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Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 91-108页

作者： wen-qing xu Sha-sha wang Da-chuan xu Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China Department of Mathematics and Statistics California State UniversityLong BeachCalifornia90840USA Department of Mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

Evaluation on Configuration Stiffness of Overconstrained 2R1T Parallel Mechanisms

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Chinese Journal of Mechanical Engineering 2024年第3期37卷 62-82页

作者： xuejian Ma Zhenghe xu yundou xu yu wang Jiantao yao yongsheng Zhao Parallel Robot and Mechatronic System Laboratory of Hebei Province Yanshan UniversityQinhuangdao 066004China Key Laboratory of Advanced Forging and Stamping Technology and Science of Ministry of National Education Yanshan UniversityQinhuangdao 066004China

Currently,two rotations and one translation(2R1T)three-degree-of-freedom(DOF)parallel mechanisms(PMs)are widely applied in five-DOF hybrid machining ***,there is a lack of an effective method to evaluate the configuration stiffness of mechanisms during the mechanism design *** is a challenge to select appropriate 2R1T PMs with excellent stiffness performance during the design *** the operational status of 2R1T PMs,the bending and torsional stiffness are considered as indices to evaluate PMs'configuration ***,a specific method is proposed to calculate these stiffness ***,the various types of structural and driving stiffness for each branch are assessed and their specific values ***,a rigid-flexible coupled force model for the over-constrained 2R1T PM is established,and the proposed evaluation method is used to analyze the configuration stiffness of the five 2R1T PMs in the entire ***,the driving force and constraint force of each branch in the whole working space are calculated to further elucidate the stiffness evaluating results by using the proposed method *** obtained results demonstrate that the bending and torsional stiffness of the 2RPU/UPR/RPR mechanism along the x and y-directions are larger than the other four mechanisms.

关键词： Parallel mechanism Stiffness Over-constrained Three degrees of freedom

SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES

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Journal of Computational Mathematics 2024年第1期42卷 111-133页

作者： Ruihan Guo yan xu School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China

In[20],a semi-implicit spectral deferred correction(SDC)method was proposed,which is efficient for highly nonlinear partial differential equations(PDEs).The semi-implicit SDC method in[20]is based on first-order time integration methods,which are corrected iteratively,with the order of accuracy increased by one for each additional *** this paper,we will develop a class of semi-implicit SDC methods,which are based on second-order time integration methods and the order of accuracy are increased by two for each additional *** spatial discretization,we employ the local discontinuous Galerkin(LDG)method to arrive at fully-discrete schemes,which are high-order accurate in both space and *** experiments are presented to demonstrate the accuracy,efficiency and robustness of the proposed semi-implicit SDC methods for solving complex nonlinear PDEs.

关键词： Spectral deferred correction method Nonlinear PDEs Local discontinuous Galerkin method Second-order scheme

Periodic Variation Studies of the Two Short Period w UMa-type Eclipsing Binaries: LX Lyn and V0853 Aur

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Research in Astronomy and Astrophysics 2024年第1期24卷 273-284页

作者： xu Zhang Bin Zhang School of Physics and Electronic Science Guizhou Normal UniversityGuiyang 550001China Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing Guizhou Normal UniversityGuiyang 550025China

In this paper,new light curves(LCs) of contact eclipsing binary(CEB) systems LX Lyn and V0853 Aur are presented and analyzed by using the 2015 version of the wilson-Devinney(w-D) *** order to explain their asymmetric LCs,cool starspots on the components were *** is suggested that their fill-out degrees are f=12.0%(LX Lyn) and f=26.3%(V0853 Aur).At the same time,we found that LX Lyn is a w-type eclipsing binary(EB) with an orbital inclination of i=84°.88 and a mass ratio of q=2.31.V0853 Aur is also a w-type CEB with a mass ratio of q=2.77 and an orbital inclination of i= 79°.*** on all available times of light minimum,their orbital period changes are studied by using the O-C *** O-C diagram of LX Lyn reveals a cyclic oscillation with a period of about 14.84 yr and an amplitude of 0.0019 days,which can be explained by the light-travel time effect(LTTE) due to the presence of a third body with a minimum mass of0.06M_⊙.For V0853 Aur,it is discovered that the O-C diagram of the system also shows a cyclic oscillation with a period of 9.64 yr and an amplitude of 0.03365 *** cyclic oscillation of V0853 Aur can be attributed to the LTTE by means of a third body with a mass no less than 3.77M_⊙.The third body may play an important role in the formation and evolution of these systems.

关键词： stars:activity (stars:)binaries(including multiple):close (stars:)binaries:eclipsing (stars:)brown dwarfs stars:evolution stars:formation

Research on key technologies of UAV cluster cooperative system for Internet of Things applications

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Journal of Control and Decision 2024年第1期11卷 26-35页

作者： xu Jing Xi’an International University Xi’anPeople’s Republic of China

The combat tasks faced by UAVs are becoming more and more *** single UAVs are limited by the constraints of platform load capacity,lightweight load,and insufficient lowpower equipment,so it is difficult to complete complex tasks *** at typical UAV collaborative confrontation application scenarios,this paper constructs a multi-agentoriented cluster collaborative intelligent system architecture and establishes a swarm-oriented intelligent UAV cluster collaborative control ***,this paper forms a simulation environment for UAV cluster collaborative confrontation and completes the design and implementation of the UAV cluster collaborative confrontation system based on swarm *** addition,this paper analyses the key technologies of the UAV cluster collaborative system with the support of the Internet of Things technology and verifies the performance of the system after constructing the corresponding *** experimental results show that the system constructed in this paper is effective.

关键词： Internet of Things UAV cluster collaborative control key technology

A novel rapid cooling assembly design in a high-pressure cubic press apparatus

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Matter and Radiation at Extremes 2024年第2期9卷 98-104页

作者： Peiyan wu yongjiang xu yanhao Lin Center for High Pressure Science and Technology Advanced Research Beijing 100193People’s Republic of China School of Earth Sciences and Resources China University of GeosciencesBeijing 100083People’s Republic of China

In traditional high-pressure–temperature assembly design, priority has been given to temperature insulation and retention at high *** limits the efficiency of cooling of samples at the end of experiments, with a negative impact on many studies in high-pressure Earth andplanetary science. Inefficient cooling of experiments containing molten phases at high temperature leads to the formation of quench textures,which makes it impossible to quantify key compositional parameters of the original molten phase, such as their volatile contents. Here,we present a new low-cost experimental assembly for rapid cooling in a six-anvil cubic press. This assembly not only retains high heatingefficiency and thermal insulation, but also enables a very high cooling rate (∼600 ℃/s from 1900 ℃ to the glass transition temperature).without using expensive materials or external modification of the press, the cooling rate in an assembly (∼600 ℃/s) with cube lengths of38.5 mm is about ten times faster than that in the traditional assembly (∼60 ℃/s). Experiments yielding inhomogeneous quenched melttextures when the traditional assembly is used are shown to yield homogeneous silicate glass without quench textures when the rapid coolingassembly is used.

关键词： cubic insulation apparatus

A Methodology for Assessing Axial Compressor Stability with Inlet Temperature Ramp Distortion

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Journal of Thermal Science 2024年第3期33卷 856-871页

作者： SUN Dakun GU Benhao NING Fangfei FANG yibo DONG xu xu Dengke SUN Xiaofeng School of Energy and Power Engineering Beihang UniversityBeijing102206China Research Institute of Aero-engine Beihang UniversityBeijing102206China

Based on a small perturbation stability model for periodic flow,the effects of inlet total temperature ramp distortion on the axial compressor are investigated and the compressor stability is quantitatively *** the beginning,a small perturbation stability model for the periodic flow in compressors is proposed,referring to the governing equations of the Harmonic Balance *** stability model is validated on a single-stage low-speed compressor TA36 with uniform inlet ***,the unsteady flow of TA36 with different inlet total temperature ramps and constant back pressure is simulated based on the Harmonic Balance *** on these simulations,the compressor stability is analyzed using the proposed small perturbation ***,the Dynamic Mode Decomposition method is employed to accurately extract pressure *** two parameters of the temperature ramp,ramp rate and Strouhal number,are discussed in this *** results indicate the occurrence and extension of hysteresis loops in the rows,and a decrease in compressor stability with increasing ramp *** performance is divided into two phases,stable and limit,based on the ramp ***,the model predictions suggest that a decrease in period length and an increase in Strouhal number lead to improved compressor *** DMD results imply that for compressors with inlet temperature ramp distortion,the increase of high-order modes and oscillations at the rotor tip is always the signal of decreasing stability.

关键词： axial compressor stability small perturbation model inlet temperature ramp distortion harmonic balance method dynamic mode decomposition method

The symmetric space,strong isotropy irreducibility and equigeodesic properties

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Science China Mathematics 2024年第1期67卷 129-148页

作者： Ming xu Ju Tan School of Mathematical Sciences Capital Normal UniversityBeijing 100048China School of Microelectronics and Data Science Anhui University of TechnologyMa'anshan 243032China

A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian *** homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=*** two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic *** prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,***,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible ***,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact *** results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic *** an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are *** suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

关键词： equigeodesic equigeodesic space flag manifold orbit type stratification symmetric space strongly isotropy irreducible space

Total synthesis of a putative yuzurimine-type Daphniphyllum alkaloid C_(14)–epi-deoxycalyciphylline H

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Chinese Chemical Letters 2024年第4期35卷 336-339页

作者： Jingping Hu Jing xu Shenzhen Grubbs Institute and Department of Chemistry and Guangdong Provincial Key Laboratory of Catalysis and Shenzhen Key Laboratory of Small Molecule Drug Discovery and Synthesis Southern University of Science and TechnologyShenzhen 518055China

One of the largest subfamilies within the famous Daphniphyllum alkaloid family is made up of the yuzurimine-type(or macrodaphniphyllamine-type) alkaloids. Their complex aza-polycyclic caged structures, several contiguous stereogenic centers, and vicinal all-carbon quaternary centers make these alkaloids formidable challenge for synthetic chemists. Recently, synthesis of these alkaloids has received extensive attention from our community. Herein, we wish to report the total synthesis of C_(14)–epideoxycalyciphylline H, a putative member of yuzurimine-type alkaloid subfamily. Key transformations employed in our approach include an intramolecular Prins reaction and a Pd-catalyzed enyne cycloisomerization. In addition, synthesis of a daphnezomine L-type alkaloid, paxdaphnidine A, was also studied.

关键词： Total synthesis Daphniphyllum alkaloids yuzurimine-type alkaloids Prins reaction Enyne cycloisomerization