China Second Affiliated Hospital Zhejiang University Hangzhou 310009 China

A theoretical model simulating the properties of frictional bridging is presented and relatively perfect stress solutions for the fiber and matrix are obtained. Based on the energy equilibrium in the process of interfacial debonding, an expression for the energy release rate G is derived to explore the interfacial fracture properties. By introducing an interfacial debonding criterion G≥Γi, a method for determining the critical debond length is proposed and the bridging constitutive relationship is also obtained. Numerical calculations are conducted for the fiber-reinforced composite SCS-6/Ti-6Al-4V and the results are also compared with those obtained by using other existing models.

关键词： interfacial stress transfer frictional sliding energy release rate bridging constitutive relationship fiber-reinforced composites.

Application of efficient and sustainable freeze-dissolving technology in manufacturing of KHCO_(3)ultrafine particles

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Green Chemical Engineering 2024年第2期5卷 266-272页

作者： Jiaqi Luo Qifan Su Qiushuo yu Xinyue zhai yuan Zou Huaiyu Yang School of Chemical Engineering Chemical Engineering Research Center of the Ministry of Education for Advanced Use Technology of Shanbei EnergyInternational Science&Technology Cooperation Base of MOST for Clean Utilization of Hydrocarbon ResourcesNorthwest UniversityXi’an710069China department of Chemical Engineering Loughborough UniversityLoughboroughLE113TUUnited Kingdom

The development of ultrafine particles provided a new way to solve problems in the fields of energy,environment,and medicine,and had become one of the most promising ***,the application of ultrafine particles required the development of cleaner,greener,and more efficient preparation *** new freeze-dissolving technology has been applied in manufacturing of KHCO_(3)ultrafine particles,with an aqueous solution of 0.02-0.1 g KHCO_(3)/g *** ice particles were formed after dripping the solution into liquid *** antisolvent ethanol was used to dissolve the ice spherical template at a temperature below 273.15 K,and the pre-formed KHCO_(3)ultrafine particles inside the ice template remained in the ethanol aqueous *** ice particles were put into the freeze dryer to isolate the ultrafine KHCO_(3)*** with the particles produced with traditional freeze-drying technology,the ultrafine powder/particles produced by the freeze-dissolving technology were smaller with narrower size *** freeze-dissolving technology has demonstrated a much more sustainable and efficient manufacturing process than the traditional freeze-drying *** addition,the influence of the concentrations of KHCO_(3)and the sizes of ice particles were investigated with the discussions of mechanisms.

关键词： Freeze-dissolving Freeze-drying Ultrafine particles Sustainable

The Synthesis and Optical Absorption of Bisazo Pigments from 1,5-Diaminoanthraquinone

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Chinese Chemical Letters 1998年第4期9卷 341-343页

作者： yu Hong ZHANG Qing Sen yu(department of Chemistry, zhejiang university, hangzhou 310027) department of Chemistry Zhejiang University Hangzhou 310027 China

Ten new bisazo pigments were synthesized by coupling 1,5-diaminoanthraquinone with various couplers. The absorption studies show that a red shift of 50 nm is obtained when the coupler component is changed.

关键词： 1,5-diaminoanthraquinone absorption pigment