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Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of systems science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu school of mathematics Statistics and Mechanics Beijing University of Technology Academy of mathematics and systems science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

Semisymmetric Graphs of Order 2p^(3)with Valency p^(2)

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Algebra Colloquium 2024年第2期31卷 199-208页

作者： Li Wang Songtao Guo Genghua Fan school of mathematics and Information science Henan Polytechnic University JiaozuoHenan 454000China school of mathematics and Statistics Henan University of Science and Technology LuoyangHenan 471023China 不详

A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not *** a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal *** complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2).The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2),Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this *** a result,there is only one infinite family of semisymmetric graphs of order 2p^(3)with valency p^(2).

关键词： semisymmetric graph semitransitive graph bi-coset graph

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Stability in Inverse Problem of Determining Two Parameters for the Moore-Gibson-Thompson Equation with Memory Terms

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Journal of systems science & Complexity 2024年

作者： FU Songren CHEN Liangbiao ZHANG Ji-Feng Key Laboratory of systems and Control Academy of Mathematics and Systems Science Chinese Academy ofSciences school of Automation and Electrical Engineering Zhongyuan University of Technology Key Laboratory of systems and Control Academy of Mathematics and Systems Science ChineseAcademy of Sciences

In this paper, the authors consider the inverse problem for the Moore-Gibson-Thompson equation with a memory term and variable diffusivity, which introduce a sort of delay in the dynamics,producing nonlocal effects in time. The H¨older stability of simultaneously determining the spatially varying viscosity coefficient and the source term is obtained by means of the key pointwise Carleman estimate for the Moore-Gibson-Thompson equation. For the sake of generality in mathematical tools,the analysis of this paper is discussed within the framework of Riemannian geometry.

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Quantum correlations in a chain-type quantum network

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Communications in Theoretical Physics 2024年第6期76卷 77-91页

作者： Xiaofei Qi Aihong Zhai Lihua Yang school of Mathematical science Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex systems and Data science of Ministry of Education Shanxi UniversityTaiyuan 030006China school of mathematics and Information Technology Yuncheng UniversityYuncheng 044000China

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some *** this paper,we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameterλ.The expressions of all post-measurement states between any two observers are obtained,and their quantifications of Bell nonlocality,Einstein-Podolsky-Rosen steering and entanglement with different ranges ofλare respectively detected and analyzed.

关键词： quantum correlation nonlocality entanglement chain-type quantum network

One-step hydrothermal synthesis of Cit-NaYbF_(4):Er^(3+)nanocrystals with enhanced red upconversion emission for in vivo fluorescence molecular tomography

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Journal of Rare Earths 2024年第1期42卷 36-45,I0002页

作者： Xiaoli Luo Qichen Chen Hongbo Guo Heng Zhang Xiaowei He Wu Zhao school of mathematics and Computer science Ningxia Normal UniversityGuyuan756099China school of Information science and Technology Northwest UniversityXi'an710127China

Fluorescence imaging techniques represent essential tools in in vitro,preclinical,and clinical *** this study,an improved one-step hydrothermal method to synthesize citric acid(CA)modifiedα-NaYbF_(4):2%Er^(3+)nanocrystals was *** introduction of various doping ions into NaYbF_(4):2%Er^(3+)and the different valence states of the same ions affect both the crystal size and upconversion luminesce *** fore,we investigated the upconversion luminesce nce enha ncement of NaYbF_(4):2%Er^(3+)by ion doping and find that the upconversion luminescence intensity of the upconversion nanoparticles(UCNPs)co-doped with 5 mol%Fe^(2+)ions shows the greatest enhancement,especially for red emission at654 ***,HeLa cells incubated with UCNPs allow for imaging with strong red upconversion emission detectio *** laser scanning microscope(CLSM)fluorescent images of HeLa cells indicate that NaYbF_(4):2%Er/5%Fe^(2+)leads to a clear outline and improves visualization of the cell *** addition,the CA coated NaYbF_(4):2%Er^(3+)/5%Fe^(2+)nanoparticles and NaYbF_(4):2%Er^(3+)/5%Fe^(2+)show low cytotoxicity in HeLa *** imaging reveals the efficiency of these UCNPs to analyze the lungs,liver,and ***,these results indicate that the Cit-NaYbF_(4):2%Er^(3+)/5%Fe^(2+)UCNPs are efficient nanoprobes for fluorescence molecular to mography.

关键词： Hydrothermal method Fe^(2+)ion doping Tuning size Nanoprobes Fluorescence imaging Rare earths

Boundary points, minimal Lintegrals and concavity property Ⅲ—linearity on Riemann surfaces and fibrations over open Riemann surfaces

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Acta Mathematica Sinica,English Series 2024年

作者： Qi'an Guan Zhitong Mi Zheng Yuan school of Mathematical sciences Peking University school of mathematics and Statistics Beijing Jiaotong University Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences

In this article, we consider a modified version of minimal L2integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As applications, we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.

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Boundary points, minimal Lintegrals and concavity property Ⅱ: Weakly pseudoconvex K?hler manifolds

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science China mathematics 2024年

作者： Qi'an Guan Zhitong Mi Zheng Yuan Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences school of mathematics and Statistics Beijing Jiaotong University school of Mathematical sciences Peking University

In this paper, we consider minimal L2integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L2integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

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THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

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Acta Mathematica Scientia 2024年第3期44卷 1115-1144页

作者：杨纪华 school of mathematics and Computer science Ningxia Normal UniversityGuyuan756000China Ningxia Basic science Research Center of mathematics Yinchuan750000China

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=*** upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions ***,the exact bound of a special case is given using the Chebyshev *** the end,some numerical simulations are given to illustrate the existence of limit cycles.

关键词： whirling pendulum limit cycle Melnikov function Picard-Fuchs equation Chebyshev system