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On Leray's problem in an infinitely long pipe with the Navier-slip boundary condition

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science China mathematics 2024年第4期67卷 819-854页

作者： Zijin Li Xinghong Pan Jiaqi Yang school of mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China school of mathematics and Key Laboratory of Ministry of Industry and Information Technology Nanjing University of Aeronautics and AstronauticsNanjing 211106China school of mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710129China

The original Leray’s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe,which approach the Poiseuille flow subject to the no-slip boundary condition at spatial *** this paper,the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition,is *** to the complexity of the boundary condition,some new ideas,presented as follows,are introduced to handle the extra difficulties caused by boundary ***,the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced,which will serve as the asymptotic profile of the solution to the generalized Leray’s problem at spatial ***,a solenoidal vector function defined in the whole pipe,satisfying the Navierslip boundary condition,having the designated flux and equalling the Poiseuille flow at a large distance,will be carefully *** plays an important role in reformulating our ***,the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity.

关键词： stationary Navier-Stokes system Navier-slip boundary condition Leray's problem

MAG molten pool edge detection algorithm based on a fusion of dark channel prior dehazing and image enhancement

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Optoelectronics Letters 2024年第10期20卷 607-613页

作者： LIU Weipeng QU Zepeng GONG Xiangrui WANG Yuheng ZHOU Zhengkui school of Electrical Engineering Hebei University of Technology school of Artificial Intelligence and data science Hebei University of Technology

Metal active gas(MAG) welding is one of the widely applied welding techniques using argon and carbon dioxide as shielding gas. In response to the problem of welding halo and drag shadow during the image acquisition process of it, which makes it difficult to accurately extract the contour of the molten pool, this paper proposes a molten pool edge detection method that combines dark channel prior dehazing(DCPD) and improved single scale Retinex image enhancement algorithm. This method overcomes the problem of excessive edge noise in the original molten pool image and the difficulty in feature extraction caused by the dark part of the molten pool after DCPD processing. Through comparative experiments and ablation experiments, it has been shown that the algorithm proposed in this paper has significantly improved the enhancement effect and feature extraction effect, extracting accurate and complete molten pool contours.

关键词： A

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

CONSERVATIVE CONFORMING AND NONCONFORMING VEMS FOR FOURTH ORDER NONLINEAR SCHRODINGER EQUATIONS WITH TRAPPED TERM

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Journal of Computational mathematics 2024年第2期42卷 454-499页

作者： Meng Li Jikun Zhao Zhongchi Wang Shaochun Chen school of mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China school of Computer science and Engineering Beihang universityBeijing 100083China

This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped *** mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual *** fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in *** prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete *** introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and ***,two numerical examples are investigated to confirm our theoretical analysis.

关键词： H^(2)conforming virtual element C^(0)nonconforming virtual element Morleytype nonconforming virtual element Nonlinear Schrodinger equation Conservation Convergence

Convergence analysis for complementary-label learning with kernel ridge regression

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Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 533-544页

作者： NIE Wei-lin WANG Cheng XIE Zhong-hua school of mathematics and Statistics Huizhou UniversityHuizhou 516007China school of Computer science and Engineering Huizhou UniversityHuizhou 516007China

Complementary-label learning(CLL)aims at finding a classifier via samples with complementary *** data is considered to contain less information than ordinary-label *** transition matrix between the true label and the complementary label,and some loss functions have been developed to handle this *** this paper,we show that CLL can be transformed into ordinary classification under some mild conditions,which indicates that the complementary labels can supply enough information in most *** an example,an extensive misclassification error analysis was performed for the Kernel Ridge Regression(KRR)method applied to multiple complementary-label learning(MCLL),which demonstrates its superior performance compared to existing approaches.

关键词： multiple complementary-label learning partial label learning error analysis reproducing kernel Hilbert spaces

Uniqueness of the Reissner-Nordstrom metric near the null infinity

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science China mathematics 2024年第8期67卷 1933-1956页

作者： Xiaokai He Xiaoning Wu Naqing Xie school of mathematics and Statistics Hunan First Normal UniversityChangsha 410205China Institute of mathematics Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China school of Mathematical sciences Fudan UniversityShanghai 200433China

In the Newman-Penrose formalism,we prove that the Reissner-Nordstrom metric is the only asymptotically fat,static,axially symmetric,Petrov type-D analytic solution of the electro-vacuum Einstein-Maxwell equations near... 详细信息

关键词： uniqueness theorem Reissner-Nordstrom metric Newman-Penrose formalism

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

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Acta Mathematica Scientia 2024年第4期44卷 1271-1279页

作者： Jiangen LIU Fazhan GENG school of mathematics and Statistics Changshu Institute of TechnologyChangshu 215500China Qin Institute of mathematics Shanghai Hanjing Centre for Science and TechnologyShanghai 201609China

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical *** this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral ***,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional ***,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville ***,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,*** terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

关键词： k-Prabhakar fractional operator Caputo-Fabrizio operator Atangana-Baleanu operator Sun-Hao-Zhang-Baleanu operator generalized Caputo type operator

STDNet: A Spatio-Temporal Decomposition Neural Network for Multivariate Time Series Forecasting

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Tsinghua science and Technology 2024年第4期29卷 1232-1247页

作者： Zhuolun Jiang Zefei Ning Hao Miao Li Wang College of Computer science and Technology(College of data science) Taiyuan University of TechnologyJinzhong 030600China

Long-term multivariate time series forecasting is an important task in engineering applications. It helps grasp the future development trend of data in real-time, which is of great significance for a wide variety of fields. Due to the non-linear and unstable characteristics of multivariate time series, the existing methods encounter difficulties in analyzing complex high-dimensional data and capturing latent relationships between multivariates in time series, thus affecting the performance of long-term prediction. In this paper, we propose a novel time series forecasting model based on multilayer perceptron that combines spatio-temporal decomposition and doubly residual stacking, namely Spatio-Temporal Decomposition Neural Network (STDNet). We decompose the originally complex and unstable time series into two parts, temporal term and spatial term. We design temporal module based on auto-correlation mechanism to discover temporal dependencies at the sub-series level, and spatial module based on convolutional neural network and self-attention mechanism to integrate multivariate information from two dimensions, global and local, respectively. Then we integrate the results obtained from the different modules to get the final forecast. Extensive experiments on four real-world datasets show that STDNet significantly outperforms other state-of-the-art methods, which provides an effective solution for long-term time series forecasting.

关键词： time series forecasting multivariate time series spatio-temporal decomposition

Blockchain-based immunization against kleptographic attacks

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science China(Information sciences) 2024年第7期67卷 172-183页

作者： Changsong JIANG Chunxiang XU Jie CHEN Kefei CHEN school of Computer science and Engineering University of Electronic Science and Technology of China Yangtze Delta Region Institute (Huzhou) University of Electronic Science and Technology of China Department of mathematics Hangzhou Normal University

Adversarial implementations of cryptographic primitives called kleptographic attacks cause the leakage of secret information. Subliminal channel attacks are one of the kleptographic attacks. In such attacks, backdoors are embedded in implementations of randomized algorithms to elaborately control randomness generation, such that the secrets will be leaked from biased outputs. To thwart subliminal channel attacks, double-splitting is a feasible solution, which splits the randomness generator of a randomized algorithm into two independent generators. In this paper, we instantiate double-splitting to propose a secure randomness generation algorithm dubbed SRG using two physically independent generators: ordinary and public randomness generators. Based on public blockchains, we construct the public randomness generator,which can be verified publicly. Hashes of a sufficient number of consecutive blocks that are newly confirmed on a blockchain are used to produce public randomness. In SRG, outputs from the two generators are taken as inputs of an immunization function. SRG accomplishes immunization against subliminal channel ***, we discuss the application strategies of SRG for symmetric and public-key encryption.

关键词： kleptographic attacks subliminal channel blockchain immunization randomized algorithm