It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman s...It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.展开更多
Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDk...Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.展开更多
This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a trip...In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.展开更多
Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition d...Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.展开更多
In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a...In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.展开更多
Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is ...Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is contained in exactly λ triples. An S<sub>2</sub>（2, 3, v）is called a twofold triple system.展开更多
Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C....Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing （X, C, L） is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP（n）, is a resolvable k-cycle packing of Kn, （X, C, L）, in which the number of almost parallel classes is as large as possible. Let D（n, k） denote the number of almost parallel classes in a k-RMCP（n）. D（n, k） for k = 3, 4 has been decided. When n ≡ k （mod 2k） and k ≡1 （mod 2） or n ≡1 （mod 2k） and k e {6, 8, 10, 14} U{m： 5 ≤ m ≤ 49, m ≡1 （mod 2）}, D（n,k） also has been decided with few possible exceptions. In this paper, we shall decide D（n, 5） for all values of n ≥ 5.展开更多
In hypersonic boundary layers,the optimal disturbance is notably caused by normalmode instabilities,such as Mack second mode.However,recent experimental and numerical efforts have demonstrated the dominance of nonmoda...In hypersonic boundary layers,the optimal disturbance is notably caused by normalmode instabilities,such as Mack second mode.However,recent experimental and numerical efforts have demonstrated the dominance of nonmodal growth in hypersonic flows with the presence of moderate nose bluntness.In this study,resolvent analysis and parabolized stability equation analysis are performed to investigate the instabilities over a blunt-tip wedge.Main parameters include Mach number 5.9,unit Reynolds number 91.5×10~6/m,half wedge angle 5°,and nose radii ranging from 2.54 mm to 15.24 mm.Two novel growth patterns of travelling waves are identified to compete,whose nature is the intersection of the energy gain of optimal and sub-optimal disturbances.Pattern A with large spanwise wavelengths has the signature of slow energy amplification over a long distance which concentrates in the entropy layer.By contrast,pattern B with relatively small spanwise wavelengths presents rapid transient growth inside the boundary layer.A systematic study is performed on the growth/attenuation mechanism of disturbance patterns and the effects of wall temperature and nose radius.Wall cooling is found to be an alternative control strategy aimed at nonmodal instabilities.The receptivity to slow acoustic waves is considered when the effect of bluntness is studied.An estimated amplitude response favorably reproduces the reversal-like phenomenon.The lift-up/Orr mechanism analysis provides an explanation of energy growth for nonmodal responses.展开更多
Nonlinear energy transfer is represented through eddy viscosity and stochastic forcing within the framework of resolvent analysis.Previous investigations estimate the contribution of eddy-viscosity-enhanced resolvent ...Nonlinear energy transfer is represented through eddy viscosity and stochastic forcing within the framework of resolvent analysis.Previous investigations estimate the contribution of eddy-viscosity-enhanced resolvent opera-tor to nonlinear energy transfer.The present article estimates the contribution of stochastic forcing to nonlinear energy transfer and demonstrates that the contribution of stochastic forcing cannot be ignored.These results are achieved by numerically comparing the eddy-viscosity-enhanced resolvent operator and stochastic forcing with nonlinear energy transfer in turbulent channel flows.Furthermore,the numerical results indicate that composite resolvent operators can improve the prediction of nonlinear energy transfer.展开更多
Granulomatosis with polyangiitis(GPA)poses significant therapeutic challenges due to its susceptibility to concurrent infections and frequent relapses.Professor SHI Zaixiang proposed the therapeutic theory of lifting ...Granulomatosis with polyangiitis(GPA)poses significant therapeutic challenges due to its susceptibility to concurrent infections and frequent relapses.Professor SHI Zaixiang proposed the therapeutic theory of lifting depression and removing blood stasis,resolving phlegm and dispelling nodulation for GPA management.He identified the core pathogenesis as“Qi collapse with collateral obstruction and phlegm-stasis intermingling”,establishing the treatment principle of comprehensive intervention through ascending ancestral Qi,activating blood circulation,and resolving phlegm-stasis nodules.In clinical practice,Professor SHI emphasizes maintaining immune homeostasis with herbal medicine to enhance efficiency,while dynamically balancing Qi,blood,Yin,and Yang.Notably,he highlights the critical role of emotional factors in autoimmune disease progression.A representative case was provided to elucidate his clinical reasoning in GPA treatment.展开更多
In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theo...In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.展开更多
Recent advances in spatially resolved transcriptomics(SRT)have provided new opportunities for characterizing spatial structures of various tissues.Graph-based geometric deep learning has gained widespread adoption for...Recent advances in spatially resolved transcriptomics(SRT)have provided new opportunities for characterizing spatial structures of various tissues.Graph-based geometric deep learning has gained widespread adoption for spatial domain identification tasks.Currently,most methods define adjacency relation between cells or spots by their spatial distance in SRT data,which overlooks key biological interactions like gene expression similarities,and leads to inaccuracies in spatial domain identification.To tackle this challenge,we propose a novel method,SpaGRA(https://github.com/sunxue-yy/SpaGRA),for automatic multi-relationship construction based on graph augmentation.SpaGRA uses spatial distance as prior knowledge and dynamically adjusts edge weights with multi-head graph attention networks(GATs).This helps SpaGRA to uncover diverse node relationships and enhance message passing in geometric contrastive learning.Additionally,SpaGRA uses these multi-view relationships to construct negative samples,addressing sampling bias posed by random selection.Experimental results show that SpaGRA presents superior domain identification performance on multiple datasets generated from different protocols.Using SpaGRA,we analyze the functional regions in the mouse hypothalamus,identify key genes related to heart development in mouse embryos,and observe cancer-associated fibroblasts enveloping cancer cells in the latest Visium HD data.Overall,SpaGRA can effectively characterize spatial structures across diverse SRT datasets.展开更多
This work investigated the effects of grain size(GS)on individual slip mode activities and the corresponding Hall-Petch coefficients in a rolled basal-textured pure Mg sheet under uniaxial tension using statistical sl...This work investigated the effects of grain size(GS)on individual slip mode activities and the corresponding Hall-Petch coefficients in a rolled basal-textured pure Mg sheet under uniaxial tension using statistical slip trace analysis and electron backscatter diffraction.The studied regions covered a total of 1150 grains,in which 136 sets of slip traces were identified and analyzed in detail.The basalslip always dominated the deformation,whose frequencies decreased(from 81.0%to 62.5%)with increasing GS(from 10 to 85μm).The prismaticslip activity increased from 10.8%(10μm)to 27.5%(85μm),while that for pyramidal II<c+a>slip was almost constant.Critical resolved shear stress(CRSS)ratios were estimated based on the identified slip activity statistics,and then the Hall-Petch coefficients(k)of individual slip modes were calculated.The k value for prismaticslip(194 MPa·μm^(1/2))was lower than that for pyramidal II<c+a>slip(309 MPa·μm^(1/2)),which implies that pyramidal II<c+a>slip was more GS sensitive.Twinning activity exhibited a positive correlation with GS,though it remained limited partly due to the unfavorable loading direction.The macroscopic Hall-Petch relationship was divided into two regions,i.e.,the k value(753 MPa·μm^(1/2))for the coarse-grain region(30-85μm)was significantly larger than that(118 MPa·μm^(1/2))of the fine-grain region(10-30μm),which could be attributed to the transition of predominant deformation mechanisms from slip to slip combined twinning with increasing GS.This work provides detailed and quantitative experimental data of the GS effects on individual slip activities of Mg and provides new insights into the Hall-Petch relationship for individual slip modes.展开更多
Silicene,a silicon analog of graphene,holds promise for next-generation electronics due to its tunable bandgap and larger spin-orbit coupling.Despite extensive efforts to synthesize and characterize silicene on metal ...Silicene,a silicon analog of graphene,holds promise for next-generation electronics due to its tunable bandgap and larger spin-orbit coupling.Despite extensive efforts to synthesize and characterize silicene on metal substrates,bondresolved imaging of its atomic structure has remained elusive.Here,we report the fabrication and bond-resolved characterization of silicene on Au(111)substrate.Three silicene phases tuned by surface reconstruction and annealing temperatures are achieved.Using CO-terminated scanning tunneling microscopy(STM)tips,we resolve these silicene phases with atomic precision,determining their bond lengths,local strain,and geometric configurations.Furthermore,we correlate these structural features with their electronic properties,revealing the effect of strain and substrate interactions on the electronic properties of silicene.This work establishes silicene's intrinsic bonding topology and resolves longstanding controversies in silicene research.展开更多
文摘It was proved in this paper that there exists a labeled resolvable block design LRB (4,3; v ) if and only if v ≡0 (mod 4) and v ≥8, with 8 possible exceptions. It was also proved that there exists a nearly Kirkman system NKS (2,4; v ) if and only if v ≡0 (mod 12) and v ≥24, except possibly when v =264 or 372.
基金Natural Science Research Leading Item ofJiangsu (No.04 DJ110144) Natural Out-standing Younger Science Foundation(No.60225007)and Postdoctoral ScienceFoundation of China(No.20020248024)
文摘Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.
文摘This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
文摘In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.
基金Supported in part by the National Key R&D Program of China(No.2020YFA0712300)NSFC(No.61872353)。
文摘Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.
基金the National Natural Science Foundation of China(No.10671055)Natural Science Foundation of Hebei(No.A2007000230)
文摘In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONA triple system S<sub>λ</sub>（2, 3, v）is an ordered pair （V,）, where Vis a v-set, is a collection of 3-subsets （called triples ） of V such that each pair of distinct dements of V is contained in exactly λ triples. An S<sub>2</sub>（2, 3, v）is called a twofold triple system.
文摘Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple （X, C, L）, where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing （X, C, L） is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP（n）, is a resolvable k-cycle packing of Kn, （X, C, L）, in which the number of almost parallel classes is as large as possible. Let D（n, k） denote the number of almost parallel classes in a k-RMCP（n）. D（n, k） for k = 3, 4 has been decided. When n ≡ k （mod 2k） and k ≡1 （mod 2） or n ≡1 （mod 2k） and k e {6, 8, 10, 14} U{m： 5 ≤ m ≤ 49, m ≡1 （mod 2）}, D（n,k） also has been decided with few possible exceptions. In this paper, we shall decide D（n, 5） for all values of n ≥ 5.
基金supported by the Hong Kong Research Grants Council(Nos.15216621,15204322,25203721)the National Natural Science Foundation of China(No.12102377)。
文摘In hypersonic boundary layers,the optimal disturbance is notably caused by normalmode instabilities,such as Mack second mode.However,recent experimental and numerical efforts have demonstrated the dominance of nonmodal growth in hypersonic flows with the presence of moderate nose bluntness.In this study,resolvent analysis and parabolized stability equation analysis are performed to investigate the instabilities over a blunt-tip wedge.Main parameters include Mach number 5.9,unit Reynolds number 91.5×10~6/m,half wedge angle 5°,and nose radii ranging from 2.54 mm to 15.24 mm.Two novel growth patterns of travelling waves are identified to compete,whose nature is the intersection of the energy gain of optimal and sub-optimal disturbances.Pattern A with large spanwise wavelengths has the signature of slow energy amplification over a long distance which concentrates in the entropy layer.By contrast,pattern B with relatively small spanwise wavelengths presents rapid transient growth inside the boundary layer.A systematic study is performed on the growth/attenuation mechanism of disturbance patterns and the effects of wall temperature and nose radius.Wall cooling is found to be an alternative control strategy aimed at nonmodal instabilities.The receptivity to slow acoustic waves is considered when the effect of bluntness is studied.An estimated amplitude response favorably reproduces the reversal-like phenomenon.The lift-up/Orr mechanism analysis provides an explanation of energy growth for nonmodal responses.
基金supported by the National Natural Science Foundation of China(NSFC)Basic Science Center Program for Multiscale Problems in Nonlinear Mechanics(Grant No.11988102).
文摘Nonlinear energy transfer is represented through eddy viscosity and stochastic forcing within the framework of resolvent analysis.Previous investigations estimate the contribution of eddy-viscosity-enhanced resolvent opera-tor to nonlinear energy transfer.The present article estimates the contribution of stochastic forcing to nonlinear energy transfer and demonstrates that the contribution of stochastic forcing cannot be ignored.These results are achieved by numerically comparing the eddy-viscosity-enhanced resolvent operator and stochastic forcing with nonlinear energy transfer in turbulent channel flows.Furthermore,the numerical results indicate that composite resolvent operators can improve the prediction of nonlinear energy transfer.
基金supported by the Seventh Batch of National Academic Experience Inheritance Project for Senior TCM Experts from the National Administration of Traditional Chinese Medicine(No.GZYRJS[2022]76)the Sixth Batch of Beijing Municipal Academic Experience Inheritance Project for TCM Experts from Beijing Administration of Traditional Chinese Medicine(No.JZYKZ[2019]139).
文摘Granulomatosis with polyangiitis(GPA)poses significant therapeutic challenges due to its susceptibility to concurrent infections and frequent relapses.Professor SHI Zaixiang proposed the therapeutic theory of lifting depression and removing blood stasis,resolving phlegm and dispelling nodulation for GPA management.He identified the core pathogenesis as“Qi collapse with collateral obstruction and phlegm-stasis intermingling”,establishing the treatment principle of comprehensive intervention through ascending ancestral Qi,activating blood circulation,and resolving phlegm-stasis nodules.In clinical practice,Professor SHI emphasizes maintaining immune homeostasis with herbal medicine to enhance efficiency,while dynamically balancing Qi,blood,Yin,and Yang.Notably,he highlights the critical role of emotional factors in autoimmune disease progression.A representative case was provided to elucidate his clinical reasoning in GPA treatment.
基金Supported by Shandong University of Finance and Economics 2023 International Collaborative Projectsthe National Natural Science Foundation of China(Grant No.62073190)。
文摘In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.
基金supported by the National Natural Science Foundation of China(Nos.62303271,U1806202,62103397)the Natural Science Foundation of Shandong Province(ZR2023QF081)Funding for open access charge:the National Natural Science Foundation of China(Nos.62303271,U1806202).
文摘Recent advances in spatially resolved transcriptomics(SRT)have provided new opportunities for characterizing spatial structures of various tissues.Graph-based geometric deep learning has gained widespread adoption for spatial domain identification tasks.Currently,most methods define adjacency relation between cells or spots by their spatial distance in SRT data,which overlooks key biological interactions like gene expression similarities,and leads to inaccuracies in spatial domain identification.To tackle this challenge,we propose a novel method,SpaGRA(https://github.com/sunxue-yy/SpaGRA),for automatic multi-relationship construction based on graph augmentation.SpaGRA uses spatial distance as prior knowledge and dynamically adjusts edge weights with multi-head graph attention networks(GATs).This helps SpaGRA to uncover diverse node relationships and enhance message passing in geometric contrastive learning.Additionally,SpaGRA uses these multi-view relationships to construct negative samples,addressing sampling bias posed by random selection.Experimental results show that SpaGRA presents superior domain identification performance on multiple datasets generated from different protocols.Using SpaGRA,we analyze the functional regions in the mouse hypothalamus,identify key genes related to heart development in mouse embryos,and observe cancer-associated fibroblasts enveloping cancer cells in the latest Visium HD data.Overall,SpaGRA can effectively characterize spatial structures across diverse SRT datasets.
基金supported by the National Natural Science Foundation of China(No.52171125)the Sichuan Science and Technology Program(No.2024NSFSC0193).
文摘This work investigated the effects of grain size(GS)on individual slip mode activities and the corresponding Hall-Petch coefficients in a rolled basal-textured pure Mg sheet under uniaxial tension using statistical slip trace analysis and electron backscatter diffraction.The studied regions covered a total of 1150 grains,in which 136 sets of slip traces were identified and analyzed in detail.The basalslip always dominated the deformation,whose frequencies decreased(from 81.0%to 62.5%)with increasing GS(from 10 to 85μm).The prismaticslip activity increased from 10.8%(10μm)to 27.5%(85μm),while that for pyramidal II<c+a>slip was almost constant.Critical resolved shear stress(CRSS)ratios were estimated based on the identified slip activity statistics,and then the Hall-Petch coefficients(k)of individual slip modes were calculated.The k value for prismaticslip(194 MPa·μm^(1/2))was lower than that for pyramidal II<c+a>slip(309 MPa·μm^(1/2)),which implies that pyramidal II<c+a>slip was more GS sensitive.Twinning activity exhibited a positive correlation with GS,though it remained limited partly due to the unfavorable loading direction.The macroscopic Hall-Petch relationship was divided into two regions,i.e.,the k value(753 MPa·μm^(1/2))for the coarse-grain region(30-85μm)was significantly larger than that(118 MPa·μm^(1/2))of the fine-grain region(10-30μm),which could be attributed to the transition of predominant deformation mechanisms from slip to slip combined twinning with increasing GS.This work provides detailed and quantitative experimental data of the GS effects on individual slip activities of Mg and provides new insights into the Hall-Petch relationship for individual slip modes.
基金Project supported by the National Natural Science Foundation of China(Grant No.12474181)the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2021B0301030002 and 2024A1515010656)the Guangdong Science and Technology Project(Grant No.2021QN02X859)。
文摘Silicene,a silicon analog of graphene,holds promise for next-generation electronics due to its tunable bandgap and larger spin-orbit coupling.Despite extensive efforts to synthesize and characterize silicene on metal substrates,bondresolved imaging of its atomic structure has remained elusive.Here,we report the fabrication and bond-resolved characterization of silicene on Au(111)substrate.Three silicene phases tuned by surface reconstruction and annealing temperatures are achieved.Using CO-terminated scanning tunneling microscopy(STM)tips,we resolve these silicene phases with atomic precision,determining their bond lengths,local strain,and geometric configurations.Furthermore,we correlate these structural features with their electronic properties,revealing the effect of strain and substrate interactions on the electronic properties of silicene.This work establishes silicene's intrinsic bonding topology and resolves longstanding controversies in silicene research.
