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Magic Labeling of Disjoint Union Graphs

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1817-1826页

作者： Tao WANG ming ju liu De ming LI College of Science North China Institute of Science and TechnologyLangfang 065201P.R.China Department of Mathematics Beihang UniversityBeijing 100083P.R.China LMIB of the Ministry of Education Beijing 100191P.R.China Department of Mathematics Capital Normal UniversityBeijing 100048P.R.China

Let G be a graph with vertex set V(G),edge set E(G)and maximum degreeΔrespectively.G is called degree-magic if it admits a labelling of the edges by integers{1,2,...,|E(G)|}such that for any vertex v the sum of the labels of the edges incident with v is equal to1+|E(G)|/2·d(v),where d(v)is the degree of *** f be a proper edge coloring of G such that for each vertex v∈V(G),|{e:e∈Ev,f(e)≤Δ/2}|=|{e:e∈Ev,f(e)>Δ/2}|,and such an f is called a balanced edge coloring of *** this paper,we show that if G is a supermagic even graph with a balanced edge coloring and m≥1,then(2m+1)G is a supermagic *** G is a d-magic even graph with a balanced edge coloring and n≥2,then n G is a d-magic *** in this paper generalise some known results.

关键词： Supermagic graphs degree-magic graphs strong vertex-magic edge coloring

A Class of Antimagic Join Graphs

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Acta Mathematica Sinica,English Series 2013年第5期29卷 1019-1026页

作者： Tao WANG ming ju liu De ming LI Department of Foundation North China Institute of Science and Technology LMIB and Department of Mathematics Beihang University Department of Mathematics Capital Normal University

A labeling f of a graph G is a bijection from its edge set E（G） to the set {1, 2, ..., ｜E（G）｜}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r - 1 （m ≥ n）, then G1 V G2 is antimagic.

关键词： Antimagic labeling join graphs

Some Estimates for Convolution Operators with Kernels of Type (l, r) on Homogeneous Groups

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Acta Mathematica Sinica,English Series 2005年第3期21卷 577-584页

作者： Yin Sheng JIANG ming ju liu Lin TANG Department of Mathematics Xinjiang University Urumqi 830046 P. R. China Department of Mathematics Beijing Normal University Beijing 100875 P. R. China Department of Mathematics Peking University Beijing 100871 P. R. China

Some estimates for the convolution operators with kernels of type （l, r） on Lebesgue spaces with power weights and Herz-type spaces in the setting of homogeneous groups are established.

关键词： Kernels of type (l r) Homogeneous group Power weight Herz-type space

Maximizing biomass utilization: An integrated strategy for coproducing multiple chemicals

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Journal of Energy Chemistry 2025年第1期100卷 180-191页

作者： Byeongchan Ahn Sua Jo Jonggeol Na J.Jay liu Young-ju Kim Wangyun Won Department of Chemical and Biological Engineering Korea University Department of Chemical Engineering (Integrated process) Kyung Hee University Department of Chemical Engineering and Materials Science Ewha Womans University Department of Chemical Engineering Pukyong National University Resources Engineering Plant Research Department Korea Institute of Geoscience and Mineral Resources

Lignocellulosic biomass is one of the viable solutions to alleviate the global warming. However, the limited utilization of biomass majorly focused on cellulose and hemicellulose restricts the economic and environmental feasibilities. To cope with this issue, we proposed an integrated process of co-producing 1,6-hexanediol（1,6-HDO） with tetrahydrofuran and adipic acid from biomass, referred to as Strategy A. To compare the impacts of lignin upgrading and feedstock, Strategy B, which co-produces tetrahydrofuran alone, and Strategy C, which is the traditional route to produce 1,6-HDO from fossil fuels, were used. Heat networks are also designed to reduce operating costs and indirect carbon emissions due to energy consumption, saving 87% and 83% of the heat and cooling requirements, respectively, in Strategy A. The market competitiveness of Strategy A was evaluated by determining the minimum selling price through techno-economic analysis, and sustainability was thoroughly investigated by quantifying the environmental impacts through both midpoint and endpoint life-cycle assessments（LCAs）.Strategy A was found to be the most favorable both economically（USRDSCHARDOLLAR3,402/ton） and environmentally（-26.9 kg CO2eq.）. This indicates that lignin valorization is not only economically but also environmentally preferred. Finally, changes in economic and environmental feasibilities depending on economic, process, and environmental parameters were investigated using sensitivity and uncertainty analyses. The results of these analyses provide valuable insight into bio-based chemical production.

关键词： Biorefinery Carbon mitigation Climate change Global warming Lignin utilization Bioeconomy

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Heisenberg群上一类算子的有界性

数学学报（中文版） 2004年第4期47卷 629-640页

作者：刘明菊北京师范大学数学系北京100875

设 F是λ阶正则的齐次分布,-Q≤λ<0。作者研究了Heisenberg群上的算子g*F在加幂权的Lebesgue空间和Herz型 Hardy空间上的有界性,其中 g是一恰当的函数。而且,本文还得到了由BMO(H^n)函数和线性算子T所生成的交换子[b,T]在Herz空间上的... 详细信息

设 F是λ阶正则的齐次分布,-Q≤λ<0。作者研究了Heisenberg群上的算子g*F在加幂权的Lebesgue空间和Herz型 Hardy空间上的有界性,其中 g是一恰当的函数。而且,本文还得到了由BMO(H^n)函数和线性算子T所生成的交换子[b,T]在Herz空间上的有界性。

关键词： Heisenberg群 Herz型空间奇异积分

Equitable Strong Edge Coloring of the Joins of Paths and Cycles

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Journal of Mathematical Research with Applications 2012年第1期32卷 11-18页

作者： Tao WANG 1,ming ju liu 2,De ming LI 3,1.Department of Basic Curriculum,North China Institute of Science and Technology,Hebei 065201,P.R.China 2.LMIB and Department of Mathematics,BeiHang University,Beijing 100083,P.R.China 3.Department of Mathematics,Capital Normal University,Beijing 100048,P.R.China Department of Basic Curriculum North China Institute of Science and Technology Hebei 065201 LMIB and Department of Mathematics BeiHang University Beijing 100083 Department of Mathematics Capital Normal University Beijing 100048

For a proper edge coloring c of a graph G,if the sets of colors of adjacent vertices are distinct,the edge coloring c is called an adjacent strong edge coloring of *** c i be the number of edges colored by *** |c i c j | ≤ 1 for any two colors i and j,then c is an equitable edge coloring of *** coloring c is an equitable adjacent strong edge coloring of G if it is both adjacent strong edge coloring and equitable edge *** least number of colors of such a coloring c is called the equitable adjacent strong chromatic index of *** this paper,we determine the equitable adjacent strong chromatic index of the joins of paths and ***,we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.

关键词： adjacent strong edge coloring equitable edge coloring joins of paths cycle,maximum degree chromatic index.

Investigation of bubbles escape behavior from low basicity mold flux for high-Mn high-Al steels using 3D X-ray microscope

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International Journal of Minerals,Metallurgy and Materials 2025年第1期32卷 102-110页

作者： Qiang liu Xiang Li Shen Du ming Gao Yanbin Yin Jiongming Zhang State Key Laboratory of Advanced Metallurgy University of Science and Technology BeijingBeijing 100083China

During the continuous casting process of high-Mn high-Al steels,various types of gases such as Ar need to escape through the top of the *** which,the behavior of bubbles traversing the liquid slag serves as a restrictive link,closely associated with viscosity and the thickness of liquid *** contrast to two-dimensional surface observation,three-dimensional(3D)analysis method can offer a more intuitive,accurate,and comprehensive ***,this study employs a 3D X-ray microscope(3D-XRM)to obtained spatial distribution and 3D morphological characteristics of residual bubbles in mold flux under different basicity of liquid slag,different temperatures,and different holding *** results indicate that as basicity of slag increases from 0.52 to 1.03,temperature increases from 1423 to 1573 K,the viscosity of slag decreases,the floating rate of bubbles *** addition,when holding time increases from 10 to 30 s,the bubbles floating distance increases,and the volume fraction and average equivalent sphere diameter of the bubbles solidified in the mold flux gradually *** one word,increasing the basicity,temperature,and holding time leading to an increase in the removal rate of bubbles especially for the *** findings of bubbles escape behavior provide valuable insights into optimizing low basicity mold flux for high-Mn high-Al steels.

关键词： mold flux low basicity bubbles three-dimensional X-ray microscope viscosity

Enhancement of motor functional recovery in thoracic spinal cord injury: voluntary wheel running versus forced treadmill exercise

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Neural Regeneration Research 2025年第3期20卷 836-844页

作者： Do-Hun Lee Dan Cao Younghye Moon Chen Chen Nai-Kui liu Xiao-ming Xu Wei Wu Spinal Cord and Brain Injury Research Group Stark Neurosciences Research InstituteIndiana University School of MedicineIndianapolisINUSA Department of Neurological Surgery Indiana University School of MedicineIndianapolisINUSA Department of Neuroscience Baylor College of MedicineHoustonTXUSA

Spinal cord injury necessitates effective rehabilitation strategies, with exercise therapies showing promise in promoting recovery. This study investigated the impact of rehabilitation exercise on functional recovery and morphological changes following thoracic contusive spinal cord injury. After a 7-day recovery period after spinal cord injury, mice were assigned to either a trained group(10 weeks of voluntary running wheel or forced treadmill exercise) or an untrained group. Bi-weekly assessments revealed that the exercise-trained group, particularly the voluntary wheel exercise subgroup, displayed significantly improved locomotor recovery, more plasticity of dopaminergic and serotonin modulation compared with the untrained group. Additionally, exercise interventions led to gait pattern restoration and enhanced transcranial magnetic motor-evoked potentials. Despite consistent injury areas across groups, exercise training promoted terminal innervation of descending axons. In summary, voluntary wheel exercise shows promise for enhancing outcomes after thoracic contusive spinal cord injury, emphasizing the role of exercise modality in promoting recovery and morphological changes in spinal cord injuries. Our findings will influence future strategies for rehabilitation exercises, restoring functional movement after spinal cord injury.

关键词： behavioral assessment motor function neural plasticity running wheel exercise spinal cord injury treadmill exercise voluntary exercise

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脉宽可调光学参量振荡器的研究

中国激光 2001年第8期28卷 689-692页

作者：王月珠于欣姚宝权何伟明鞠有伦柳强王骐哈尔滨工业大学光电子技术研究所可调谐激光技术国家级重点实验室哈尔滨150001

利用振放双池受激布里渊散射 (SBS)脉宽可调激光系统抽运非临界相位匹配KTP光学参量振荡器(OPO) ,在脉宽从小于 1ns至 6ns之间变化。小能量抽运的情况下 ,实现了OPO低阈值、较高转换效率运转 ,获得了脉宽可调参量激光 ,并且根据长脉冲... 详细信息

利用振放双池受激布里渊散射 (SBS)脉宽可调激光系统抽运非临界相位匹配KTP光学参量振荡器(OPO) ,在脉宽从小于 1ns至 6ns之间变化。小能量抽运的情况下 ,实现了OPO低阈值、较高转换效率运转 ,获得了脉宽可调参量激光 ,并且根据长脉冲抽运光学参量振荡器特点 ,结合实验结果对光学参量振荡器的输出特性进行了分析。

关键词：光学参量振荡器受激布里渊散射脉宽可调