AIM:To investigate the effect of pentagonal conjunctival autograft on reducing graft retraction following pterygium surgery.METHODS:This retrospective comparative study included patients who underwent primary pterygiu...AIM:To investigate the effect of pentagonal conjunctival autograft on reducing graft retraction following pterygium surgery.METHODS:This retrospective comparative study included patients who underwent primary pterygium excision with either pentagonal(created by shaping the junction with the recipient conjunctiva into a wedge)or quadrangular conjunctival autograft transplantation.All patients completed a 6mo postoperative follow-up.The primary outcome measure was the incidence of graft retraction;secondary outcomes included graft displacement requiring re-suturing and pterygium recurrence rate.RESULTS:The study enrolled 58 participants,comprising 26(15 males,11 females)in the pentagonal graft group(mean age:54.9±13.1y),and 32(17 males,15 females)in the quadrangular graft group(mean age:57.6±10.4y).Graft retraction occurred in only 1 eye(3.8%)in the pentagonal autograft group,compared to 9 eyes(28.1%)in the quadrangular autograft group.No cases of graft displacement requiring re-suturing were reported in the pentagonal autograft group.Although graft displacement and recurrence requiring re-suturing were observed less frequently in surgeries with a pentagonal graft,the difference was not statistically significant(P>0.05).CONCLUSION:Designing the conjunctival autograft in a pentagonal shape—mimicking geodesic dome architecture and conforming to the eye’s spherical structure—enhances compatibility with the recipient conjunctiva and improves resistance to physical traction forces.This design effectively reduces the incidence of graft retraction and other related complications,providing a more favorable surgical option for pterygium treatment.展开更多
Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modelingarbitrary shapes compared to triangles.In this study,a pentagonal membrane element was developed wit...Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modelingarbitrary shapes compared to triangles.In this study,a pentagonal membrane element was developed with thestrain approach for the first time.The element possesses invariance,and the equilibrium constraint was appliedto the assumed strain field using corrective coefficients.Inspired by the advancing front technique,a pentagonalmesh was generated,and the mesh quality was enhanced with Laplacian smoothing.The performance of thedeveloped pentagonal element was assessed in a few numerical tests,and the results revealed its suitability inmodeling the bending of beams.Besides,the numerical results are enhanced when pentagonal elements are usedin mesh transitions along boundaries to smoothen curved edges and capture distributed loads.展开更多
为了解决Duval Pentagon1法不能表征各种变压器故障模式可信度的问题,提出了一种基于空间分析理论改进的方法。首先,采用核密度估计(kernel density estimation,KDE)方法对各种变压器故障模式数据进行空间分布密度分析;其次,应用B样条...为了解决Duval Pentagon1法不能表征各种变压器故障模式可信度的问题,提出了一种基于空间分析理论改进的方法。首先,采用核密度估计(kernel density estimation,KDE)方法对各种变压器故障模式数据进行空间分布密度分析;其次,应用B样条理论构造各种变压器故障模式密度曲面;最后,利用空间叠置分析方法实现变压器故障模式识别。实例分析结果表明:与Duval Pentagon1法相比,改进后的Duval Pentagon1法的总体诊断准确率提升了8.42%,并且能够定量地表征各种变压器故障模式可信度。研究结果可为变压器油中溶解气体图形分析方法的改进提供参考。展开更多
The petroleum industry has a complex,inflexible and challenging supply chain(SC)that impacts both the national economy as well as people’s daily lives with a range of services,including transportation,heating,electri...The petroleum industry has a complex,inflexible and challenging supply chain(SC)that impacts both the national economy as well as people’s daily lives with a range of services,including transportation,heating,electricity,lubricants,as well as chemicals and petrochemicals.In the petroleum industry,supply chain management presents several challenges,especially in the logistics sector,that are not found in other industries.In addition,logistical challenges contribute significantly to the cost of oil.Uncertainty regarding customer demand and supply significantly affects SC networks.Hence,SC flexibility can be maintained by addressing uncertainty.On the other hand,in the real world,decision-making challenges are often ambiguous or vague.In some cases,measurements are incorrect owing to measurement errors,instrument faults,etc.,which lead to a pentagonal fuzzy number(PFN)which is the extension of a fuzzy number.Therefore,it is necessary to develop quantitative models to optimize logistics operations and supply chain networks.This study proposed a linear programming model under an uncertain environment.The model minimizes the cost along the refineries,depots,multimode transport and demand nodes.Further developed pentagonal fuzzy optimization,an alternative approach is developed to solve the downstream supply chain using themixed-integer linear programming(MILP)model to obtain a feasible solution to the fuzzy transportation cost problem.In this model,the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number.Furthermore,defuzzification is performed using an accuracy function.To validate the model and technique and feasibility solution,an illustrative example of the oil and gas SC is considered,providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.展开更多
In this study, the effective resistance between any two lattice sites in a two-dimensional pentagonal lattice structure of identical resistors is determined by means of the lattice Green’s function method.Some numeri...In this study, the effective resistance between any two lattice sites in a two-dimensional pentagonal lattice structure of identical resistors is determined by means of the lattice Green’s function method.Some numerical results of the resistance for small separations between lattice sites are presented.展开更多
Intrinsic topological defect engineering has been proven as a promising strategy to elevate the electrocatalytic activity of carbon materials.However,the controllable construction of high-density and specific topologi...Intrinsic topological defect engineering has been proven as a promising strategy to elevate the electrocatalytic activity of carbon materials.However,the controllable construction of high-density and specific topological defects in carbon frameworks to reveal the relationship between reactivity and defect structure remains a challenging task.Herein,the intrinsic pentagon carbon sites that can favor electron overflow and enhance their binding affinity towards the intermediates of catalytic reaction are firstly presented by the work function and the p-band center calculations.To experimentally verify this,the cage-opening reaction of fullerene is proposed and utilized for synthesizing carbon quantum dots with specific pentagon configuration(CQDs-P),subsequently utilizing CQDs-P to modulate the micro-scale defect density of three-dimensional reduced graphene oxide(rGO)viaπ-πinteractions.The multiple spatial-scale rGO-conjugated CQDs-P structure simultaneously possesses abundant pentagon and edge defects as catalytic active sites and long-range-orderedπelectron delocalization system as conductive network.The defects-rich CQDs-P/rGO-4 all-carbon-based catalyst exhibits superb catalytic activity for triiodide reduction reaction with a high photoelectric conversion efficiency of 8.40%,superior to the Pt reference(7.97%).Theoretical calculations suggest that pentagon defects in the carbon frameworks can promote charge transfer and modulate the adsorption/dissociation behavior of the reaction intermediates,thus enhancing the electrocatalytic activity of the catalyst.This work confirms the role of intrinsic pentagon defects in catalytic reactions and provides a new insight into the synthesis of defects-rich carbon catalysts.展开更多
This paper describes the multiband behaviour as well as the response for dielectric loading of a pentagonal fractal patch antenna designed at frequency f = 2.45 GHz. The proposed antenna shape has been obtained by int...This paper describes the multiband behaviour as well as the response for dielectric loading of a pentagonal fractal patch antenna designed at frequency f = 2.45 GHz. The proposed antenna shape has been obtained by introducing slots in a pentagonal patch antenna up to second iteration. Detailed design steps and results of the designs are studied and investigated in this paper. Simulated and measured results reveal that the antenna will be operated at three different frequency bands—2.17 GHz, 3.56 GHz, and 7.93 GHz with acceptable performances (i.e. VSWR < 2). The measured results for the antennas are in good agreement with simulated results. The proposed antenna maintains good radiation pattern with gain. However dielectric loading increases its radiation efficiency at the cost of significant decrease in gain and directivity.展开更多
In this paper the percolation behavior with a specific concentration of the defects was discussed on the twodimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degre...In this paper the percolation behavior with a specific concentration of the defects was discussed on the twodimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice.展开更多
Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configu...Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with a concave pentagonal base in 7-body problems are proved and the range of the ratio between radius and half-height is obtained, within which the 7 bodies involved form a central configuration or form uniquely a central configuration.展开更多
Microscope observations of normal human ke- ratinocytes (NHK) propagated in a serum-free medium reveal a high frequency (>70%) of pentagonally-shaped colonies over a wide range of colony sizes that persist over man...Microscope observations of normal human ke- ratinocytes (NHK) propagated in a serum-free medium reveal a high frequency (>70%) of pentagonally-shaped colonies over a wide range of colony sizes that persist over many sequential cell generations. NHK colonies derived from sin- gle cell isolates also display pentagonal symme- try as confirmed by a photographic technique known as “Markham Rotation”. The generality of pentagonal cellular morphology was extended to observations in situ of pentagonally-shaped basal layer epidermal cells of normal human epidermis, monolayer cultures of normal and immortalized keratinocytes, several different ch- ick embryo cells, and in previously published photographs. Statistical methods were applied that differentiate planar close-packing of polygonal configurations observed in living cellular system from several examples of non-living cellular aggregates that were produced spontaneously in nature or in the laboratory under defined physico-chemical conditions.展开更多
Two-dimensional planar pentagonal crystals,long pursued for their geometrically frustrated lattice configurations and emergent quantum phenomena,have remained challenging to realize due to the intrinsic incompatibilit...Two-dimensional planar pentagonal crystals,long pursued for their geometrically frustrated lattice configurations and emergent quantum phenomena,have remained challenging to realize due to the intrinsic incompatibility of regular pentagons with Euclidean tiling.Here,we unveil 37 dynamically stable binary planar pentagonal monolayers through high-throughput computational screening of 1470 stoichiometric candidates.These materials exhibit room-temperature magnetism,including ferromagnetic(Curie temperature(T_(C))up to 521 K),antiferromagnetic(Néel temperature(T_(N))up to 761 K),and altermagnetic(TN=984 K)ground states,alongside unprecedented electronic states:Dirac semimetals,Dirac half-metal,nodal-loop semimetal,nodal-loop half-metal,and altermagnetic semiconductors(Mn_(4)N_(2))with giant spin splitting(0.78 eV).The latter achieves pure spin-polarized transport windows(-0.04 to 0.36 eV)and strain-tunable valley splitting(18.2 meV under 4%uniaxial strain).Intrinsic type-Ⅱ multiferroicity emerges in Fe_(4)C_(2) and Mn_(4)C_(2),featuring in-plane electric polarization(1.4 and 1.6 pC/m),ferroelasticity(0.8%and 1.2%reversible strain),and reversal chirality.Topological band analysis identifies chiral edge states in Dirac semimetal pentagons,alongside a magnetic topological insulator with Chern number|C|=2 in Mo_(2)S_(4) and W_(2)Te_(4).Temperature-driven structural transitions in Os_(2)S_(4) and Tc_(2)S_(4) from pentagonal to Lieb lattices accompany topological state switching and metal-to-semiconductor transitions.This work establishes pentagonal lattices as a platform for symmetry-driven multifunctionality,bridging geometric frustration with applications in spintronics,nanoelectronics,and quantum devices.展开更多
The synthesis of nonbenzenoid nanographenes(NGs)with a high density of nonhexagonal rings remains a significant challenge,leaving this structural class largely unexplored.In this work,we report the efficient synthesis...The synthesis of nonbenzenoid nanographenes(NGs)with a high density of nonhexagonal rings remains a significant challenge,leaving this structural class largely unexplored.In this work,we report the efficient synthesis of a novel nonbenzenoid isomer of decacyclene,namely cyclopenta[cd]azulene trimer(CPAT),derived from the natural product guaiazulene.The key step involves an acid–base bufferassisted cyclotrimerization of cyclopenta[cd]azulen-2(1H)-one that can be further extended to produce halogenated derivative,enabling structural tunability.The resulting molecules feature a unique backbone comprising nine nonhexagonal rings arranged around a central benzenoid core,representing the highest pentagon–heptagon ring density among all reportedπ-extended NGs with ten or more fused rings.Compared to the pristine decacyclene,the synthesized compounds exhibit excellent ambient stability,narrower bandgaps,and distinct aromaticity profiles.Moreover,femtosecond transient absorption measurements of CPAT-a reveal an ultrafast singlet-state relaxation(∼14 ps),significantly shorter than that of decacyclene,highlighting the pronounced impact of nonbenzenoid topology on excited-state dynamics.This study introduces a new family of nonbenzenoid NGs and paves the way for the synthesis of newsp2 carbon allotrope featuring exclusively nonhexagonal ring systems.展开更多
The Turán number, denoted by ex (n, H), is the maximum number of edges of a graph on n vertices containing no graph H as a subgraph. Denote by kCℓ the union of k vertex-disjoint copies of Cℓ. In this paper, we pr...The Turán number, denoted by ex (n, H), is the maximum number of edges of a graph on n vertices containing no graph H as a subgraph. Denote by kCℓ the union of k vertex-disjoint copies of Cℓ. In this paper, we present new results for the Turán numbers of vertex-disjoint cycles. Our first results deal with the Turán number of vertex-disjoint triangles ex (n, kC_(3)). We determine the Turán number ex(n, kC_(3)) for n≥k^(2)+5k/2 when k ≤ 4, and n ≥ k^(2) + 2 when k ≥ 4. Moreover, we give lower and upper bounds for ex (n, kC_(3)) with 3k≤n≤k^(2)+5k/2 when k ≤ 4, and 3k ≤ n ≤ k^(2) + 2 when k ≥ 4. Next, we give a lower bound for the Turán number of vertex-disjoint pentagons ex (n, kC_(5)). Finally, we determine the Turán number ex (n, kC_(5)) for n = 5k, and propose two conjectures for ex (n, kC_(5)) for the other values of n.展开更多
Single-crystal graphene domains grown by chemical vapor deposition （CVD） intrinsically tend to have a six-fold symmetry; however, several factors can influence the growth kinetics, which can in turn lead to the form...Single-crystal graphene domains grown by chemical vapor deposition （CVD） intrinsically tend to have a six-fold symmetry; however, several factors can influence the growth kinetics, which can in turn lead to the formation of graphene with different shapes. Here we report the growth of oriented large-area pentagonal single-crystal graphene domains on Cu foils by CVD. We found that high-index Cu planes contributed selectively to the formation of pentagonal graphene. Our results indicated that lattice steps present on the crystalline surface of the underlying Cu promoted graphene growth in the direction perpendicular to the steps and finally led to the disappearance of one of the edges forming a pentagon. In addition, hydrogen promoted the formation of pentagonal domains. This work provides new insights into the mechanism of graphene growth.展开更多
Magnetism has revolutionized important technologies,and continues to bring forth new phenomena in emergent materials and reduced dimensions.Here,using first-principles calculations,we demonstrate that the already-synt...Magnetism has revolutionized important technologies,and continues to bring forth new phenomena in emergent materials and reduced dimensions.Here,using first-principles calculations,we demonstrate that the already-synthesized two-dimensional(2D)Ni-tetracyanoquinodimethane(Ni_(2)(TCNQ)_(2))lattice is a stable ferromagnetism material with multiple spin-polarized Dirac cones.The conical bands in proximity of the Fermi level can be tuned by external tensile strain and show the fourfold degenerate electronic states at the critical tensile strain of~2.35%,whose energy dispersion is consistent with 2D Cairo pentagonal lattice.In addition,spin-orbital coupling can open a band gap at the Dirac point of A,leading to topologically nontrivial electronic states characterized by the non-zero Chern number and the edge states of nanoribbon.Our results offer versatile platforms for the realization of massless spintronics with full-spin polarization in 2D Cairo pentagonal Ni_(2)(TCNQ)_(2) Lattice.展开更多
Two-dimensional(2D)magnetic crystals have been extensively explored thanks to their potential applications in spintronics,valleytronics,and topological superconductivity.Here we report a novel monolayer magnet,namely ...Two-dimensional(2D)magnetic crystals have been extensively explored thanks to their potential applications in spintronics,valleytronics,and topological superconductivity.Here we report a novel monolayer magnet,namely puckered pentagonal VTe_(2)(PP-VTe_(2)),intriguing atomic and electronic structures of which were firmly validated from first-principles calculations.The PP-VTe_(2) exhibits strong intrinsic ferromagnetism and semiconducting property distinct from the half-metallic bulk pyrite VTe_(2)(BP-VTe_(2))phase.An unusual magnetic anisotropy with large magnetic exchange energies is found.More interestingly,the multiferroic coupling between its 2D ferroelasticity and in-plane magnetization is further identified in PP-VTe_(2),lending it unprecedented controllability with external strains and electric fields.Serving as an emergent 2D ferromagnetic semiconductor with a novel crystal structure,monolayer PP-VTe_(2) provides an ideal platform for exploring exotic crystalline and spin configurations in low-dimensional systems.展开更多
文摘AIM:To investigate the effect of pentagonal conjunctival autograft on reducing graft retraction following pterygium surgery.METHODS:This retrospective comparative study included patients who underwent primary pterygium excision with either pentagonal(created by shaping the junction with the recipient conjunctiva into a wedge)or quadrangular conjunctival autograft transplantation.All patients completed a 6mo postoperative follow-up.The primary outcome measure was the incidence of graft retraction;secondary outcomes included graft displacement requiring re-suturing and pterygium recurrence rate.RESULTS:The study enrolled 58 participants,comprising 26(15 males,11 females)in the pentagonal graft group(mean age:54.9±13.1y),and 32(17 males,15 females)in the quadrangular graft group(mean age:57.6±10.4y).Graft retraction occurred in only 1 eye(3.8%)in the pentagonal autograft group,compared to 9 eyes(28.1%)in the quadrangular autograft group.No cases of graft displacement requiring re-suturing were reported in the pentagonal autograft group.Although graft displacement and recurrence requiring re-suturing were observed less frequently in surgeries with a pentagonal graft,the difference was not statistically significant(P>0.05).CONCLUSION:Designing the conjunctival autograft in a pentagonal shape—mimicking geodesic dome architecture and conforming to the eye’s spherical structure—enhances compatibility with the recipient conjunctiva and improves resistance to physical traction forces.This design effectively reduces the incidence of graft retraction and other related complications,providing a more favorable surgical option for pterygium treatment.
基金supported by the Research Management Centre(RMC)of Multimedia University,Malaysia(Grant No.MMUI/220016).
文摘Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modelingarbitrary shapes compared to triangles.In this study,a pentagonal membrane element was developed with thestrain approach for the first time.The element possesses invariance,and the equilibrium constraint was appliedto the assumed strain field using corrective coefficients.Inspired by the advancing front technique,a pentagonalmesh was generated,and the mesh quality was enhanced with Laplacian smoothing.The performance of thedeveloped pentagonal element was assessed in a few numerical tests,and the results revealed its suitability inmodeling the bending of beams.Besides,the numerical results are enhanced when pentagonal elements are usedin mesh transitions along boundaries to smoothen curved edges and capture distributed loads.
文摘The petroleum industry has a complex,inflexible and challenging supply chain(SC)that impacts both the national economy as well as people’s daily lives with a range of services,including transportation,heating,electricity,lubricants,as well as chemicals and petrochemicals.In the petroleum industry,supply chain management presents several challenges,especially in the logistics sector,that are not found in other industries.In addition,logistical challenges contribute significantly to the cost of oil.Uncertainty regarding customer demand and supply significantly affects SC networks.Hence,SC flexibility can be maintained by addressing uncertainty.On the other hand,in the real world,decision-making challenges are often ambiguous or vague.In some cases,measurements are incorrect owing to measurement errors,instrument faults,etc.,which lead to a pentagonal fuzzy number(PFN)which is the extension of a fuzzy number.Therefore,it is necessary to develop quantitative models to optimize logistics operations and supply chain networks.This study proposed a linear programming model under an uncertain environment.The model minimizes the cost along the refineries,depots,multimode transport and demand nodes.Further developed pentagonal fuzzy optimization,an alternative approach is developed to solve the downstream supply chain using themixed-integer linear programming(MILP)model to obtain a feasible solution to the fuzzy transportation cost problem.In this model,the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number.Furthermore,defuzzification is performed using an accuracy function.To validate the model and technique and feasibility solution,an illustrative example of the oil and gas SC is considered,providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.
文摘In this study, the effective resistance between any two lattice sites in a two-dimensional pentagonal lattice structure of identical resistors is determined by means of the lattice Green’s function method.Some numerical results of the resistance for small separations between lattice sites are presented.
基金partly supported by the National Natural Science Foundation of China(22078052)the National Key R&D Program of China(2022YFB4101602)the Fundamental Research Funds for the Central Universities(DUT22LAB612)。
文摘Intrinsic topological defect engineering has been proven as a promising strategy to elevate the electrocatalytic activity of carbon materials.However,the controllable construction of high-density and specific topological defects in carbon frameworks to reveal the relationship between reactivity and defect structure remains a challenging task.Herein,the intrinsic pentagon carbon sites that can favor electron overflow and enhance their binding affinity towards the intermediates of catalytic reaction are firstly presented by the work function and the p-band center calculations.To experimentally verify this,the cage-opening reaction of fullerene is proposed and utilized for synthesizing carbon quantum dots with specific pentagon configuration(CQDs-P),subsequently utilizing CQDs-P to modulate the micro-scale defect density of three-dimensional reduced graphene oxide(rGO)viaπ-πinteractions.The multiple spatial-scale rGO-conjugated CQDs-P structure simultaneously possesses abundant pentagon and edge defects as catalytic active sites and long-range-orderedπelectron delocalization system as conductive network.The defects-rich CQDs-P/rGO-4 all-carbon-based catalyst exhibits superb catalytic activity for triiodide reduction reaction with a high photoelectric conversion efficiency of 8.40%,superior to the Pt reference(7.97%).Theoretical calculations suggest that pentagon defects in the carbon frameworks can promote charge transfer and modulate the adsorption/dissociation behavior of the reaction intermediates,thus enhancing the electrocatalytic activity of the catalyst.This work confirms the role of intrinsic pentagon defects in catalytic reactions and provides a new insight into the synthesis of defects-rich carbon catalysts.
文摘This paper describes the multiband behaviour as well as the response for dielectric loading of a pentagonal fractal patch antenna designed at frequency f = 2.45 GHz. The proposed antenna shape has been obtained by introducing slots in a pentagonal patch antenna up to second iteration. Detailed design steps and results of the designs are studied and investigated in this paper. Simulated and measured results reveal that the antenna will be operated at three different frequency bands—2.17 GHz, 3.56 GHz, and 7.93 GHz with acceptable performances (i.e. VSWR < 2). The measured results for the antennas are in good agreement with simulated results. The proposed antenna maintains good radiation pattern with gain. However dielectric loading increases its radiation efficiency at the cost of significant decrease in gain and directivity.
文摘In this paper the percolation behavior with a specific concentration of the defects was discussed on the twodimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice.
基金Natural Science Foundation of China (No.19871096)
文摘Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with a concave pentagonal base in 7-body problems are proved and the range of the ratio between radius and half-height is obtained, within which the 7 bodies involved form a central configuration or form uniquely a central configuration.
文摘Microscope observations of normal human ke- ratinocytes (NHK) propagated in a serum-free medium reveal a high frequency (>70%) of pentagonally-shaped colonies over a wide range of colony sizes that persist over many sequential cell generations. NHK colonies derived from sin- gle cell isolates also display pentagonal symme- try as confirmed by a photographic technique known as “Markham Rotation”. The generality of pentagonal cellular morphology was extended to observations in situ of pentagonally-shaped basal layer epidermal cells of normal human epidermis, monolayer cultures of normal and immortalized keratinocytes, several different ch- ick embryo cells, and in previously published photographs. Statistical methods were applied that differentiate planar close-packing of polygonal configurations observed in living cellular system from several examples of non-living cellular aggregates that were produced spontaneously in nature or in the laboratory under defined physico-chemical conditions.
基金supported by the National Natural Science Foundation of China (22225301, 22303092)the Anhui Provincial Natural Science Foundation (2308085QB51)+4 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0450101)the Fundamental Research Funds for the Central Universities (WK9990000153)the Innovation Program for Quantum Science and Technology (2021ZD0303302)the Supercomputing Centers of both the University of Science and Technology of China (USTCSCC)the Chinese Academy of Sciences (SCCAS)。
文摘Two-dimensional planar pentagonal crystals,long pursued for their geometrically frustrated lattice configurations and emergent quantum phenomena,have remained challenging to realize due to the intrinsic incompatibility of regular pentagons with Euclidean tiling.Here,we unveil 37 dynamically stable binary planar pentagonal monolayers through high-throughput computational screening of 1470 stoichiometric candidates.These materials exhibit room-temperature magnetism,including ferromagnetic(Curie temperature(T_(C))up to 521 K),antiferromagnetic(Néel temperature(T_(N))up to 761 K),and altermagnetic(TN=984 K)ground states,alongside unprecedented electronic states:Dirac semimetals,Dirac half-metal,nodal-loop semimetal,nodal-loop half-metal,and altermagnetic semiconductors(Mn_(4)N_(2))with giant spin splitting(0.78 eV).The latter achieves pure spin-polarized transport windows(-0.04 to 0.36 eV)and strain-tunable valley splitting(18.2 meV under 4%uniaxial strain).Intrinsic type-Ⅱ multiferroicity emerges in Fe_(4)C_(2) and Mn_(4)C_(2),featuring in-plane electric polarization(1.4 and 1.6 pC/m),ferroelasticity(0.8%and 1.2%reversible strain),and reversal chirality.Topological band analysis identifies chiral edge states in Dirac semimetal pentagons,alongside a magnetic topological insulator with Chern number|C|=2 in Mo_(2)S_(4) and W_(2)Te_(4).Temperature-driven structural transitions in Os_(2)S_(4) and Tc_(2)S_(4) from pentagonal to Lieb lattices accompany topological state switching and metal-to-semiconductor transitions.This work establishes pentagonal lattices as a platform for symmetry-driven multifunctionality,bridging geometric frustration with applications in spintronics,nanoelectronics,and quantum devices.
基金supported by the EU Graphene Flagship(Graphene Core 3,881603)EIC-2022-Pathfinder Open(ATYPIQUAL,101099098)+3 种基金the Center for Advancing Electronics Dresden(cfaed)the National Natural Science Foundation of China for funding(grant no.92463307)support for funding this project by providing computing time through the Center for Information Services and HPC(ZIH)at TU DresdenThis research was also made possible as a result of a generous grant from XYZ Foundation(grant no.123567).
文摘The synthesis of nonbenzenoid nanographenes(NGs)with a high density of nonhexagonal rings remains a significant challenge,leaving this structural class largely unexplored.In this work,we report the efficient synthesis of a novel nonbenzenoid isomer of decacyclene,namely cyclopenta[cd]azulene trimer(CPAT),derived from the natural product guaiazulene.The key step involves an acid–base bufferassisted cyclotrimerization of cyclopenta[cd]azulen-2(1H)-one that can be further extended to produce halogenated derivative,enabling structural tunability.The resulting molecules feature a unique backbone comprising nine nonhexagonal rings arranged around a central benzenoid core,representing the highest pentagon–heptagon ring density among all reportedπ-extended NGs with ten or more fused rings.Compared to the pristine decacyclene,the synthesized compounds exhibit excellent ambient stability,narrower bandgaps,and distinct aromaticity profiles.Moreover,femtosecond transient absorption measurements of CPAT-a reveal an ultrafast singlet-state relaxation(∼14 ps),significantly shorter than that of decacyclene,highlighting the pronounced impact of nonbenzenoid topology on excited-state dynamics.This study introduces a new family of nonbenzenoid NGs and paves the way for the synthesis of newsp2 carbon allotrope featuring exclusively nonhexagonal ring systems.
基金Supported by NSFC(Grant Nos.12071370,12131013 and 12171393),China Scholarship Council(Grant No.202106290008)Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSZ009)。
文摘The Turán number, denoted by ex (n, H), is the maximum number of edges of a graph on n vertices containing no graph H as a subgraph. Denote by kCℓ the union of k vertex-disjoint copies of Cℓ. In this paper, we present new results for the Turán numbers of vertex-disjoint cycles. Our first results deal with the Turán number of vertex-disjoint triangles ex (n, kC_(3)). We determine the Turán number ex(n, kC_(3)) for n≥k^(2)+5k/2 when k ≤ 4, and n ≥ k^(2) + 2 when k ≥ 4. Moreover, we give lower and upper bounds for ex (n, kC_(3)) with 3k≤n≤k^(2)+5k/2 when k ≤ 4, and 3k ≤ n ≤ k^(2) + 2 when k ≥ 4. Next, we give a lower bound for the Turán number of vertex-disjoint pentagons ex (n, kC_(5)). Finally, we determine the Turán number ex (n, kC_(5)) for n = 5k, and propose two conjectures for ex (n, kC_(5)) for the other values of n.
基金This work was supported by the National Natural Science Foundation of China （Nos. 51422204 and 51372132） and the National Basic Research Program of China （No. 2013CB228506）.
文摘Single-crystal graphene domains grown by chemical vapor deposition （CVD） intrinsically tend to have a six-fold symmetry; however, several factors can influence the growth kinetics, which can in turn lead to the formation of graphene with different shapes. Here we report the growth of oriented large-area pentagonal single-crystal graphene domains on Cu foils by CVD. We found that high-index Cu planes contributed selectively to the formation of pentagonal graphene. Our results indicated that lattice steps present on the crystalline surface of the underlying Cu promoted graphene growth in the direction perpendicular to the steps and finally led to the disappearance of one of the edges forming a pentagon. In addition, hydrogen promoted the formation of pentagonal domains. This work provides new insights into the mechanism of graphene growth.
基金A.W.greatly appreciates the National Natural Science Foundation of China(No.11904131)the Natural Science Foundation of Shandong Province(No.ZR2019BA006)+2 种基金M.Z.thanks the supports from the National Natural Science Foundation of China(No.11774201)the Taishan scholarship of Shandong Province.N.R.appreciates the National Natural Science Foundation of China(No.51972148)L.D.thanks the support from the National Natural Science Foundation of China(No.51802118).
文摘Magnetism has revolutionized important technologies,and continues to bring forth new phenomena in emergent materials and reduced dimensions.Here,using first-principles calculations,we demonstrate that the already-synthesized two-dimensional(2D)Ni-tetracyanoquinodimethane(Ni_(2)(TCNQ)_(2))lattice is a stable ferromagnetism material with multiple spin-polarized Dirac cones.The conical bands in proximity of the Fermi level can be tuned by external tensile strain and show the fourfold degenerate electronic states at the critical tensile strain of~2.35%,whose energy dispersion is consistent with 2D Cairo pentagonal lattice.In addition,spin-orbital coupling can open a band gap at the Dirac point of A,leading to topologically nontrivial electronic states characterized by the non-zero Chern number and the edge states of nanoribbon.Our results offer versatile platforms for the realization of massless spintronics with full-spin polarization in 2D Cairo pentagonal Ni_(2)(TCNQ)_(2) Lattice.
基金supported by the National Key Research and Development Program of China(Nos.2020YFA0308800,2016YFA0202300,and 2016YFA0300902)the National Natural Science Foundation of China(Nos.91850120 and 11974045)the Strategic Priority Research Program(B)of CAS(No.XDB30000000)。
文摘Two-dimensional(2D)magnetic crystals have been extensively explored thanks to their potential applications in spintronics,valleytronics,and topological superconductivity.Here we report a novel monolayer magnet,namely puckered pentagonal VTe_(2)(PP-VTe_(2)),intriguing atomic and electronic structures of which were firmly validated from first-principles calculations.The PP-VTe_(2) exhibits strong intrinsic ferromagnetism and semiconducting property distinct from the half-metallic bulk pyrite VTe_(2)(BP-VTe_(2))phase.An unusual magnetic anisotropy with large magnetic exchange energies is found.More interestingly,the multiferroic coupling between its 2D ferroelasticity and in-plane magnetization is further identified in PP-VTe_(2),lending it unprecedented controllability with external strains and electric fields.Serving as an emergent 2D ferromagnetic semiconductor with a novel crystal structure,monolayer PP-VTe_(2) provides an ideal platform for exploring exotic crystalline and spin configurations in low-dimensional systems.
