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Regulation of tillering and panicle branching in rice and wheat 被引量:1
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作者 Ning Zhang Yuhao Liu +1 位作者 Songtao Gui Yonghong Wang 《Journal of Genetics and Genomics》 2025年第7期869-886,共18页
Branching is a critical aspect of plant architecture that significantly impacts the yield and adaptability of staple cereal crops like rice and wheat.Cereal crops develop tillers during the vegetative stage and panicl... Branching is a critical aspect of plant architecture that significantly impacts the yield and adaptability of staple cereal crops like rice and wheat.Cereal crops develop tillers during the vegetative stage and panicle or spike branches during the reproductive stage,respectively,both of which are significantly impacted by hormones and genetic factors.Tillering and panicle branching are closely interconnected and exhibit high environmental plasticity.Here,we summarize the recent progress in genetic,hormonal,and environmental factors regulation in the branching of rice and wheat.This review not only provides a comprehensive overview of the current knowledge on branching mechanisms in rice and wheat,but also explores the prospects for future research aimed at optimizing crop architecture for enhanced productivity. 展开更多
关键词 RICE WHEAT Crop architecture TILLERING Panicle branching
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Identification of QTLs for plant height and branching-related traits in cultivated peanut
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作者 Shengzhong Zhang Xiaohui Hu +5 位作者 Feifei Wang Huarong Miao Chu Ye Weiqiang Yang Wen Zhong Jing Chen 《Journal of Integrative Agriculture》 2025年第7期2511-2524,共14页
Plant height(PH),primary lateral branch length(PBL),and branch number(BN)are architectural components impacting peanut pod yield,biomass production,and adaptivity to mechanical harvesting.In this study,a recombinant i... Plant height(PH),primary lateral branch length(PBL),and branch number(BN)are architectural components impacting peanut pod yield,biomass production,and adaptivity to mechanical harvesting.In this study,a recombinant inbred population consisting of 181 individual lines was used to determine genetic controls of PH,PBL,and BN across three environments.Phenotypic data collected from the population demonstrated continuous distributions and transgressive segregation patterns.Broad-sense heritability of PH,PBL,and BN was found to be 0.87,0.88,and 0.92,respectively.Unconditional individual environmental analysis revealed 35 additive QTLs with phenotypic variation explained(PVE)ranging from 4.57 to 21.68%.A two-round meta-analysis resulted in 24consensus and 19 unique QTLs.Five unique QTLs exhibited pleiotropic effects and their genetic bases(pleiotropy or tight linkage)were evaluated.A joint analysis was performed to estimate the QTL by environment interaction(QEI)effects on PH,PBL,and BN,collectively explaining phenotypic variations of 10.80,11.02,and 7.89%,respectively.We identified 3 major and stable QTL regions(uq9-3,uq10-2,and uq16-1)on chromosomes 9,10,and 16,spanning1.43-1.53 Mb genomic regions.Candidate genes involved in phytohormones biosynthesis,signaling,and cell wall development were proposed to regulate these morphological traits.These results provide valuable information for further genetic studies and the development of molecular markers applicable to peanut architecture improvement. 展开更多
关键词 PEANUT plant height branching QTL mapping candidate gene
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REMAINING-LIFETIME AGE-STRUCTURED BRANCHING PROCESSES
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作者 Ziling CHENG Zenghu LI 《Acta Mathematica Scientia》 2025年第3期1107-1136,共30页
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the un... We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved. 展开更多
关键词 branching process remaining lifetime IMMIGRATION stochastic equation ergod-icity occupation time large number law central limit theorem MSC202060J80 60J85 60H15 60F15 60F05
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Tailoring End-Use Properties of Polypropylene through a Combination of Specific Nucleation and Long-Chain Branching
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作者 Lenka Gajzlerova Jana Navratilova +4 位作者 Martina Polaskova Lubomir Benicek David Jaska Sona Zenzingerova Roman Cermak 《Chinese Journal of Polymer Science》 2025年第1期101-109,I0009,共10页
The present study presents an assessment of the interrelations between long-chain branching,specific nucleation,and end-use properties of polypropylene blends:blends of linear polypropylene(L-PP)and long-chain branche... The present study presents an assessment of the interrelations between long-chain branching,specific nucleation,and end-use properties of polypropylene blends:blends of linear polypropylene(L-PP)and long-chain branched polypropylene(LCB-PP)modified by a specificβ-nucleating agent(NA).Specimens with various LCB-PP compositions with and without NA were prepared under complex flow fields by injection molding.Wide-angle X-ray scattering was employed to capture the X-ray patterns of both the skin and core of the specimens,determining the overall crystallinity and amounts of individual polymorphs.The increasing content of LCB-PP andγ-phase,at the same time,in the blends is reflected in both increasing crystallinity and improved mechanical properties,namely,yield stress and Young’s modulus.On the other hand,the composition of the blends had no significant effect on the impact strength,except for nucleated L-PP.It has been demonstrated that adding a relatively small amount of LCB-PP is sufficient to modify the mechanical properties of linear polypropylene.Even a very small amount of LCB-PP in the L-PP suppressed the effectiveness of NA. 展开更多
关键词 Polymeric blend Long-chain branched polypropylene Polymorphism Mechanical property
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Engineering high amylose and resistant starch in maize by CRISPR/Cas9-mediated editing of starch branching enzymes 被引量:2
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作者 Mingzheng Ma Shanqiu Sun +5 位作者 Jinjie Zhu Xiantao Qi Gaoke Li Jianguang Hu Chuanxiao Xie Changlin Liu 《The Crop Journal》 SCIE CSCD 2024年第4期1252-1258,共7页
To improve the amylose content(AC)and resistant starch content(RSC)of maize kernel starch,we employed the CRISPR/Cas9 system to create mutants of starch branching enzyme I(SBEI)and starch branching enzyme IIb(SBEIIb).... To improve the amylose content(AC)and resistant starch content(RSC)of maize kernel starch,we employed the CRISPR/Cas9 system to create mutants of starch branching enzyme I(SBEI)and starch branching enzyme IIb(SBEIIb).A frameshift mutation in SBEI(E1,a nucleotide insertion in exon 6)led to plants with higher RSC(1.07%),lower hundred-kernel weight(HKW,24.71±0.14 g),and lower plant height(PH,218.50±9.42 cm)compared to the wild type(WT).Like the WT,E1 kernel starch had irregular,polygonal shapes with sharp edges.A frameshift mutation in SBEIIb(E2,a four-nucleotide deletion in exon 8)led to higher AC(53.48%)and higher RSC(26.93%)than that for the WT.E2 kernel starch was significantly different from the WT regarding granule morphology,chain length distribution pattern,X-ray diffraction pattern,and thermal characteristics;the starch granules were more irregular in shape and comprised typical B-type crystals.Mutating SBEI and SBEIIb(E12)had a synergistic effect on RSC,HKW,PH,starch properties,and starch biosynthesis-associated gene expression.SBEIIa,SS1,SSIIa,SSIIIa,and SSIIIb were upregulated in E12 endosperm compared to WT endosperm.This study lays the foundation for rapidly improving the starch properties of elite maize lines. 展开更多
关键词 MAIZE Gene editing Starch branching enzyme I Starch branching enzyme IIb
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ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK
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作者 Shuxiong ZHANG Jie XIONG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期2051-2072,共22页
Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈... Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process. 展开更多
关键词 empty ball DIMENSION branching random walk super-Brownian motion
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Drosophila adhesion GPCR Remoulade regulates axon growth, branching, and guidance by modulating Rac1 GTPase
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作者 Xi Yang Changkun Pan +7 位作者 Meitong Ye Jinshuo Liang Haoyang Cheng Qing Liang Shu Huang Jianshu Wang Hoi Yee Chow Haihuai He 《Journal of Genetics and Genomics》 SCIE CAS CSCD 2024年第4期458-461,共4页
The assembly of neurons into complex circuits relies upon appropriate axonal navigation to distant targets.Although considerable progress has been made toward understanding the regulation of the guidance and branching... The assembly of neurons into complex circuits relies upon appropriate axonal navigation to distant targets.Although considerable progress has been made toward understanding the regulation of the guidance and branching of axon extension,the molecular and cellular mechanisms underlying the coordination of the motility of the axon tip,axon growth,and branching remain largely unknown(Sudhof,2017).The Drosophila mushroom body(MB),the major site for associative learning and memory,is a powerful model system to investigate complex axon behaviors.The MB is a bilaterally symmetric central brain structure,mainly composed of Kenyon cells,MB output neurons,and dopaminergic neurons(Li et al.,2020).Among the seven neuronal subtypes of~2000 Kenyon cells,Y,a/β,and a/β'subtypes extend axons in a fascicle and bifurcate to produce two sister branches,one projecting into the dorsal lobe and the other into the medial lobe. 展开更多
关键词 branching MEDIAL AXON
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Preparation and Rheological Characterization of Long Chain Branching Polyglycolide
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作者 Wei-Lin Liu Ming-Fu Lyu +2 位作者 Heng-Yuan Zhang Jian-Ye Liu Shi-Jun Zhang 《Chinese Journal of Polymer Science》 SCIE EI CAS CSCD 2024年第8期1177-1184,共8页
The long chain branching(LCB)polyglycolide(PGA)was successfully prepared by the successive reactions of the terminal hydroxyl groups of PGA with triglycidyl isocyanurate(TGIC)and pyromellitic dianhydride(PMDA).The inf... The long chain branching(LCB)polyglycolide(PGA)was successfully prepared by the successive reactions of the terminal hydroxyl groups of PGA with triglycidyl isocyanurate(TGIC)and pyromellitic dianhydride(PMDA).The influence of LCB produced by functional group reaction on rheological and crystallization behavior was studied and discussed through linear rheology,uniaxial elongation and DSC(differential scanning calorimetry).The much higher viscosity and the more notable strain hardening behavior of modified PGA indicates the LCB with high degree of entanglements are created.The melt strength of PGA is finally improved greatly and can make su re that the supercritical CO_(2)foaming can be carried out successfully. 展开更多
关键词 Polyglycolide(PGA) Long chain branching(LCB) RHEOLOGY
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THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT(I):MODEL,MARKOV PROPERTY,MOMENTS
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作者 胡迪鹤 胡晓予 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1669-1678,共10页
There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE), i.e., the coupling of branching chain and random walk. In Section... There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE), i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE. 展开更多
关键词 branching chain with drift in space-time random enviromnent randombranching generating function local random transition generating function random drift law random branching law
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An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation 被引量:4
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作者 马明书 王肖凤 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第4期98-103,共6页
This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△... This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2. 展开更多
关键词 parabolic type equation explicit difference scheme high accuracy branching stability truncation er
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THE EXISTENCE AND MOMENTS OF CANONICAL BRANCHING CHAIN IN RANDOM ENVIRONMENT 被引量:19
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作者 Hu Dihe 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期499-506,共8页
The concepts of branching chain in random environmnet and canonical branching chain in random environment are introduced.Moreover the existence of these chains is proved.Finally the exact formulas of mathematical expe... The concepts of branching chain in random environmnet and canonical branching chain in random environment are introduced.Moreover the existence of these chains is proved.Finally the exact formulas of mathematical expectation and variance of branching chain in random environment are also given. 展开更多
关键词 Random transition matrix branching chain in random environment canonical branching chains in random environments generator random varialble
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THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS 被引量:2
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作者 胡迪鹤 《Acta Mathematica Scientia》 SCIE CSCD 2006年第3期431-442,共12页
The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introd... The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment (CMBCRE) and multitype Markov branching chain in random environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties. 展开更多
关键词 Random Markov matrix Markov chain in random environment Markov branching chain in random environment canonical Markov branching chain in random environment generator random variables
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Cloning and Expression of the Promoter of Maize Starch-Branching Enzyme sbeⅡb Gene
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作者 徐亚维 王丕武 柴晓杰 《Agricultural Science & Technology》 CAS 2010年第11期84-88,共5页
[Objective] The aim was to construct promoter of maize starch-branching enzyme sbe Ⅱb gene specifically expressed in seed.[Method] The promoter sequence of maize starch-branching enzyme sbe Ⅱb gene was amplified by ... [Objective] The aim was to construct promoter of maize starch-branching enzyme sbe Ⅱb gene specifically expressed in seed.[Method] The promoter sequence of maize starch-branching enzyme sbe Ⅱb gene was amplified by LA-PCR and then cloned into pMD18-T vector.Subsequently,the promoter was cloned into pBI121 vector to construct plant expression vector pBI121-sbe Ⅱb.Recombinant plasmid pSBE-GUS was constructed by connecting GUS gene into pBI121-sbe Ⅱb and transformed into tobacco mediated by Agrobacterium tumefaciens,before detection by PCR and Southern blot.The biochemical analysis and fluorescence detection of GUS activity were performed in different parts of the tobacco by Gene Gun Method and Agrobacterium tumefaciens transformation respectively.[Result] The homology between promoter sequence cloned in this experiment and the corresponding sequence announced in the GenBank reached 98.52%.Four transformed tobaccos were obtained by PCR and Southern blot after co-culture and selective culture.A small number of blue spots appeared in leaves,and the spots could barely been seen in the stems and roots,while a large number of blue spots were found in seeds.So,it could be concluded that the promoter of sbeⅡb gene was specifically expressed in seeds.[Conclusion] Promoter of maize starch branching enzyme sbe Ⅱb specifically expressed in seeds was successfully cloned. 展开更多
关键词 Starch branching enzyme PROMOTER AMPLIFICATION EXPRESSION
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Research Progress and Application of Plant Branching
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作者 Yaru Yang Yulan Hu +2 位作者 Ping Li John T.Hancock Xiangyang Hu 《Phyton-International Journal of Experimental Botany》 SCIE 2023年第3期679-689,共11页
Plant branching development plays an important role in plant morphogenesis(aboveground plant type),the number and angle of branches are important agronomic characters that determine crop plant type.Effective branches ... Plant branching development plays an important role in plant morphogenesis(aboveground plant type),the number and angle of branches are important agronomic characters that determine crop plant type.Effective branches determine the number of panicles or pods of crops and then control the yield of crops.With the rapid development of plant genomics and molecular genetics,great progress has been made in the study of branching development.In recent years,a series of important branching-related genes have been validated from Arabidopsis thaliana,rice,pea,tomato and maize mutants.It is reviewed that plant branching development is controlled by genetic elements and plant hormones,such as auxin,cytokinin and lactones(or lactone derivatives),as well as by environment and genetic elements.Meanwhile,shoot architecture in crop breeding was discussed in order to provide theoretical basis for the study of crop branching regulation. 展开更多
关键词 Plant branching branching development genes HORMONE ENVIRONMENT crop breeding
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CHARACTERIZATION OF BRANCHING POINT DISTRIBUTION IN THE SOL OF IRRADIATED POLYSTYRENE WITH SEC-LALLS
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作者 张万喜 王谋智 孙家珍 《Chinese Journal of Polymer Science》 SCIE CAS CSCD 1991年第2期177-179,共3页
In this paper, the change behavior of branching point distribution of irradiated polystyrene in sol has been first studied by the SEC-LALLS method. The experimental results show that branching parameter of the part wi... In this paper, the change behavior of branching point distribution of irradiated polystyrene in sol has been first studied by the SEC-LALLS method. The experimental results show that branching parameter of the part with lower molecular weight in the sol changes little at the early stage of irradiation and that of the part with the higher molecular weight becomes greater with the increase in radiation dose. 展开更多
关键词 Irradiation of polystyrene branching point distribution of the sol branching parameter SEC-LALLS.
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Photodissociation of HOD via the C1B1 State: OD/OH Branching Ratio and OD Bond Dissociation Energy
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作者 程丽娜 程元 +4 位作者 袁开军 郭庆 汪涛 戴东旭 杨学明 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2011年第2期129-133,I0003,共6页
Photodissociation of jet-cooled HOD via the C state around 124 nm has been studied using the H(D)-atom Rydberg tagging time-of-flight technique. Rotational state resolved action spectrum and the product translationa... Photodissociation of jet-cooled HOD via the C state around 124 nm has been studied using the H(D)-atom Rydberg tagging time-of-flight technique. Rotational state resolved action spectrum and the product translational energy distribution spectra have been recorded for both D+OH and H+OD dissociation channels. Product channel OH/OD branching ratios for the individual C-X rotational transition have been determined. A comparison is also given with the B-X and A-X transitions. In addition, the dissociation energy of the OD bond in HOD has been determined accurately to be 41751.3±5 cm-1. 展开更多
关键词 PHOTODISSOCIATION Rydberg tagging branching ratio Dissociation energy
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Crack branching mechanism of rock-like quasi-brittle materials under dynamic stress 被引量:12
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作者 唐春安 杨岳峰 《Journal of Central South University》 SCIE EI CAS 2012年第11期3273-3284,共12页
The cracking patterns of a thin sheet with a pre-existing crack subjected to dynamic loading are numerically simulated to investigate the mechanism of crack branching by using the FEM method.Six numerical models were ... The cracking patterns of a thin sheet with a pre-existing crack subjected to dynamic loading are numerically simulated to investigate the mechanism of crack branching by using the FEM method.Six numerical models were set up to study the effects of load,tensile strength and heterogeneity on crack branching.The crack propagation is affected by the applied loads,tensile strength and heterogeneity.Before crack branching,the crack propagates by some distance along the direction of the pre-existing crack.For the materials with low heterogeneity,the higher the applied stress level is and the lower the tensile strength of the material is,the shorter the propagation distance is.Moreover,the branching angle becomes larger and the number of branching cracks increases.In the case of the materials with high heterogeneity,a lot of disordered voids and microcracks randomly occur along the main crack,so the former law is not obvious.The numerical results not only are in good agreement with the experimental observations in laboratory,but also can be extended to heterogeneity media.The work can provide a good approach to model the cracking and fracturing of heterogeneous quasi-brittle materials,such as rock,under dynamic loading. 展开更多
关键词 crack propagation branching HETEROGENEITY Weibull distribution MICROCRACK ROCK
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Analysis of the Flow Rate Characteristics of Valveless Piezoelectric Pump with Fractal-like Y-shape Branching Tubes 被引量:7
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作者 HUANG Jun ZHANG Jianhui +1 位作者 WANG Shouyin LIU Weidong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2014年第3期628-634,共7页
Microchannel heat sink with high heat transfer coefficients has been extensively investigated due to its wide application prospective in electronic cooling. However, this cooling system requires a separate pump to dri... Microchannel heat sink with high heat transfer coefficients has been extensively investigated due to its wide application prospective in electronic cooling. However, this cooling system requires a separate pump to drive the fluid transfer, which is uneasy to minimize and reduces their reliability and applicability of the whole system. In order to avoid these problems, valveless piezoelectric pump with fractal-like Y-shape branching tubes is proposed. Fractal-like Y-shape branching tube used in microchannel heat sinks is exploited as no-moving-part valve of the valveless piezoelectric pump. In order to obtain flow characteristics of the pump, the relationship between tube structure and flow rate of the pump is studied. Specifically, the flow resistances of fractal-like Y-shape branching tubes and flow rate of the pump are analyzed by using fractal theory. Then, finite element software is employed to simulate the flow field of the tube, and the relationships between pressure drop and flow rate along merging and dividing flows are obtained. Finally, valveless piezoelectric pumps with fractal-like Y-shape branching tubes with different fractal dimensions of diameter distribution are fabricated, and flow rate experiment is conducted. The experimental results show that the flow rate of the pump increases with the rise of fractal dimension of the tube diameter. When fractal dimension is 3, the maximum flow rate of the valveless pump is 29.16 mL/min under 100 V peak to peak (13 Hz) power supply, which reveals the relationship between flow rate and fractal dimensions of tube diameter distribution. This paper investigates the flow characteristics of valveless piezoelectric pump with fractal-like Y-shape branching tubes, which provides certain references for valveless piezoelectric pump with fractal-like Y-shape branching tubes in application on electronic chip cooling. 展开更多
关键词 PIEZOELECTRIC PUMP valveless fractal-like Y-shape branching tube
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Characterization and Expression Analysis of Starch Branching Enzymes in Sweet Potato 被引量:6
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作者 QIN Hua ZHOU Shuang ZHANG Yi-zheng 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2013年第9期1530-1539,共10页
Spatial and temporal expression patterns of Sbel and Sbe2 that encode starch branching enzyme (SBE) Ⅰ and Ⅱ, respectively, in sweet potato (Ipomoea batatas L.) were analyzed. Expression of both genes in Escheric... Spatial and temporal expression patterns of Sbel and Sbe2 that encode starch branching enzyme (SBE) Ⅰ and Ⅱ, respectively, in sweet potato (Ipomoea batatas L.) were analyzed. Expression of both genes in Escherichia coli indicate that both genes encoded active SBE. Analysis with real-time quantitative polymerase chain reaction technique indicates that IbSbel mRNA was expressed at very low levels in leaves but was the predominant isoform in tuberous root while the reverse case was found for lbSbe2. The expression pattern of IbSbel, closely resembles that of AGPase S, a gene coding for one of the subunits ofADP-glucose pyrophosphorylase, which is the key regulatory enzyme in the starch biosynthetic pathway. Western analysis detected at least two isoforms of SBE I in tuberous roots, those two isoforms showed adverse expression patterns with the development of the tuberous roots. Expression of the two IbSbe genes exhibited a diurnal rhythm during a 12-h cycle when fed a continuous solution of sucrose. Abscisic acid (ABA) was aother potent inducer of IbSbe expression, but bypassed the semidian oscillator. 展开更多
关键词 sweet potato starch branching enzyme cDNA cloning cDNA expression expression patterns sucroseinduction ABA induction
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ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME 被引量:5
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作者 Yuejiao WANG Zaiming LIU +1 位作者 Quansheng LIU Yingqiu LI 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1345-1362,共18页
We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoti... We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate. 展开更多
关键词 branching RANDOM WALK RANDOM ENVIRONMENT quenched MOMENTS WEIGHTED MOMENTS
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