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1-Planar Graphs with Girth at Least 7 are(1,1,1,0)-Colorable 被引量:1
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作者 Ya-nan CHU Lei SUN 《Journal of Mathematical Research with Applications》 CSCD 2016年第6期643-650,共8页
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.In this paper,it is shown that 1-planar graphs with girth at least7 are(1,1,1,0)-colorable.
关键词 vertex coloring crossing planar undirected colorable Figure subgraph integers incident
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Uniquely Tree Colorable Graphs
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作者 Deng Ping Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China 《Journal of Modern Transportation》 1997年第1期90-95,共6页
In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tr... In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed. 展开更多
关键词 tree chromatic number tree partition uniquely tree colorable graph
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Plane Graphs with Maximum Degree 5 Are 11-Linear-Colorable
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作者 Kan WANG Weifan WANG 《Journal of Mathematical Research with Applications》 CSCD 2012年第6期647-653,共7页
A linear coloring of a graph G is a proper vertex coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of G is the sm... A linear coloring of a graph G is a proper vertex coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of G is the smallest number of colors in a linear coloring of G. In this paper, we prove that every planar graph G with maximum degree 5 is 11-linear-colorable. 展开更多
关键词 planar graph linear coloring maximum degree.
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Colorable photothermal-induced self-repairing anti-corrosion coating based on confined solid-liquid transition
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作者 Jiahong Wei Ting Shen +3 位作者 Wenkai Cao Long Jiang Yu He Weihua Li 《Journal of Materials Science & Technology》 CSCD 2024年第30期227-237,共11页
Self-repairing coatings hold promise for prolonging the lifespan of steel structures and reducing carbon dioxide emissions from metal corrosion.Reversible chemistry-based intrinsic self-repairing has emerged as a cutt... Self-repairing coatings hold promise for prolonging the lifespan of steel structures and reducing carbon dioxide emissions from metal corrosion.Reversible chemistry-based intrinsic self-repairing has emerged as a cutting-edge strategy for addressing material damage.However,achieving effective repair at damaged coating interfaces remains challenging due to adhesion limitations between the coating and substrate.In this study,we propose an innovative approach to efficiently repair coating damage using photothermal-induced confined solid-liquid transition.We developed a unique structured coating by incorporating ther-moplastic epoxy resin(EP)into a polyethersulfone(PES)network skeleton through controlled reaction-induced phase separation.Additionally,we synthesized visible-light transmittable copper sulfide(CuS)nanocrystals as photothermal fillers to impart PES/EP-CuS coating with colorability.Upon near-infrared(NIR)laser irradiation,the EP phase undergoes confined solid-liquid transition at the crack site,enabling it to flow through the PES skeleton and seal the crack.This process promotes contact between damaged interfaces and closes the crack through interfacial tension.The PES/EP-CuS coating exhibited exceptional anti-corrosion restoration during service,showcasing its robust self-repairing capability. 展开更多
关键词 Confined solid-liquid transition Photothermal effect Colorability SELF-REPAIRING Anti-corrosion coating
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1-planar Graphs without 4-cycles or 5-cycles are 5-colorable
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作者 Li-li SONG Lei SUN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2022年第1期169-177,共9页
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 ... 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 k-cycle.In this paper,it is proved that 1-planar graphs without 4-cycles or 5-cycles are 5-colorable. 展开更多
关键词 1-planar colorable DISCHARGING VERTICES FACES
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Planar graphs with maximum degree 8 and without intersecting chordal 4-cycles are 9-totally colorable 被引量:5
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作者 CAI JianSheng WANG GuangHui YAN GuiYing 《Science China Mathematics》 SCIE 2012年第12期2601-2612,共12页
The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum deg... The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9. 展开更多
关键词 total coloring planar graph chordal 4-cycles TRIANGLES
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Planar graphs without 4,6,8-cycles are 3-colorable 被引量:1
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作者 Wei-fan WANG Min CHEN 《Science China Mathematics》 SCIE 2007年第11期1552-1562,共11页
In this paper we prove that every planar graph without 4,6 and 8-cycles is 3-colorable.
关键词 PLANAR GRAPHS COLORING CYCLE
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A Totally(Δ+1)-colorable 1-planar Graph with Girth at Least Five 被引量:1
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作者 Lin SUN Jian Liang WU Hua CAI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第11期1337-1349,共13页
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree △(G) 〉 12 and girth at least five... A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree △(G) 〉 12 and girth at least five is totally (△(G)+1)-colorable. 展开更多
关键词 1-planar graph total coloring discharging method GIRTH
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A Sufficient Condition on 3-colorable Plane Graphs Without 5- and 6-circuits
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作者 Bao-gang Xu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2014年第3期765-772,共8页
In 2003, Borodin and Raspaud proved that if G is a plane graph without 5-circuits and without triangles of distance less than four, then G is 3-colorable. In this paper, we prove that if G is a plane graph without 5- ... In 2003, Borodin and Raspaud proved that if G is a plane graph without 5-circuits and without triangles of distance less than four, then G is 3-colorable. In this paper, we prove that if G is a plane graph without 5- and 6-circuits and without triangles of distance less than 2, then G is 3-colorable. 展开更多
关键词 plane graph CIRCUIT COLORING
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Connectivity of Minimum Non-5-injectively Colorable Planar Cubic Graphs
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作者 Jing Jin Bao-Gang Xu 《Journal of the Operations Research Society of China》 EI CSCD 2020年第1期105-116,共12页
Suppose that G is a planar cubic graph withχi(G)>5.We show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtaine... Suppose that G is a planar cubic graph withχi(G)>5.We show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtained from a simple cubic 3-connected planar graph by adding some earrings.This shows that a minimum non-5-injectively colorable simple planar cubic graph must be 3-connected. 展开更多
关键词 Planar cubic graphs CONNECTIVITY 3-connected Injective coloring
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A Sufficient Condition for Planar Graphs with Maximum Degree 8 to Be 9-totally Colorable
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作者 Jian Sheng CAI Chang Chun TENG Gui Ying YAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第6期993-1006,共14页
A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ''(G) is the smallest integer k ... A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ''(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree △≥ 9, then )χ″(G) =△+ 1. In this paper, we prove that if O is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ″(G) =- 9. 展开更多
关键词 Total coloring planar graph a fan of four adjacent 3-cycles
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Structural Color Dynamic Graphics Display Based on Microlens Array 被引量:1
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作者 LI Xue-han LIU Ling-zhi +1 位作者 HUANG Min LI Xiu 《印刷与数字媒体技术研究》 北大核心 2025年第2期162-168,共7页
It is of great scientific significance to construct a 3D dynamic structural color with a special color effect based on the microlens array.However,the problems of imperfect mechanisms and poor color quality need to be... It is of great scientific significance to construct a 3D dynamic structural color with a special color effect based on the microlens array.However,the problems of imperfect mechanisms and poor color quality need to be solved.A method of 3D structural color turning on periodic metasurfaces fabricated by the microlens array and self-assembly technology was proposed in this study.In the experiment,Polydimethylsiloxane(PDMS)flexible film was used as a substrate,and SiO2 microspheres were scraped into grooves of the PDMS film to form 3D photonic crystal structures.By adjusting the number of blade-coated times and microsphere concentrations,high-saturation structural color micropatterns were obtained.These films were then matched with microlens arrays to produce dynamic graphics with iridescent effects.The results showed that by blade-coated two times and SiO2 microsphere concentrations of 50%are the best conditions.This method demonstrates the potential for being widely applied in the anticounterfeiting printing and ultra-high-resolution display. 展开更多
关键词 Structural color Microlens array Dynamic graphics display Moirémagnification Optical anti-counterfeiting
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Fine mapping and identification of CaTTG1,a candidate gene that regulates the hypocotyl anthocyanin accumulation in Capsicum annuum 被引量:2
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作者 Jin Wang Yao Dai +9 位作者 Luzhao Pan Ying Chen Li Dai Yanqing Ma Xiaoxun Zhou Wu Miao Muhammad Rizwan Hamid Xuexiao Zou Feng Liu Cheng Xiong 《Horticultural Plant Journal》 2025年第1期264-274,共11页
Pepper(Capsicum annuum L.)is a typical self-pollinating crop with obvious heterosis in hybrids.Consequently,the use of morphological markers during the pepper seedling stage is crucial for pepper breeding.The color of... Pepper(Capsicum annuum L.)is a typical self-pollinating crop with obvious heterosis in hybrids.Consequently,the use of morphological markers during the pepper seedling stage is crucial for pepper breeding.The color of hypocotyl is widely used as a phenotypic marker in crossing studies of pepper.Pepper accessions generally have purple hypocotyls,which are mainly due to the anthocyanin accumulation in seedlings,and green hypocotyls are rarely observed in pepper.Here we reported the characterization of a green hypocotyl mutant of pepper,Cha1,which was identified from a pepper ethyl methanesulfonate(EMS)mutant library.Fine mapping revealed that the causal gene,CaTTG1,belonging to the WD40 repeat family,controlled the green hypocotyl phenotype of the mutant.Virus-induced gene silencing(VIGS)confirmed that CaTTG1 regulated anthocyanin accumulation.RNA-seq data showed that expression of structural genes CaDFR,CaANS,and CaUF3GT in the anthocyanin biosynthetic pathway was significantly decreased in Cha1 compared to the wild type.Yeast two-hybrid(Y2H)experiments also confirmed that CaTTG1 activated the synthesis of anthocyanin structural genes by forming a MBW complex with CaAN1 and CaGL3.In summary,this study provided a green hypocotyl mutant of pepper,and the Kompetitive Allele Specific PCR(KASP)marker developed based on the mutation site of the underlying gene would be helpful for pepper breeding. 展开更多
关键词 PEPPER CaTTG1 ANTHOCYANIN Hypocotyl color FINE-MAPPING
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Solvent engineering in perovskite nanocrystal colloid inks for super-fine electrohydrodynamic inkjet printing of color conversion microstructures in micro-LED displays 被引量:2
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作者 Shuli Wang Xuemin Kong +7 位作者 Siting Cai Yunshu Luo Yuxuan Gu Xiaotong Fan Guolong Chen Xiao Yang Zhong Chen Yue Lin 《Chinese Chemical Letters》 2025年第8期554-559,共6页
Super-fine electrohydrodynamic inkjet(SIJ)printing of perovskite nanocrystal(PNC)colloid ink exhibits significant potential in the fabrication of high-resolution color conversion microstructures arrays for fullcolor m... Super-fine electrohydrodynamic inkjet(SIJ)printing of perovskite nanocrystal(PNC)colloid ink exhibits significant potential in the fabrication of high-resolution color conversion microstructures arrays for fullcolor micro-LED displays.However,the impact of solvent on both the printing process and the morphology of SIJ-printed PNC color conversion microstructures remains underexplored.In this study,we prepared samples of CsPbBr3PNC colloid inks in various solvents and investigated the solvent's impact on SIJ printed PNC microstructures.Our findings reveal that the boiling point of the solvent is crucial to the SIJ printing process of PNC colloid inks.Only does the boiling point of the solvent fall in the optimal range,the regular positioned,micron-scaled,conical PNC microstructures can be successfully printed.Below this optimal range,the ink is unable to be ejected from the nozzle;while above this range,irregular positioned microstructures with nanoscale height and coffee-ring-like morphology are produced.Based on these observations,high-resolution color conversion PNC microstructures were effectively prepared using SIJ printing of PNC colloid ink dispersed in dimethylbenzene solvent. 展开更多
关键词 SOLVENT Perovskite nanocrystal Electrohydrodynamic inkjet printing Color conversion microstructures arrays Micro-LED display
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Fast full-color pathological imaging using Fourier ptychographic microscopy via closed-form model-based colorization 被引量:2
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作者 Yanqi Chen Jiurun Chen +4 位作者 Zhiping Wang Yuting Gao Yonghong He Yishi Shi An Pan 《Advanced Photonics Nexus》 2025年第2期7-16,共10页
Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution fo... Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution for high-throughput digital pathology,combining high resolution,large field of view,and extended depth of field(DOF).However,the full-color capabilities of FPM are hindered by coherent color artifacts and reduced computational efficiency,which significantly limits its practical applications.Color-transferbased FPM(CFPM)has emerged as a potential solution,theoretically reducing both acquisition and reconstruction threefold time.Yet,existing methods fall short of achieving the desired reconstruction speed and colorization quality.In this study,we report a generalized dual-color-space constrained model for FPM colorization.This model provides a mathematical framework for model-based FPM colorization,enabling a closed-form solution without the need for redundant iterative calculations.Our approach,termed generalized CFPM(gCFPM),achieves colorization within seconds for megapixel-scale images,delivering superior colorization quality in terms of both colorfulness and sharpness,along with an extended DOF.Both simulations and experiments demonstrate that gCFPM surpasses state-of-the-art methods across all evaluated criteria.Our work offers a robust and comprehensive workflow for high-throughput full-color pathological imaging using FPM platforms,laying a solid foundation for future advancements in methodology and engineering. 展开更多
关键词 Fourier ptychographic microscopy color transfer dual-color-space constrained model
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Identification and molecular marker development for peel color gene in melon(Cucumis melo L.) 被引量:1
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作者 Jian Ma Guoliang Yuan +4 位作者 Xinyang Xu Haijun Zhang Yanhong Qiu Congcong Li Huijun Zhang 《Journal of Integrative Agriculture》 2025年第7期2589-2600,共12页
Peel color is an important appearance quality of melons that significantly affects consumer preferences.In this study,a near-isogenic line NIL-G(dark green peel)was generated from B8(grey-green peel)and B15(white peel... Peel color is an important appearance quality of melons that significantly affects consumer preferences.In this study,a near-isogenic line NIL-G(dark green peel)was generated from B8(grey-green peel)and B15(white peel).The F_2 population constructed by crossing NIL-G and B15 was used to study the inheritance pattern of peel color,and bulked-segregant analysis sequencing(BSA-seq)was employed to identify the interval in which the target gene was located.Genetic analysis showed that a dominant gene controls the dark green peel trait at maturity.BSAseq and molecular markers were used to localize the candidate gene in a 263.7 kb interval of chromosome 4,which contained the CmAPRR2 gene with known functions.Moreover,allelic sequence analysis revealed four SNP variations of the CmAPRR2 gene in B15,of which SNP.G614331A was located at the junction of the 6th exon and 6th intron.The G-to-A mutation caused alternative splicing of the transcript of CmAPRR2 in B15,generating two transcripts(CmAPRR2-A and CmAPRR2-B)with premature termination codons.Furthermore,the Kompetitive Allele Specific PCR(KASP)marker,APRR2-G/A,was developed based on this SNP and shown to co-segregate with the peel color phenotype in the F_(2) population.Compared to white-peel B15,the expression level of CmAPRR2 in dark green peel NIL-G was higher at each growth stage.Therefore,CmAPRR2 may be the key gene controlling the fruit color of melons.This study identified a novel allelic variant of CmAPRR2 that leads to white peel formation in mature melons.We also provides a theoretical basis for further research on the gene regulatory mechanism of melon peel colors,which promotes using molecular marker-assisted selection to modify melon peel colors in the future. 展开更多
关键词 MELON BSA-seq MAPPING CmAPRR2 peel color KASP marker
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Why is supercritical fluid technology environmentally-friendly? 被引量:1
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作者 Zhong Mengxia 《China Textile》 2025年第1期22-22,共1页
Textile dyeing is a significant reason of colored wastewater.If this wastewater is discharged directly into natural water sources,it can be detrimental to the ecosystem.Supercritical anhydrous dyeing technology provid... Textile dyeing is a significant reason of colored wastewater.If this wastewater is discharged directly into natural water sources,it can be detrimental to the ecosystem.Supercritical anhydrous dyeing technology provides a solution to this challenge.Supercritical fluids possess both liquid and gaseous properties,enabling them to dissolve materials and penetrate substances. 展开更多
关键词 DYEING WASTEWATER COLORED
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Dynamic Structural Colors in Helical Superstructures:from Supramolecules to Polymers 被引量:1
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作者 Bo Ji Lang Qin Yan-Lei Yu 《Chinese Journal of Polymer Science》 2025年第3期406-428,共23页
Cholesteric liquid crystals(CLCs)exhibit unique helical superstructures that selectively reflect circularly polarized light,enabling them to dynamically respond to environmental changes with tunable structural colors.... Cholesteric liquid crystals(CLCs)exhibit unique helical superstructures that selectively reflect circularly polarized light,enabling them to dynamically respond to environmental changes with tunable structural colors.This dynamic color-changing capability is crucial for applications that require adaptable optical properties,positioning CLCs as key materials in advanced photonic technologies.This review focuses on the mechanisms of dynamic color tuning in CLCs across various forms,including small molecules,cholesteric liquid crystal elastomers(CLCEs),and cholesteric liquid crystal networks(CLCNs),and emphasizes the distinct responsive coloration each structure provides.Key developments in photochromic mechanisms based on azobenzene,dithienylethene,and molecular motor switches,are discussed for their roles in enhancing the stability and tuning range of CLCs.We examine the color-changing behaviors of CLCEs under mechanical stimuli and CLCNs under swelling,highlighting the advantages of each form.Following this,applications of dynamic color-tuning CLCs in information encryption,adaptive camouflage,and smart sensing technologies are explored.The review concludes with an outlook on current challenges and future directions in CLC research,particularly in biomimetic systems and dynamic photonic devices,aiming to broaden their functional applications and impact. 展开更多
关键词 Structural colors Cholesteric liquid crystals Elastomers Polymer network
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Nanograting‑Based Dynamic Structural Colors Using Heterogeneous Materials
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作者 Jingang Wang Haibo Yu +6 位作者 Jianchen Zheng Yuzhao Zhang Hongji Guo Ye Qiu Xiaoduo Wang Yongliang Yang Lianqing Liu 《Nano-Micro Letters》 SCIE EI CAS 2025年第3期138-151,共14页
Dynamic structuralcolors can change in response todifferent environmental stimuli.This ability remains effectiveeven when the size of the speciesresponsible for the structural coloris reduced to a few micrometers,prov... Dynamic structuralcolors can change in response todifferent environmental stimuli.This ability remains effectiveeven when the size of the speciesresponsible for the structural coloris reduced to a few micrometers,providing a promising sensingmechanism for solving microenvironmentalsensing problems inmicro-robotics and microfluidics.However, the lack of dynamicstructural colors that can encoderapidly, easily integrate, and accuratelyreflect changes in physical quantities hinders their use in microscale sensing applications. Herein, we present a 2.5-dimensionaldynamic structural color based on nanogratings of heterogeneous materials, which were obtained by interweaving a pH-responsive hydrogelwith an IP-L photoresist. Transverse gratings printed with pH-responsive hydrogels elongated the period of longitudinal grating in the swollenstate, resulting in pH-tuned structural colors at a 45° incidence. Moreover, the patterned encoding and array printing of dynamic structuralcolors were achieved using grayscale stripe images to accurately encode the periods and heights of the nanogrid structures. Overall, dynamicstructural color networks exhibit promising potential for applications in information encryption and in situ sensing for microfluidic chips. 展开更多
关键词 Dynamic structural colors Four-dimensional printing PH-RESPONSIVE Nanogrid Heterogeneous materials
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The telomere-to-telomere gap-free genome assembly of Juglans sigillata 被引量:1
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作者 Delu Ning Tao Wu +7 位作者 Wenlong Lei Shengcheng Zhang Ting Ma Li Pan Liangjun Xiao Noor-ul-Ain Xingtan Zhang Fuliang Cao 《Horticultural Plant Journal》 2025年第4期1551-1563,共13页
Juglans sigillata is an economically valuable nut crop renowned for its nutritional richness,including essential nutrients,antioxidants,and healthy fats,which boost human cardial,brain and gut health.Despite its impor... Juglans sigillata is an economically valuable nut crop renowned for its nutritional richness,including essential nutrients,antioxidants,and healthy fats,which boost human cardial,brain and gut health.Despite its importance,the lack of a complete genome assembly has been a stumbling block in its biological breeding process.Therefore,we generated deep coverage ultralong Oxford Nanopore Technology(ONT)and PacBio HiFi reads to construct a telomere-to-telomere(T2T)genome assembly.The final assembly spans 537.27 Mb with no gaps,demonstrating a remarkable completeness of 98.1%.We utilized a combination of transcriptome data and homologous proteins to annotate the genome,identifying 36018 protein-coding genes.Furthermore,we profiled global cytosine DNA methylations using ONT sequencing data.Global methylome analysis revealed high methylation levels in transposable element(TE)-rich chromosomal regions juxtaposed with comparatively lower methylation in gene-rich areas.By integrating a detailed multi-omics data analysis,we obtained valuable insights into the mechanism underlying endopleura coloration.This investigation led to the identification of eight candidate genes(e.g.ANR)involved in anthocyanin biosynthesis pathways,which are crucial for the development of color in plants.The comprehensive genome assembly and the understanding of the genetic basis of important traits like endopleura coloration will open avenues for more efficient breeding programs and improved crop quality. 展开更多
关键词 Juglans sigillata Telomere-to-telomere(T2T)genome assembly Global methylation Endopleura color
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