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Tree decomposition

Chinese Science Bulletin 1998年第19期43卷 1599-1601页

作者： Xudong Yuan maocheng cai Chinese Acad Sci Inst Syst Sci Beijing 100080 Peoples R China

A tree decomposition of graph G=(V, E) is referred to as a partition of edge set E into edge-disjoint trees. Given (not necessarily distinct) vertices u-1, u-2...u-k∈V with k≥2, a sufficient and necessary condition is given for a connected graph G=(V,E) to have a tree decomposition {T-1, T-2...T-k} such that V(T-i)=V{u-i}, i=1,2,... k.

关键词： tree decomposition vertex set edge set edge-disjoint set.

A DEGREE CONDITION FOR THE EXISTENCE OF CONNECTED [k, k + 1]-FACTORS

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Systems Science and Mathematical Sciences 1995年第4期8卷 364-368页

作者： cai maocheng (Institute of Systems Science, Academia Sinica,Beijing 100080, China) 中科院系统科学所北京

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关键词： Connected factor matching graph.

PACKING AND COVERING WITH ARBORESCENCES

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Systems Science and Mathematical Sciences 1991年第4期4卷 362-367页

作者：蔡茂诚 Institute of Systems Science Academia SinicaBeijing 100080China

The aim of this note is to exhibit some recent results on packing and covering witharborescences.

关键词： Digraph arborescence packing covering

EDGE FORWARDING INDICES OF 2-EDGE-CONNECTED GRAPHS

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新疆大学学报(自然科学版)(中英文) 1990年第4期 11-13页

作者： cai maocheng (Institute of Systems Science, Acadcmia Sinica, Beijing, China)

For a given graph G of order n, a routing R is a set of n(n—1) elementary paths, one for every ordered pair of distinct vertices in G. Let π(G,R) denote the maximum number of paths of R passing through any edge of G. The edge-forwarding index π(G) is minimum of π(G,R) over all the routings R of G. In this note it is proved that for any 2-edge-connected graph G of order n, which was conjectured by Heydemann et al. in [3].

关键词： EDGE FORWARDING INDICES OF 2-EDGE-CONNECTED GRAPHS

Experimental and theoretical analysis of loading characteristics of electret filter media for charged particles

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Particuology 2024年第10期93卷 87-98页

作者： Yiqi cai Rongrong cai Lizhi Zhang Key Laboratory of Enhanced Heat Transfer and Energy Conservation of Education Ministry School of Chemistry and Chemical EngineeringSouth China University of TechnologyGuangzhou510640China State Key Laboratory of Subtropical Building Science South China University of TechnologyGuangzhou510640China

The degradation of filtration performance in electret filter media during usage poses a significant challenge. Pre-charging of aerosols has been identified as an effective method to mitigate this issue. However, the effects of particle charging characteristics on the loading characteristics of electret filters still need a comprehensive understanding. In this study, a needle-cylinder corona charger was employed to pre-charge aerosols, and the particle charge state was determined by multiphysics simulation. The effects of particle charge polarity and charge quantity on the loading performance of the electret filter were quantitatively investigated. The results showed that the particle charge polarity had a negligible impact on the loading performance under the condition of the equivalent particle charge quantity. In addition, the charged particles effectively improved the efficiency degradation during the loading process of electret media, with higher charge quantities resulting in more pronounced improvements. The electrostatic attenuation factor showed a negative exponential correlation with the particle charge quantity. This was attributed to the uneven particle deposition on fiber surface due to the attraction of charged particles by the opposite charges on the electret fibers, which alleviated the effect of electrostatic shielding.

关键词： Electret filter Charged particles Loadingcharacteristic Corona charging Electrostatic screening

Shor's algorithm does not factor large integers in the presence of noise

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Science China(Information Sciences) 2024年第7期67卷 305-320页

作者： Jin-Yi cai College of Letters and Science University of Wisconsin

We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for(controlled) rotation gates, we prove that the algorithm does not factor integers of the form pq when the noise exceeds a vanishingly small level in terms of n—the number of bits of the integer to be factored, where p and q are from a well-defined set of primes of positive density. We further prove that with probability 1-o(1) over random prime pairs(p, q), Shor's factoring algorithm does not factor numbers of the form pq, with the same level of random noise present.

关键词： random noise Shor's algorithm rotation gates quantum computing prime factorization

Whittle’s Index Based Sensor Scheduling for Multiprocess Systems Under DoS Attacks

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Journal of Systems Science & Complexity 2024年第1期37卷 329-350页

作者： cai Zai DING Kemi Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and TechnologyShenzhen 518055China.

In this paper,the authors consider how to design defensive countermeasures against DoS attacks for remote state estimation of multiprocess *** each system,a sensor will measure its state and transmits the data packets through an unreliable channel which is vulnerable to be jammed by an *** limited communication bandwidth,only a subset of sensors are allowed for data transmission,and how to select the optimal one to maximize the accuracy of remote state estimation is the focus of the proposed *** authors first formulate this problem as a Markov decision process and investigate the existence of optimal ***,the authors demonstrate the piecewise monotonicity structure of optimal *** the difficulty of obtaining an optimal policy of large-scale problems,the authors develop a suboptimal heuristic policy based on the aforementioned policy structure and Whittle’s ***,a closed form of the indices is derived in order to reduce implementation complexity of proposed scheduling policy and numerical examples are provided to illustrate the proposed developed results.

关键词： DoS attacks Kalman filter remote state estimation Whittle’s index.

Polarized imaging dynamic light scattering for simultaneous measurement of nanoparticle size and morphology

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Particuology 2024年第2期85卷 213-223页

作者： Bingyao Wang Tianyi cai Xiaoshu cai Wu Zhou Zeqi Liu Schoolof Energy and Power Engineering University of Shanghai for Science and TechnologyShanghai200093China Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering Shanghai200093China Jiaxing MeaParTech Instrument Technology Co. LtdZhejiang314000China

The performance of nanoparticles is often affected by particle size and ***,electron microscopy or atomic force microscopy is typically utilized to determine the size and morphology of ***,there are issues such as difficult sample preparation,long processing times,and challenges in quantitative ***,it is of great significance to develop a fast,accu-rate,and statistical method to measure the size and morphology of *** this study,a new method,called polarized imaging dynamic light scattering(PIDLS),is *** nanoparticles are irradiated with a vertical linearly polarized laser beam,and a polarization camera collected the dynamic light scattering images of particles at four different polarization directions(0°,45°,90°,and 135°)at a scattering angle of 90°.The average particle size and distribution are obtained using the imaging dy-namic light scattering method at 0°polarization direction,and the morphology of the particles is ob-tained based on the depolarization patterns of the scattered *** optical sphericityΦis defined based on the degree of linear polarization(DoLP).It is also implemented for the quantitative evaluation of the sphericity of the nanoparticles,including spherical,octahedral,nanoplate,nanorod,and linear *** with the Poincarésphere parameterψ,the morphology of the nanoparticles can be roughly *** addition,PIDLS enables the measurement of particle size and morphology distributions simultaneously for evaluating the uniformity of *** effectiveness of PIDLS is verified by the measurement of five kinds of industrial titanium dioxide as well.

关键词： Imaging dynamic light scattering Polarized light scattering Non-spherical nanoparticles Morphology Online measurement

An ultra-porous g-C_(3)N_(4) micro-tube coupled with MXene(Ti_(3)C_(2)TX)nanosheets for efficient degradation of organics under natural sunlight

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Journal of Environmental Sciences 2024年第3期137卷 258-270页

作者： Zongyang Ya Qiyou Wang Jingjin cai Peng Wang Xinyu Jiang Zhiyin cai Shanglin Xiang Tingwei Wang Dongyu cai College of Materials Science&Engineering Nanjing Tech University30 South PuZhu RoadNanjing 211816China Key Laboratory of Flexible Electronics(KLOFE)&Institute of Advanced Materials(IAM) Jiangsu National Synergetic Innovation Center for Advanced Materials(SICAM)Nanjing Tech University30 South PuZhu RoadNanjing 211816China

It remains as a challenge for realizing efficient photo-responsive catalysts towards largescale degradation of organic pollutants under natural *** work reports a new pore engineering strategy for creating ultra-porous g-C_(3)N_(4) micro-tubes with an unprecedentedly high specific surface area of 152.96 m^(2)/*** is mainly associated with releasing internal vapor pressure in the autoclave where the hydrothermal treatment of the urea/melamine mixture is *** by microscopic observation,porosity measurement and spectroscopic characterization,it is found that releasing the pressure at halfway of hydrothermal process is vital for forming exfoliated rod-like precursors and the de-aggregation of these rods presents substantial benefits on the production of mesopores on g-C_(3)N_(4) microtubes during the calcination of *** offers a large number of reactive sites required by photocatalytic *** these micro-tubes with Ti_(3)C_(2)T_(X) nanosheets via electrostatic interaction yields a 1D/2D heterojunction with a close interfacial *** addition of metallically conductive Ti_(3)C_(2)T_(X) nanosheets accelerates the separation between electrons and holes,and also enhances the light *** these merits of structural design lead to forming a group of highly efficient catalysts demonstrating an excellent photocatalytic degradation rate of k=0.0560 min^(-1)for RhB dyes under 100 mW/cm~2 visible light radiation that micks sunlight *** laboratory valuation is further supported by an outdoor test that shows a fast degradation rate of 0.0744 min^(-1)under natural sunlight.

关键词： Carbon nitride MXene Heterojunction Photocatalysis