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World Journal of Clinical Cases 2025年第3期13卷 42-49页

作者： Na li Yue-Yue Ren Ying Tang Qi Yang Tian-Tian Meng song li Jing Zhang Stomatological Hospital and College Anhui Medical UniversityHefei 230032Anhui ProvinceChina Department of Endodontics The Affiliated Stomatological Hospital of Xuzhou Medical UniversityXuzhou 221000Jiangsu ProvinceChina

BACKGROUND Complicated crown–root fracture (CRF) involves severe injury to the crown, root,and pulp, and may be accompanied by multiple root fractures. The loss of a toothhas lifelong consequences for children and teenagers, but the maintenance of pulphealth and the calcific healing of multiple root fractures are rarely reported in *** SUMMARY This case reports healing of a permanent tooth with complicated crown–root andadditional root fractures, in which pulp health was maintained. A 10-year-old girlfell and fractured the root of her maxillary left central incisor at the cervical *** the coronal fragment was repositioned, the tooth was splinted until thetooth was no longer mobile, 2 years later. Eight years after treatment, the toothhas remained asymptomatic with vital pulp and localized gingival ***-beam computed tomography revealed not only calcified healing of the CRFbut also spontaneous healing in an additional undiagnosed root fracture. Thefracture line on the enamel could not be healed by hard tissue and formed agroove in the cervical crown. It was speculated that the groove was related to thelocalized gingival *** This case provides a clinical perspective of the treatment of a tooth with acomplicated CRF and an additional root fracture.

关键词： Complicated crown-root fracture Multiple root fracture Spontaneous healing Cone-beam computed tomography Long-term follow-up Case report

Multivariate Refinement Equations and Convergence of Cascade Algorithms in L_(p)(0

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Acta Mathematica Sinica,English Series 2003年第1期19卷 97-106页

作者： song li Department of Mathematices Zhejiang UniversityHangzhou 310027P.R.China Institute of Mathematics Academy of Mathematics and System sciencesChinese Academy of SciencesBeijing 100080P.R.China

We consider the solutions of refinement equations written in the form$$\varphi \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi \left( {Mx - \alpha } \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$where the vector of functions } = (}1, ..., }r)T is unknown, g is a given vector of compactly supported functions on A^s, a is a finitely supported sequence of r 2 r matrices called the refinement mask, and M is an s 2 s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence }n, n = 1, 2, ..., by the iterative process$$\varphi _n \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi _{n - 1} \left(Mx - \alpha \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$from a starting vector of function }0. We characterize the Lp-convergence (0 linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation.

关键词： Inhomogeneous refinement equation Joint spectral radius Cascade algorithm L_(p)(R^(s))(0

1-planar Graphs without 4-cycles or 5-cycles are 5-colorable

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 169-177页

作者： li-li song Lei SUN Department of Mathematics and Statistics Shandong Normal UniversityJinan 250358China

A graph is 1-planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge.A proper vertex k-coloring of a graph G is defined as a vertex coloring from a set of k colors such that no two adjacent vertices have the same color.A graph that can be assigned a proper k-coloring is k-colorable.A cycle is a path of edges and vertices wherein a vertex is reachable from itself.A cycle contains k vertices and k edges is a *** this paper,it is proved that 1-planar graphs without 4-cycles or 5-cycles are 5-colorable.

关键词： 1-planar colorable discharging vertices faces

Phase retrieval with Phaselift algorithm

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Applied Mathematics(A Journal of Chinese Universities) 2020年第4期35卷 479-502页

作者： li Hui-ping li song School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

This paper provides a contemporary overview of phase retrieval problem with Phaselift algorithm and summarizes theoretical results which have been derived during the past few *** on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as ***,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal ***,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.

关键词： phase retrieval Phaselift algorithm random measurements masked Fourier measurements sparsity

Refill Friction Stir Spot Welding of Similar and Dissimilar Alloys:A Review

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Acta Metallurgica Sinica(English Letters) 2020年第1期33卷 30-42页

作者： Xiao-song Feng song-Bin li li-Na Tang Hui-Min Wang Shanghai Aerospace Equipments Manufacturer Co. LtdShanghai 200245China National Center for Materials Service Safety University of Science and TechnologyBeijingBeijing 100083China

Refi ll friction stir spot welding,also known as friction spot welding(FSpW),is a solid-state welding process suitable for spot joining of lightweight *** the eff orts of improving joint quality for similar and dissimilar materials,for example,aluminum and magnesium,this joining technology is well *** joining mechanism and process characteristics of FSpW have been widely ***,the application of FSpW in industry has not been entirely *** this review article,the research of similar and dissimilar material joints,such as,Al/Cu,Al/Ti,Al/Mg and Al/Steel,is *** microstructural features and mechanical properties of the joints,welding tool and the application development are discussed in detail.

关键词： Refill friction stir spot welding Dissimilar joints Microstructure Mechanical properties Welding parameters

Magnetic field annealing of FeCo-based amorphous alloys to enhance thermal stability and Curie temperature

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Rare Metals 2023年第6期42卷 2000-2006页

作者： Zai-Dao li Wei-Wei Zhang Ge-Tian li song-song li Hong-Sheng Ding Tao Zhang Yu-Jun song Center for Modern Physics Technology Department of Applied PhysicsBeijing Key Laboratory for Magneto-Photoelectrical Composite and Interface ScienceUniversity of Science and Technology BeijingBeijing100083China School of Materials Science and Engineering Beihang UniversityBeijing100191China

Annealing temperatures and applied magnetic fields are two important parameters for the performance modification of magnetic *** article investigated the effect of different annealing temperatures on crystallization condition,magnetic properties and thermal stability of the amorphous magnetic alloy Co_(36)Fe_(36)Si_(4.8)B1_(9.2)Nb_(4)(at%).Results indicate that the annealing temperature can significantly affect the size and content of precipitated nanocrystals in the amorphous alloy,and the precipitation of nanocrystalline phases can result in the distinct change of magnetic properties and Curie *** the annealing was performed at 595 ℃ for 30 min under an applied transverse external magnetic field of 9550.0A·m^(-1),the amorphous alloy shows excellent soft magnetic properties with the saturation magnetization of alloy reaching 110.00 mA·m^(2)·g^(-1),the residual magnetic induction intensity of 4 × 10^(-6) T and the coercivity as low as57.3 A·m^(-1).Furthermore,the Curie temperature of the field-annealed samples can reach up to 440 0C,approximately 58℃ higher than that of the as-quenched species.

关键词： Soft magnetic alloys Amorphous alloy Field annealing

Frequency Effect of Harmonic Noise on the FitzHugh–Nagumo Neuron Model

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Chinese Physics Letters 2011年第12期28卷 47-50页

作者： song Yan-li School of Sciences Tianjin UniversityTianjin 300072

Using harmonic noise,the frequency effect of noise on the FitzHugh–Nagumo neuron model is *** results show that the neuron has a resonance characteristic and responds strongly to the noise with a certain frequency at fixed *** by the noise with this frequency,the train is most regular and the coefficient of variation R has a *** imperfect synchronization takes place,which,however,is optimal only for noise with an appropriate *** is shown that there exists coherence resonance related to frequency.

关键词： harmonic Harmonic resonance

Compressed data separation via dual frames based split-analysis with Weibull matrices

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 427-437页

作者： CAI Yun li song Department of Mathematics Zhejiang University

In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.

关键词： Compressed sensing data separation dual frames split-analysis Weibull random matrices

The Support of a Refinable Vector Satisfying an Inhomogeneous Refinement Equation

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Acta Mathematica Sinica,English Series 2010年第4期26卷 691-698页

作者： song li Yi SHEN Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

In this paper, we investigate the support of a refinable vector satisfying an inhomoge- neous refinement equation. By using some methods introduced by So and Wang, an estimate is given for the support of each component function of a compactly supported refinable vector satisfying an inhomogeneous matrix refinement equation with finitely supported masks.

关键词： support inhomogeneous refnement equation refinable vector

Convergence analysis of projected gradient descent for Schatten-p nonconvex matrix recovery

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Science China Mathematics 2015年第4期58卷 845-858页

作者： CAI Yun li song Department of Mathematics Zhejiang University

The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) *** on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.

关键词： low rank matrix recovery nonconvex matrix recovery projected gradient descent restricted isometry property