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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

Distributed Stochastic Optimization with Compression for Non-Strongly Convex Objectives

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Computer Modeling in Engineering & Sciences 2024年第4期139卷 459-481页

作者： xuanjie Li Yuedong xu School of Information Science and Technology Fudan UniversityShanghaiChina

We are investigating the distributed optimization problem,where a network of nodes works together to minimize a global objective that is a finite sum of their stored local *** nodes exchange optimization parameters through the wireless network,large-scale training models can create communication bottlenecks,resulting in slower training *** address this issue,CHOCO-SGD was proposed,which allows compressing information with arbitrary precision without reducing the convergence rate for strongly convex objective ***,most convex functions are not strongly convex(such as logistic regression or Lasso),which raises the question of whether this algorithm can be applied to non-strongly convex *** this paper,we provide the first theoretical analysis of the convergence rate of CHOCO-SGD on non-strongly convex *** derive a sufficient condition,which limits the fidelity of compression,to guarantee ***,our analysis demonstrates that within the fidelity threshold,this algorithm can significantly reduce transmission burden while maintaining the same convergence rate order as its no-compression *** experiments further validate the theoretical findings by demonstrating that CHOCO-SGD improves communication efficiency and keeps the same convergence rate order *** experiments also show that the algorithm fails to converge with low compression fidelity and in time-varying ***,our study offers valuable insights into the potential applicability of CHOCO-SGD for non-strongly convex ***,we provide practical guidelines for researchers seeking to utilize this algorithm in real-world scenarios.

关键词： Distributed stochastic optimization arbitrary compression fidelity non-strongly convex objective function

The fate of eclogites in the lithosphere

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Science China Earth Sciences 2024年第3期67卷 879-884页

作者： Zhensheng WANG Yixian xu State Key Laboratory of Geological Processes and Mineral Resources China University of GeosciencesWuhan 430074China Key Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province School of Earth SciencesZhejiang UniversityHangzhou 310058China

1. Eclogites and the concept of viscous drainage Eclogites are a distinctive rock type, mainly composed of garnet and omphacite and formed through ultra-high-pressure metamorphism, wherein oceanic or continental crust... 详细信息

关键词： crustal garnet rock

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Millimeter-wave PA design techniques in ISSCC 2024

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Journal of Semiconductors 2024年第4期45卷 16-18页

作者： Yun Wang Hongtao xu State Key Laboratory of Integrated Chips and Systems School of MicroelectronicsFudan UniversityShanghai 201203China

Millimeter-wave systems with high integration level have been rapidly developed to enable modern wireless communication,sensing,and *** millimeter-wave power amplifier(PA)is one of the most challenging and critical components in a millimeter-wave transceiver,it is the last active stage in a transmitter amplifying spectrally efficient complex modulation signal for radiation with high output power.

关键词： millimeter Millimeter ISSCC

Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

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Computer Modeling in Engineering & Sciences 2024年第4期139卷 515-536页

作者： Cheng Han Zhengguang xu School of Automation and Electrical Engineering University of Science and Technology BeijingBeijing100083China Key Laboratory of Knowledge Automation for Industrial Processes University of Science and Technology BeijingBeijing100083China

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems,assuming that the system satisfies the generalized Lipschitz *** a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics,the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables,which poses difficulties in predicting and estimating the system’s *** this article,the temporal variation of the system is described by constructing pattern category variables,which are non-deterministic *** pattern category variables have statistical attributes but not operational attributes,operational attributes are assigned to them by posterior probability density,and a method for analyzing their motion laws using probability density evolution is ***,a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative(PPD),achieving prediction of the probability density satisfying the system’s output *** on this,the final prediction estimation of the system’s output value is realized by minimum variance unbiased ***,a corresponding PPD estimation algorithm is designed using an extended state observer(ESO)to estimate the parameters to be estimated in the proposed prediction *** effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis,and the accuracy of the algorithm is verified by two numerical simulation examples.

关键词： Non-newtonian mechanical systems prediction and estimation pattern moving probability density evolution pseudo partial derivative

Scattering for the Radial Schrodinger Equation with Combined Power-type and Choquard-type Nonlinearities

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1029-1041页

作者： Ying WANG Cheng Bin xu The Graduate School of China Academy of Engineering Physics Beijing 100088P.R.China School of Mathematics and Statistics Qinghai Normal UniversityXining 810008P.R.China

In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)*** the energy space H^(1)(R^(N))forλ_(1)λ_(2)=-*** establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering *** show that the defocusing perturbation terms does not determine the scattering solution in energy space.

关键词： Schrodinger equation Choquard-type Scattering theory

Phonon-blockade-based multiple-photon bundle emission in a quadratically coupled optomechanical system

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Frontiers of physics 2024年第3期19卷 207-215页

作者： Ye-Jun xu Hong Xie Interdisciplinary Research Center of Quantum and Photoelectric Information Chizhou UniversityChizhou 247000China Department of Mathematics and Physics Fujian Jiangxia UniversityFuzhou 350108China

We propose a scheme to realize antibunched multiple-photon bundles based on phonon blockade in a quadratically coupled optomechanical *** adjusting the detunings to match the conditions of phonon blockade in the photon sidebands,we establish super-Rabi oscillation between zero-photon state and multiple-photon states with adjustable super-Rabi frequencies under appropriate single-phonon resonant *** the system dissipation into account,we numerically calculate the standard and generalized second-order functions of the cavity mode as well as the quantum trajectories of the state populations with Monte Carlo simulation to confirm that the emitted photons form antibunched multiple-photon ***,the desirable n-photon states are reconstructed after a direct phonon emission based on phonon blockade,and thus the single-phonon emission heralds the cascade emission of n-photon *** proposal shows that the optomechanical system can simultaneously behave as antibunched multiple-photon emitter and single-phonon *** a nonclassical source could have potential applications in quantum information science.

关键词： multiple-photon bundle emission phonon blockade optomechanical system

(Lu_(1/7)Yb_(1/7)Sc_(1/7)Er_(1/7)Y_(1/7)Ho_(1/7)Dy_(1/7))_(2)Si_(2)O_(7)high entropy rare-earth disilicate with low thermal conductivity and excellent resistance to CMAS corrosion

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Journal of Advanced Ceramics 2024年第5期13卷 549-560页

作者： xu Wang Mingyu Meng Feihan xu Ling Liu Lihong Gao Shizhen Zhu Zhuang Ma School of Materials Science and Engineering Beijing Institute of TechnologyBeijing 100081China National Key Laboratory of Science and Technology on Materials under Shock and Impact Beijing 100081China Tangshan Research Institute Beijing Institute of TechnologyTangshan 063000China

Low thermal conductivity,compatible thermal expansion coefficient,and good calcium–magnesium–aluminosilicate(CMAS)corrosion resistance are critical requirements for environmental barrier coatings used on silicon-based ***2Si2O7(RE=rare earth)has been widely recognized as one of the most promising candidates for environmental barrier coatings due to its good water vapor corrosion ***,the relatively high thermal conductivity and poor resistance to CMAS corrosion have limited its practical *** by the high entropy effect,in this work,a novel rare earth disilicate(Lu_(_(1/7))Yb_(_(1/7))Sc_(_(1/7))Er_(_(1/7))Y_(_(1/7))Ho_(_(1/7))Dy_(_(1/7)))2Si2O7((7RE_(_(1/7)))2Si2O7)has been designed and synthesized by a solid reaction process.(7RE_(_(1/7)))2Si2O7 showed a low thermal conductivity of 1.81 W·m^(−1)·K^(−1)at 1273 ***,the thermal expansion coefficient of(7RE_(_(1/7)))_(2)Si_(2)O_(7)(4.07×10^(−6)℃^(−1)from room temperature(RT)to 1400℃)is close to that of the SiC-based ceramic matrix composites(SiC-CMCs)((4.5–5.5)×10^(−6)℃^(−1)).Additionally,(7RE_(_(1/7)))2Si2O7 exhibited excellent resistance to CMAS *** exposed to CMAS at 1300℃for 48 h,the reaction layer thickness was 22μ*** improved performance of(7RE_(_(1/7)))2Si2O7 highlights its potential as a promising candidate for thermal/environmental barrier coatings.

关键词： high entropy disilicate (Lu_(1/7)Yb_(1/7)Sc_(1/7)Er_(1/7)Y_(1/7)Ho_(1/7)Dy_(1/7))_(2)Si_(2)O_(7)((7RE_(1/7))_(2)Si_(2)O_(7)) high-temperature thermal properties calcium-magnesium-aluminosilicate(CMAS)corrosion

Boundary Behaviors for a Continuous-state Nonlinear Neveu’s Branching Process

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Acta Mathematica Sinica,English Series 2024年第8期40卷 2005-2016页

作者： Lin Yu BAI xu YANG School of Mathematics and Information Science North Minzu UniversityYinchuan 750021P.R.China

By generalizing a criterion of Mufa Chen for Markov jump processes,we establish the necessary and sufficient conditions for the extinction,explosion and coming down from infinity of a continuous-state nonlinear Neveu... 详细信息

关键词： Continuous-state branching process nonlinear branching Neveu’s branching extinction explosion coming down from infinity