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Maximizing the Minimum and Maximum Forcing Numbers of Perfect Matchings of Graphs

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Acta Mathematica Sinica,English Series 2023年第7期39卷 1289-1304页

作者： qian qian liu He Ping ZHANG School of Mathematics and Statistics Lanzhou UniversityLanzhou 730000China

Let G be a simple graph with 2n vertices and a perfect *** forcing number f(G,M) of a perfect matching M of G is the smallest cardinality of a subset of M that is contained in no other perfect matching of *** all perfect matchings M of G,the minimum and maximum values of f(G,M) are called the minimum and maximum forcing numbers of G,denoted by f(G) and F(G),*** f(G)≤F(G) ≤*** and Chen(2011) proposed an open problem:how to characterize the graphs G with f(G)=*** they showed that for a bipartite graph G,f(G)=n-1 if and only if G is complete bipartite graph K_(n,n).In this paper,we completely solve the problem of Che and Chen,and show that f(G)=n-1 if and only if G is a complete multipartite graph or a graph obtained from complete bipartite graph K_(n,n) by adding arbitrary edges in one partite *** all graphs G with F(G)=n-1,we prove that the forcing spectrum of each such graph G forms an integer interval by matching 2-switches and the minimum forcing numbers of all such graphs G form an integer interval from [n/2] to n-1.

关键词： Perfect matching minimum forcing number maximum forcing number forcing spectrum complete multipartite graph

Low Valent Palladium Clusters: Synthesis, Structures and Catalytic Applications

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Chinese Journal of Chemistry 2020年第12期38卷 1897-1908页

作者： qian liu Liang Zhao Kkey laboratory of Bioorganic Phosphorus Chemistry&Chemical Biology Department of ChemistryTsinghua UniversityBeijing 100084China

Ay one of the most common transition metal catalysts,mononuclear palladium catalysts have been develped systematcally and a widely recognizedcatalytic mechanism featured with a pd/Pd catalytic cycle for a palladium center has been ***,recent research works have revealed thatpalladium clusters may also be catalysts or catalyti intermediates involved in the catalytic *** major discovery brings new perspectives for adeep and comprehensive understanding of the PRd-catalyzed reaction *** with the latest advances in the field of organometllicchemistry,we here highlight the synthesis,structures,and catalytic reactivities of palladium custer *** reviw discusses severalwel-defined syntheticstrategies and diversepalladum cluster-based catalytic systems in detail,to provide insights into the rational design of promisingpalladium cluster catalysts and the effective search for appropriate synthetic methods.

关键词： palladium catalytic cluster

Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 253-262页

作者： Yan liu Min-qian liu School of Mathematical Sciences Tianjin Normal University Department of Statistics School of Mathematical Sciences and LPMC Nankai University

Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.

关键词： balanced design coincidence number complementary design equidistant design weak equidistantdesign

Isentropic Analysis of Regional Cold Events over Northern China

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Advances in Atmospheric Sciences 2020年第7期37卷 718-734页

作者： Qingyi liu qian liu Guixing CHEN School of Atmospheric Sciences and Guangdong Province Key Laboratory for Climate Change and Natural Disaster StudiesSun Yat-sen Universityand Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)Zhuhai 519082China

From the perspective of cold air mass(CAM)analysis,we examine the characteristics and mechanisms of regional cold events(RCEs)over northwestern and northeastern China in the past 58 years(1958/59-2015/16).The RCEs in northwestern(northeastern)China are shown to have an average duration of 6.8(4.7)days with a moderate(sharp)temperature *** quantitatively estimate the RCE-related CAM,for the first time,using an isentropic analysis *** an RCE in northwestern China,CAM is accumulated in western Siberia with convergent CAM flux under a blocking pattern in the Urals *** RCE outbreak,CAM penetrates the valleys of the Tianshan-Altay Mountains to the Tarim Basin and Hexi *** CAM moves slowly because of the blocking pattern and orographic effect,which explains the relatively long duration of ***,during RCEs in northeastern China,the CAM depth anomaly originates more to the east and quickly passes the Mongolian Plateau guided by an eastward-moving *** analyses further show that adiabatic processes play a crucial role in regulating the local change of CAM depth during the two kinds of *** advection term of adiabatic processes mainly increases the CAM depth during RCE outbreak,while the convergence term increases(reduces)CAM depth before(after)RCE *** terms are relatively strong during RCEs in northeastern China,resulting in the rate of change in CAM depth being^50%larger than for those in northwestern ***,the variations of RCEs in duration and intensity can be well explained by the different evolution of CAM depth and flux.

关键词： China. northwestern northeastern

Relationship Between Microstructures and Microhardness in High-Speed Friction Stir Welding of AA6005A-T6 Aluminum Hollow Extrusions

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Acta Metallurgica Sinica(English Letters) 2020年第1期33卷 115-126页

作者： Xiang-qian liu Hui-Jie liu Yan Yu Luoyang Ship Material Research Institute Luoyang 471023China State Key Laboratory of Advanced Welding and Joining Harbin Institute of TechnologyHarbin 150001China

AA6005 A-T6 aluminum hollow extrusions were friction stir welded at a fixed high welding speed of 2000 mm/min and various rotation *** results showed that the heat-aff ected zone(HAZ)retained the similar grain structure as the base material except some grain coarsening,and the density of dislocations andβ′precipitates were almost unchanged,indicating that the high welding speed inhibited the coarsening and dissolution ofβ″precipitates via fast cooling *** thermo-mechanically aff ected zone(TMAZ)was characterized by elongated and rotated grains,in which a low density ofβ′precipitates and the highest density of dislocations were *** highest heat input and severest plastic deformation occurring in the nugget zone(NZ)resulted in the occurrence of dynamic recrystallization and a high density of ***,all theβ″precipitates and most of theβ′precipitates dissolved into the matrix,and a fewβ′precipitates were transformed intoβ*** microhardness was controlled by the precipitation and solution strengthening in the HAZ,by the dislocation and precipitation strengthening in the TMAZ,and by the fine-grain and dislocation strengthening in the *** the increase in rotation speed,the peak and the lowest microhardness value increased monotonously.

关键词： Aluminum hollow extrusions High-speed friction stir welding Grain structure Dislocation and precipitates Microhardness distribution

Asymptotic properties of distributed social sampling algorithm

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Science China(Information Sciences) 2020年第1期63卷 152-166页

作者： qian liu Xingkang HE Haitao FANG The Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences ACCESS Linnaeus Centre School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technology

Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of social opinions at initial time, and it collaborates with other agents in a distributed manner to estimate the initial empirical distribution by randomly sampling a message from current distribution estimate. In this paper, we focus on analyzing the theoretical properties of the distributed social sampling algorithm over random networks. First, we provide a framework based on stochastic approximation to study the asymptotic properties of the algorithm. Then, under mild conditions, we prove that the estimates of all agents converge to a common random distribution, which is composed of the initial empirical distribution and the accumulation of quantized error. Besides, by tuning algorithm parameters, we prove the strong consistency, namely, the distribution estimates of agents almost surely converge to the initial empirical distribution. Furthermore, the asymptotic normality of estimation error generated by distributed social sample algorithm is addressed. Finally, we provide a numerical simulation to validate the theoretical results of this paper.

关键词： social networks opinion formation social sampling stochastic approximation random networks asymptotic normality

扬子板块西南缘早前寒武纪地质演化:来自撮科元古宙变沉积岩碎屑锆石U-Pb年龄、Hf-O同位素的制约

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岩石学报 2025年第1期41卷 304-320页

作者：高嘉敏谢士稳刘倩王舫陶鹏龙涛中国地质大学(北京)地球科学与资源学院北京100083 中国地质科学院地质研究所北京离子探针中心北京100037 山东省第四地质矿产勘查院潍坊261021

扬子板块的太古宙-古元古代基底出露十分有限,制约了对扬子早前寒武纪地质演化的认识。本次研究对扬子板块西南缘撮科地区的大红山群和昆阳群变沉积岩开展了碎屑锆石原位U-Pb年龄、Hf-O同位素及微量元素研究。测年结果显示,大红山群谐... 详细信息

扬子板块的太古宙-古元古代基底出露十分有限,制约了对扬子早前寒武纪地质演化的认识。本次研究对扬子板块西南缘撮科地区的大红山群和昆阳群变沉积岩开展了碎屑锆石原位U-Pb年龄、Hf-O同位素及微量元素研究。测年结果显示,大红山群谐和锆石年龄分布于3092~1786Ma之间,最年轻碎屑锆石年龄为1786Ma,限定大红山群最大沉积时代为古元古代晚期。昆阳群谐和锆石年龄分布于2874~1031Ma之间,最年轻碎屑锆石年龄为1031Ma,表明昆阳群最大沉积时代为中元古代晚期。除少量较年轻锆石(<1.75Ga)外,昆阳群和大红山群具有相似的年龄分布特征,两个主要的年龄峰为2.0~1.85Ga和2.4~2.2Ga。尽管古元古代碎屑锆石的年龄峰与撮科地区已报道的古元古代岩浆活动期次一致,但仅有少部分碎屑锆石的Hf-O同位素特征与撮科古元古代岩浆岩相似,大多数碎屑锆石Hf-O同位素组成与加拿大Rae克拉通古元古代变沉积岩中碎屑锆石相似,暗示古元古代碎屑物质可能仅少部分来自撮科地区已识别的古元古代岩浆岩,而大部分可能来自与Rae克拉通发育的古元古岩浆岩相似的源区。大红山群和昆阳群中1.9~1.03Ga的碎屑锆石可能来自扬子西南缘发育的古元古代晚期-中元古代晚期岩浆岩。结合前人的资料,我们认为我国撮科和越南北部的Phan Si Pan带经历了与加拿大Rae克拉通相似的古元古代演化过程,支持2.4~2.3Ga扬子西南缘卷入Arrowsmith造山事件,并与Rae克拉通一起参与哥伦比亚超大陆聚合过程的认识。

关键词：扬子西南缘撮科地区哥伦比亚超大陆大红山群和昆阳群碎屑锆石

Single image haze removal via depth-based contrast stretching transform

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Science China(Information Sciences) 2015年第1期58卷 56-72页

作者： liu qian CHEN MaoYin ZHOU DongHua Department of Automation Tsinghua National Laboratory for Information Science and TechnologyTsinghua University

Under the weather of haze, fog, or smoke, outdoor images show poor visibility and low *** contrast results in the difficulty for carrying out basic local feature(e.g., interest points and edges) detection algorithms, which are necessary procedures in some computer vision applications. Hence, increasing contrast of degraded images is very important since it is helpful in finding more distinct features from haze ***, few single image haze removal methods can simultaneously achieve clear visibility, sufficiently high contrast, and simplicity. In this paper, we propose an intuitive and effective method, called the depth-based contrast stretching transform(DCST), to simultaneously obtain clear visibility and enhance contrast of a single haze gray image. The DCST stretches the contrast of haze images based on the coarse depth layers of *** method is simple and almost real time and can be extended to color images. We analyze in detail that the image stretched by the DCST has a higher local contrast than the image recovered via the physical-based *** demonstrate that images stretched by the DCST have excellent visibility and contrast compared with a few existing algorithms. Compelling performance is also presented by comparing the proposed method with other representative methods in the application of local feature detection.

关键词： image dehazing image defogging image enhancement image restoration local features detection

Effect of Coarse Aggregate Size on and Crack Opening in Normal and Relationship between Stress High Strength Concretes

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Journal of Materials Science & Technology 2005年第5期21卷 691-700页

作者： Jun ZHANG qian liu Lin WANG Department of Civil Engineering Tsinghua University Beijing 100084 China

Fine and coarse aggregates play an important role in the fracture of concrete. However, quantitative information available on the effect of the coarse aggregate size on the fracture properties of concrete is still limited. In the present paper, the effect of coarse aggregate size （single grade of 5～10, 10～16, 16～20 and 20～25 mm） on stress-crack opening （σ-w） relation in normal and high strength concretes （compressive strength of 40 and 80 MPa, respectively） was studied. The investigation was based on three-point bending tests implemented by fictitious crack analysis. The result shows that coarse aggregate size and cement matrix strength significantly influence the shape of σ-w curve. For a given total aggregate content, in normal strength concrete, smaller size of aggregate leads to a high tensile strength and a sharp stress drop after the peak stress. The smaller the coarse aggregate, the steeper the σ-w curve. By contrast, in high strength concrete, the effect of aggregate size on σ-w relation almost vanishes. A similar σ-w relation is obtained for the concrete except for the case of 20～25 mm coarse aggregate size. The stress drop after the peak stress is more significant for high strength concrete than that for normal strength concrete. Meanwhile, the smaller the coarse aggregate size, the higher the flexural strength. Fracture energy and characteristic length increase with increasing coarse aggregate size in both normal and high strength concretes.

关键词： Aggregate size Stress-crack opening relation Fracture energy Bending test