We assign vertex v of G a list L(v)which L(v)∈2^(N)and N is the set of positive integers.A graph G is k-L(p,1)-choosable if G has a mappingφ:φ(v)2 L(v)which|L(v)|≥k for every v 2 V(G)such that for any two vertices...We assign vertex v of G a list L(v)which L(v)∈2^(N)and N is the set of positive integers.A graph G is k-L(p,1)-choosable if G has a mappingφ:φ(v)2 L(v)which|L(v)|≥k for every v 2 V(G)such that for any two vertices u and w,|φ(u)-φ(w)|≥p when they are adjacent,and|φ(u)-φ(w)|≥1 when they are at distance 2.In this paper,we proved that:(1)for every planar graph with g(G)≥5 andΔ≥5,G is 12-L(1,1)-choosable.(2)for every planar graph with g(G)≥6 andΔ≥15,G is(Δ+6)-L(2,1)-choosable.展开更多
A graph G is called（k,d）＊-choosable if for every list assignment L satisfying ｜L（v）｜=k for all v ∈ V（G）,there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same co...A graph G is called（k,d）＊-choosable if for every list assignment L satisfying ｜L（v）｜=k for all v ∈ V（G）,there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself.In this paper,it is shown that every planar graph without 6-circuits and a triangle adjacent to itself or a quadrangle is（3,1）＊-choosable.展开更多
A list assignment of a graph G is a function L:V(G)∪E(G)→2^(N).A graph G is L-(2,1)-Total labeling if there exists a function c such that c(x)∈L(x)for all x∈V(G)∪E(G),|c(u)-c(v)|≥1 if uv∈E(G),|c(e_(1))-c(e_(2))...A list assignment of a graph G is a function L:V(G)∪E(G)→2^(N).A graph G is L-(2,1)-Total labeling if there exists a function c such that c(x)∈L(x)for all x∈V(G)∪E(G),|c(u)-c(v)|≥1 if uv∈E(G),|c(e_(1))-c(e_(2))|≥1 if the edges e_(1)and e_(2)are adjacent,and|c(u)-c(e)|≥2 if the vertex u is incident to the edge e.A graph G is k-(2,1)-Total choosable if G is L-(2,1)-Total labeling for every list assignment L provided that|L(x)|=k,x∈V(G)∪E(G).The(2,1)-Total choice number of G,denoted by C_(2,1)^T(G),is the minimum k such that G is k-(2,1)-Total choosable.In this paper,we prove that if G is a planar graph with△(G)≥11,then C_(2,1)^T(G)≤△+4.展开更多
An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),i...An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.展开更多
A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in al...A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in all t-tone colorings of that graph.In this article,we study t-tone coloring of some finite planar lattices and obtain exact formulas for their t-tone chromatic number.展开更多
Sodium layered oxides stand out as one of the most promising cathodes for sodium-ion batteries due to their high energy density,elemental abundance,and scalability.However,their practical applications are restricted b...Sodium layered oxides stand out as one of the most promising cathodes for sodium-ion batteries due to their high energy density,elemental abundance,and scalability.However,their practical applications are restricted by interplanar gliding,cation migration,and the formation of intragranular microcracks,which collectively lead to rapid structural degradation and capacity loss.Herein,we rationally design an ultrastable O3-type Na_(0.94)Ca_(0.03)Ni_(1/3)Fe_(1/3)Mn_(1/3)O_(2) cathode,in which Ca^(2+)cations act as pillars within the NaO_(2)slabs,suppressing the irreversible phase transitions and Na/TM cation migration commonly observed in layered oxides.Multiscale in situ and ex situ techniques,combined with post-mortem analysis,reveal that the Ca-pillared pinning effect not only effectively suppresses the interplanar gliding and stress accumulation within the crystal phase but also restrains Na/TM cation migration and surface reconstruction in near-surface regions.Benefiting from the combined effects of structural stabilization,the Ca-pillared cathode exhibits a superior cycling stability,retaining 81.6%of its capacity after 1000 cycles at 2 C within the voltage range of 2.0-4.0 V,along with significantly enhanced wide-temperature(from-40 to 80℃)performance.This work highlights another critical role of Ca pillars in suppressing cation migration and surface structural degradation beyond preventing adverse interplanar gliding,offering valuable insights for designing long-life and wide-temperature layered oxide cathodes.展开更多
Energetic materials face critical challenges in balancing energy density and safety,driving the development of low-sensitivity high-energy materials.Though vital for modern defense and civilian applications,low-sensit...Energetic materials face critical challenges in balancing energy density and safety,driving the development of low-sensitivity high-energy materials.Though vital for modern defense and civilian applications,low-sensitivity high-energy materials remain scarce,with 1,3,5-trinitro-2,4,6-triaminobenzene as the only deployed example.Planar lamellar energetic crystals,which utilize weak interlamellarπ-πstacking for mechanical energy dissipation,have shown significant promise.However,their rational design is constrained by insufficient understanding of intermolecular interaction synergy.This review synthesizes the structural features of planar lamellar energetic crystals,emphasizing three core elements:the single-atomic-thickness planar stacking architecture,the"strong intralamellar and weak interlamellar interaction"paradigm(key to balancing energy density and safety for low-sensitivity high-energy materials,LSHEMs),and the role of molecular planarity in reducing shear slip barriers.It categorizes design strategies into two frameworks:H–bonding dominated(single-component:cross-shaped assembly,strong H–bonding in high symmetric molecules;multi-component methods:tenon-and-mortise,acceptor-donor separation)and other intermolecular interactions(e.g.,π-πstacking-drivenπ-π2max model,π-hole recognition).Case studies in single/multi-component crystals confirm that these strategies tune interaction synergy to achieve target packing motifs.The review highlights that interaction engineering is pivotal for PLEC design,offering a targeted theoretical framework for rational development of LSHEMs(to address the scarcity of practical LSHEMs)and guiding future crystal engineering for energy-safety balanced systems.展开更多
A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-dege...A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-degenerate.In this paper,we show that if G is a planar graph without kites and 9-or 10-cycles,then G is 3-degenerate,hence 4-choosable and list vertex 2-arborable.展开更多
Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we ...Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we callϕa neighbor sum distinguishing total coloring of G.Let L={Lx∣x∈V⋃E}be a set of lists of real numbers,each of size k.The neighbor sum distinguishing total choosability of G is the smallest k for which for any specified collection of such lists,there exists a neighbor sum distinguishing total coloring using colors from Lx for each x∈V⋃E,and we denote it by[Math Processing Error].The known results of neighbor sum distinguishing total choosability are mainly about planar graphs.In this paper,we focus on 1-planar graphs.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.We prove that[Math Processing Error]for any 1-planar graph G withΔ≥15,whereΔis the maximum degree of G.展开更多
The quantum phase transition between Z_(2) plaquette valence bound solid(PVBS) and superfluid(SF) phases on the planar pyrochlore lattice(square ice) is under debate. To gain further insight, here, we focus on the dyn...The quantum phase transition between Z_(2) plaquette valence bound solid(PVBS) and superfluid(SF) phases on the planar pyrochlore lattice(square ice) is under debate. To gain further insight, here, we focus on the dynamical features of the hard-core Bose–Hubbard model on this lattice and study the excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases,a flat band with bow-tie structure is observed and can be explained by certain symmetries. At the transition point,the spectra turn to be continuous and gapless. A(2+1)-dimensional Abelian–Higgs model with mixed 't Hooft anomaly is proposed to describe the transition, where the anomaly matching predicts that the deconfinement can exist on the domain walls. From the snapshot of the spin configuration in real space, we found the existence of the domain wall. We also found that the spectrum along a specific path in momentum space from PVBS phase to the transition point can be well described by an XXZ spin chain, and the critical theory of XXZ spin chain matches the anomaly. The two-spinon continuum along this specific path implies additional domain walls(point defect) can emerge in the domain walls(line defect) and take the role of deconfinement at the transition point.展开更多
DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improve...DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].展开更多
The advancement of planar micro-supercapacitors(PMSCs)for micro-electromechanical systems(MEMS)has been significantly hindered by the challenge of achieving high energy and power densities.This study addresses this is...The advancement of planar micro-supercapacitors(PMSCs)for micro-electromechanical systems(MEMS)has been significantly hindered by the challenge of achieving high energy and power densities.This study addresses this issue by leveraging screen-printing technology to fabricate high-performance PMSCs using innovative composite ink.The ink,a synergistic blend of few-layer graphene(Gt),carbon black(CB),and NiCo_(2)O_(4),was meticulously mixed to form a conductive and robust coating that enhanced the capacitive performance of the PMSCs.The optimized ink formulation and printing process result in a micro-supercapacitor with an exceptional areal capacitance of 18.95 mF/cm^(2)and an areal energy density of 2.63μW·h/cm^(2)at a current density of 0.05 mA/cm^(2),along with an areal power density of 0.025 mW/cm^(2).The devices demonstrated impressive durability with a capacitance retention rate of 94.7%after a stringent 20000-cycle test,demonstrating their potential for long-term applications.Moreover,the PMSCs displayed excellent mechanical flexibility,with a capacitance decrease of only 3.43%after 5000 bending cycles,highlighting their suitability for flexible electronic devices.The ease of integrating these PMSCs into series and parallel configurations for customized power further underscores their practicality for integrated power supply solutions in various technologies.展开更多
Multispectral imaging plays a crucial role in simultaneously capturing detailed spatial and spectral information,which is fundamental for understanding complex phenomena across various domains.Traditional systems face...Multispectral imaging plays a crucial role in simultaneously capturing detailed spatial and spectral information,which is fundamental for understanding complex phenomena across various domains.Traditional systems face significant challenges,such as large volume,static function,and limited wavelength selectivity.Here,we propose an innovative dynamic reflective multispectral imaging system via a thermally responsive cholesteric liquid crystal based planar lens.By employing advanced photoalignment technology,the phase distribution of a lens is imprinted to the liquid crystal director.The reflection band is reversibly tuned from 450 nm to 750 nm by thermally controlling the helical pitch of the cholesteric liquid crystal,allowing selectively capturing images in different colors.This capability increases imaging versatility,showing great potential in precision agriculture for assessing crop health,noninvasive diagnostics in healthcare,and advanced remote sensing for environmental monitoring.展开更多
The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the ...The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.展开更多
Planar chiral cyclophanes are a type of structurally intriguing organic molecules,which have found increasingly applications in the field of biologically active compounds,asymmetric catalysis,and optically pure materi...Planar chiral cyclophanes are a type of structurally intriguing organic molecules,which have found increasingly applications in the field of biologically active compounds,asymmetric catalysis,and optically pure materials.As such,significant efforts in the development of new methods to build up enantioenriched cyclophanes in a precise manner have attracted increased attention in recent years.Among the plethora of reported synthetic strategies,catalytic enantioselective method has emerged as one of the most straightforward and efficient ways to deliver optically pure planar chiral cyclophanes.In this review,the recent progress in catalytic enantioselective reactions for the synthesis of planar chiral cyclophanes will be discussed,which would stimulate the research interest of chemists for the discovery of novel asymmetric strategies for the preparation of valuable and previously difficult-to-access chiral molecules.展开更多
In this paper,a 4×4 wideband linearly po-larization(LP)antenna array is proposed by using pla-nar dual-arm spiral structures.Wideband balun struc-tures,composed of microstrip line-fed coupling slots,are adopted t...In this paper,a 4×4 wideband linearly po-larization(LP)antenna array is proposed by using pla-nar dual-arm spiral structures.Wideband balun struc-tures,composed of microstrip line-fed coupling slots,are adopted to feed two dual-arms spiral structures with opposite phases.Then,by combining the left-and right-hand circular polarizations,a linearly polar-ization is achieved.The proposed antenna has a wide operating bandwidth due to the wideband nature of the spiral structure.Simulated results show that the an-tenna element can achieve a 68.73%impedance band-width and a maximum gain of 6.64 dBi within 19.44–38.83 GHz.A 4×4 array prototype is designed to verify the concept.Measured results show that an impedance bandwidth of 63.73%is obtained.The pro-posed array has the merits of a wide bandwidth,a low profile,a low cost,and a small size,which is promis-ing for the application in millimeter wave wireless sys-tems.展开更多
Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventio...Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventional geometric arrangements and bonding patterns that facilitate the synthesis of new 2D materials with diverse applications.Among these,yet the design of 2D transition metal systems featuring planar pentacoordinate boron(ppB)is particularly intriguing.Here we address this gap by proposing a novel family of transition metal boride monolayers(MBenes)composed of ppB and heptacoordinate M motifs.The novelty of our MBenes stems from their distinct atomic arrangements and bonding configurations,setting them apart from traditional 2D materials.High-throughput calculations identified 10 stable MBenes(with the stoichiometry of MB,M=Cr,Fe,Co,Ni,Cu,Mo,Pd,Ag,Pt,Au)with exceptional thermodynamic,dynamic,thermal,and mechanical stabilities attributed to strong BB covalent bonds and MB ionic interactions.Notably,five of these MBenes(M=Ni,Pd,Pt,Ag,Au)hold high promise as topological superconducting materials with superconducting transition temperatures of 2.4-5.2 K.This discovery not only enriches the family of topological superconducting materials but also opens new avenues for quantum device development.Meanwhile,FeB monolayer exhibits robust ferromagnetic properties with a high Curie temperature of~750 K,which is particularly significant for spintronics applications.In addition,NiB and CuB MBenes demonstrate extremely low sodium diffusion barriers(about 30 and 90 meV)and high sodium storage capacities(788 and 734 mAh g1,respectively),making them promising anode materials for sodium-ion batteries(SIBs).This study expands the selection of electrode materials for SIBs and mitigates some existing limitations in battery technology.Overall,these findings underscore the multifunctional potential of MBenes,positioning them as transformative materials for quantum computing,spintronics,and energy storage applications.展开更多
Diffractive optical neural networks(DONNs)have exhibited the advantages of parallelization,high speed,and low consumption.However,the existing DONNs based on free-space diffractive optical elements are bulky and unste...Diffractive optical neural networks(DONNs)have exhibited the advantages of parallelization,high speed,and low consumption.However,the existing DONNs based on free-space diffractive optical elements are bulky and unsteady.In this study,we propose a planar-waveguide integrated diffractive neural network chip architecture.The three diffractive layers are engraved on the same side of a quartz wafer.The three-layer chip is designed with 32-mm3 processing space and enables a computing speed of 3.1×109 Tera operations per second.The results show that the proposed chip achieves 73.4%experimental accuracy for the Modified National Institute of Standards and Technology database while showing the system’s robustness in a cycle test.The consistency of experiments is 88.6%,and the arithmetic mean standard deviation of the results is~4.7%.The proposed chip architecture can potentially revolutionize high-resolution optical processing tasks with high robustness.展开更多
Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such ...Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such as sensitivity enhancement,scanning range extension,and sidelobe level suppression,need to be solved urgently.Here,we propose a sparse optimization scheme based on a genetic algorithm for a 64-array element planar radio antenna array.As optimization targets for the iterative process of the genetic algorithm,we use the maximum sidelobe levels and beamwidth of multiple cross-section patterns that pass through the main beam in three-dimensions,with the maximum sidelobe levels of the patterns at several different scanning angles.Element positions are adjusted for iterations,to select the optimal array configuration.Following sparse layout optimization,the simulated 64-element planar radio antenna array shows that the maximum sidelobe level decreases by 1.79 dB,and the beamwidth narrows by 3°.Within the scan range of±30°,after sparse array optimization,all sidelobe levels decrease,and all beamwidths narrow.This performance improvement can potentially enhance the sensitivity and spatial resolution of radio telescope systems.展开更多
文摘We assign vertex v of G a list L(v)which L(v)∈2^(N)and N is the set of positive integers.A graph G is k-L(p,1)-choosable if G has a mappingφ:φ(v)2 L(v)which|L(v)|≥k for every v 2 V(G)such that for any two vertices u and w,|φ(u)-φ(w)|≥p when they are adjacent,and|φ(u)-φ(w)|≥1 when they are at distance 2.In this paper,we proved that:(1)for every planar graph with g(G)≥5 andΔ≥5,G is 12-L(1,1)-choosable.(2)for every planar graph with g(G)≥6 andΔ≥15,G is(Δ+6)-L(2,1)-choosable.
基金Supported by the Natural Science Research Project of Ordinary Universities in Jiangsu(08KJB110002)Supported by the Program for ETHYTC(08QNZCK03)Supported by the NSFC(10671095)
文摘A graph G is called（k,d）＊-choosable if for every list assignment L satisfying ｜L（v）｜=k for all v ∈ V（G）,there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself.In this paper,it is shown that every planar graph without 6-circuits and a triangle adjacent to itself or a quadrangle is（3,1）＊-choosable.
基金Supported by the National Natural Science Foundation of China(Grant No.12071265)the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA032)。
文摘A list assignment of a graph G is a function L:V(G)∪E(G)→2^(N).A graph G is L-(2,1)-Total labeling if there exists a function c such that c(x)∈L(x)for all x∈V(G)∪E(G),|c(u)-c(v)|≥1 if uv∈E(G),|c(e_(1))-c(e_(2))|≥1 if the edges e_(1)and e_(2)are adjacent,and|c(u)-c(e)|≥2 if the vertex u is incident to the edge e.A graph G is k-(2,1)-Total choosable if G is L-(2,1)-Total labeling for every list assignment L provided that|L(x)|=k,x∈V(G)∪E(G).The(2,1)-Total choice number of G,denoted by C_(2,1)^T(G),is the minimum k such that G is k-(2,1)-Total choosable.In this paper,we prove that if G is a planar graph with△(G)≥11,then C_(2,1)^T(G)≤△+4.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071265,12001481)the Natural Science Foundation of Shandong Province(Grant No.ZR2021MA103)the Youth Innovation Team Project of Shandong Province Universities(Grant No.2024KJG078).
文摘An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.
基金Supported by the National Natural Science Foundation of China(Grant No.12271210)the Scientific Research Foundation of Jimei University(Grant No.Q202201).
文摘A t-tone coloring of a graph assigns t distinct colors to each vertex with vertices at distance d having fewer than d colors in common.The t-tone chromatic number of a graph is the smallest number of colors used in all t-tone colorings of that graph.In this article,we study t-tone coloring of some finite planar lattices and obtain exact formulas for their t-tone chromatic number.
基金supported by the National Key R&D Program of China(2023YFB2406000)the National Natural Science Foundation of China(22479057,52172201,51732005)。
文摘Sodium layered oxides stand out as one of the most promising cathodes for sodium-ion batteries due to their high energy density,elemental abundance,and scalability.However,their practical applications are restricted by interplanar gliding,cation migration,and the formation of intragranular microcracks,which collectively lead to rapid structural degradation and capacity loss.Herein,we rationally design an ultrastable O3-type Na_(0.94)Ca_(0.03)Ni_(1/3)Fe_(1/3)Mn_(1/3)O_(2) cathode,in which Ca^(2+)cations act as pillars within the NaO_(2)slabs,suppressing the irreversible phase transitions and Na/TM cation migration commonly observed in layered oxides.Multiscale in situ and ex situ techniques,combined with post-mortem analysis,reveal that the Ca-pillared pinning effect not only effectively suppresses the interplanar gliding and stress accumulation within the crystal phase but also restrains Na/TM cation migration and surface reconstruction in near-surface regions.Benefiting from the combined effects of structural stabilization,the Ca-pillared cathode exhibits a superior cycling stability,retaining 81.6%of its capacity after 1000 cycles at 2 C within the voltage range of 2.0-4.0 V,along with significantly enhanced wide-temperature(from-40 to 80℃)performance.This work highlights another critical role of Ca pillars in suppressing cation migration and surface structural degradation beyond preventing adverse interplanar gliding,offering valuable insights for designing long-life and wide-temperature layered oxide cathodes.
基金supported by the National Natural Science Foundation of China under Grant No.22505100.
文摘Energetic materials face critical challenges in balancing energy density and safety,driving the development of low-sensitivity high-energy materials.Though vital for modern defense and civilian applications,low-sensitivity high-energy materials remain scarce,with 1,3,5-trinitro-2,4,6-triaminobenzene as the only deployed example.Planar lamellar energetic crystals,which utilize weak interlamellarπ-πstacking for mechanical energy dissipation,have shown significant promise.However,their rational design is constrained by insufficient understanding of intermolecular interaction synergy.This review synthesizes the structural features of planar lamellar energetic crystals,emphasizing three core elements:the single-atomic-thickness planar stacking architecture,the"strong intralamellar and weak interlamellar interaction"paradigm(key to balancing energy density and safety for low-sensitivity high-energy materials,LSHEMs),and the role of molecular planarity in reducing shear slip barriers.It categorizes design strategies into two frameworks:H–bonding dominated(single-component:cross-shaped assembly,strong H–bonding in high symmetric molecules;multi-component methods:tenon-and-mortise,acceptor-donor separation)and other intermolecular interactions(e.g.,π-πstacking-drivenπ-π2max model,π-hole recognition).Case studies in single/multi-component crystals confirm that these strategies tune interaction synergy to achieve target packing motifs.The review highlights that interaction engineering is pivotal for PLEC design,offering a targeted theoretical framework for rational development of LSHEMs(to address the scarcity of practical LSHEMs)and guiding future crystal engineering for energy-safety balanced systems.
文摘A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-degenerate.In this paper,we show that if G is a planar graph without kites and 9-or 10-cycles,then G is 3-degenerate,hence 4-choosable and list vertex 2-arborable.
基金supported by Guangdong Basic and Applied Basic Research Foundation(Natural Science Foundation of Guangdong Province,China,Grant No.2025A1515011904)the National Natural Science Foundation of China(Nos.12101285,12171222)+4 种基金the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2016D01C006)Guangdong Philosophy and Social Sciences Planning Project(Grant No.GD22CXW01)Research Platforms and Projects of Colleges and Universities in Guangdong(Grant No.2022KTSCX071)Scientific Research Innovation Project of Lingnan Normal University(LT2401)Lingnan Normal University(No.LT2410).
文摘Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we callϕa neighbor sum distinguishing total coloring of G.Let L={Lx∣x∈V⋃E}be a set of lists of real numbers,each of size k.The neighbor sum distinguishing total choosability of G is the smallest k for which for any specified collection of such lists,there exists a neighbor sum distinguishing total coloring using colors from Lx for each x∈V⋃E,and we denote it by[Math Processing Error].The known results of neighbor sum distinguishing total choosability are mainly about planar graphs.In this paper,we focus on 1-planar graphs.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.We prove that[Math Processing Error]for any 1-planar graph G withΔ≥15,whereΔis the maximum degree of G.
基金supported by the start-up funding of CQNU (Grant No. 24XLB010)supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202100514)+3 种基金funding from Chongqing Natural Science Foundation under Grant No. CSTB2022NSCQ-JQX0018the Fundamental Research Funds for the Central Universities Grant No. 2021CDJZYJH-003Xiaomi Foundation/Xiaomi Young Talents Programfunding from the National Science Foundation of China under Grant Nos. 12404169, 12147172, 12274046, 11874094, 12147102, and 12347101。
文摘The quantum phase transition between Z_(2) plaquette valence bound solid(PVBS) and superfluid(SF) phases on the planar pyrochlore lattice(square ice) is under debate. To gain further insight, here, we focus on the dynamical features of the hard-core Bose–Hubbard model on this lattice and study the excitation spectra by combining stochastic analytic continuation and quantum Monte Carlo simulation. In both PVBS and SF phases,a flat band with bow-tie structure is observed and can be explained by certain symmetries. At the transition point,the spectra turn to be continuous and gapless. A(2+1)-dimensional Abelian–Higgs model with mixed 't Hooft anomaly is proposed to describe the transition, where the anomaly matching predicts that the deconfinement can exist on the domain walls. From the snapshot of the spin configuration in real space, we found the existence of the domain wall. We also found that the spectrum along a specific path in momentum space from PVBS phase to the transition point can be well described by an XXZ spin chain, and the critical theory of XXZ spin chain matches the anomaly. The two-spinon continuum along this specific path implies additional domain walls(point defect) can emerge in the domain walls(line defect) and take the role of deconfinement at the transition point.
基金Partially supported by NSFC(No.12301436)NSF of Guangxi Province(No.2025GXNSFAA069811)。
文摘DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].
文摘In this paper,by using the method of Lyapunov-Schmidt reduction,we obtain the existence of multi-bump solutions for planar Schrödinger-Poisson system.
基金supported by the Shanxi Province Central Guidance Fund for Local Science and Technology Development Project(YDZJSX2024D030)the National Natural Science Foundation of China(22075197,22278290)+2 种基金the Shanxi Province Key Research and Development Program Project(2021020660301013)the Shanxi Provincial Natural Science Foundation of China(202103021224079)the Research and Development Project of Key Core and Common Technology of Shanxi Province(20201102018).
文摘The advancement of planar micro-supercapacitors(PMSCs)for micro-electromechanical systems(MEMS)has been significantly hindered by the challenge of achieving high energy and power densities.This study addresses this issue by leveraging screen-printing technology to fabricate high-performance PMSCs using innovative composite ink.The ink,a synergistic blend of few-layer graphene(Gt),carbon black(CB),and NiCo_(2)O_(4),was meticulously mixed to form a conductive and robust coating that enhanced the capacitive performance of the PMSCs.The optimized ink formulation and printing process result in a micro-supercapacitor with an exceptional areal capacitance of 18.95 mF/cm^(2)and an areal energy density of 2.63μW·h/cm^(2)at a current density of 0.05 mA/cm^(2),along with an areal power density of 0.025 mW/cm^(2).The devices demonstrated impressive durability with a capacitance retention rate of 94.7%after a stringent 20000-cycle test,demonstrating their potential for long-term applications.Moreover,the PMSCs displayed excellent mechanical flexibility,with a capacitance decrease of only 3.43%after 5000 bending cycles,highlighting their suitability for flexible electronic devices.The ease of integrating these PMSCs into series and parallel configurations for customized power further underscores their practicality for integrated power supply solutions in various technologies.
基金supported by the National Key Research and Development Program of China(No.2022YFA1203700)the National Natural Science Foundation of China(NSFC)(Nos.62405129 and 62035008)+1 种基金the University Research Project of Guangzhou Education Bureau(No.202235053)the Natural Science Foundation of Jiangsu Province(No.BK20241197).
文摘Multispectral imaging plays a crucial role in simultaneously capturing detailed spatial and spectral information,which is fundamental for understanding complex phenomena across various domains.Traditional systems face significant challenges,such as large volume,static function,and limited wavelength selectivity.Here,we propose an innovative dynamic reflective multispectral imaging system via a thermally responsive cholesteric liquid crystal based planar lens.By employing advanced photoalignment technology,the phase distribution of a lens is imprinted to the liquid crystal director.The reflection band is reversibly tuned from 450 nm to 750 nm by thermally controlling the helical pitch of the cholesteric liquid crystal,allowing selectively capturing images in different colors.This capability increases imaging versatility,showing great potential in precision agriculture for assessing crop health,noninvasive diagnostics in healthcare,and advanced remote sensing for environmental monitoring.
基金supported by NSFC(No.12201202)NSF of Hunan Province(No.2023JJ30180)NSFC(No.12471022)。
文摘The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.
基金financial support provided by Huanghuai University and Hangzhou Medical College.
文摘Planar chiral cyclophanes are a type of structurally intriguing organic molecules,which have found increasingly applications in the field of biologically active compounds,asymmetric catalysis,and optically pure materials.As such,significant efforts in the development of new methods to build up enantioenriched cyclophanes in a precise manner have attracted increased attention in recent years.Among the plethora of reported synthetic strategies,catalytic enantioselective method has emerged as one of the most straightforward and efficient ways to deliver optically pure planar chiral cyclophanes.In this review,the recent progress in catalytic enantioselective reactions for the synthesis of planar chiral cyclophanes will be discussed,which would stimulate the research interest of chemists for the discovery of novel asymmetric strategies for the preparation of valuable and previously difficult-to-access chiral molecules.
基金supported in part by the National Natural Science Foundation of China under Grant 62131008the Fundamental Research Funds for the Central Universities 2242022k60003.
文摘In this paper,a 4×4 wideband linearly po-larization(LP)antenna array is proposed by using pla-nar dual-arm spiral structures.Wideband balun struc-tures,composed of microstrip line-fed coupling slots,are adopted to feed two dual-arms spiral structures with opposite phases.Then,by combining the left-and right-hand circular polarizations,a linearly polar-ization is achieved.The proposed antenna has a wide operating bandwidth due to the wideband nature of the spiral structure.Simulated results show that the an-tenna element can achieve a 68.73%impedance band-width and a maximum gain of 6.64 dBi within 19.44–38.83 GHz.A 4×4 array prototype is designed to verify the concept.Measured results show that an impedance bandwidth of 63.73%is obtained.The pro-posed array has the merits of a wide bandwidth,a low profile,a low cost,and a small size,which is promis-ing for the application in millimeter wave wireless sys-tems.
基金supported by Research Foundation for Advanced Talents of Inner Mongolia Normal University(2025YJRC005)the National Natural Science Foundation of China(12364038)+5 种基金the“Grassland Talents”project of the Inner Mongolia Autonomous Region(12000-12102613)the Young Science and Technology Talents Cultivation Project of Inner Mongolia University(21200-5223708)the Industrial Technology Innovation Projects of Inner Mongolia Academy of Science and Technology of China(2023JSYD01002)Science and Technology Plan Projects of Inner Mongolia Autonomous Region of China(2023KYPT0012)Key Project Funding from the Inner Mongolia Autonomous Region Natural Science Foundation(2023ZD27)High Level Introduction of Talent Research Start-up Fund(5909002405).
文摘Pursuing new two-dimensional(2D)materials has been a hot topic in materials science,driven by their potential for diverse applications.Recent research has unveiled stable planar hypercoordinate motifs with unconventional geometric arrangements and bonding patterns that facilitate the synthesis of new 2D materials with diverse applications.Among these,yet the design of 2D transition metal systems featuring planar pentacoordinate boron(ppB)is particularly intriguing.Here we address this gap by proposing a novel family of transition metal boride monolayers(MBenes)composed of ppB and heptacoordinate M motifs.The novelty of our MBenes stems from their distinct atomic arrangements and bonding configurations,setting them apart from traditional 2D materials.High-throughput calculations identified 10 stable MBenes(with the stoichiometry of MB,M=Cr,Fe,Co,Ni,Cu,Mo,Pd,Ag,Pt,Au)with exceptional thermodynamic,dynamic,thermal,and mechanical stabilities attributed to strong BB covalent bonds and MB ionic interactions.Notably,five of these MBenes(M=Ni,Pd,Pt,Ag,Au)hold high promise as topological superconducting materials with superconducting transition temperatures of 2.4-5.2 K.This discovery not only enriches the family of topological superconducting materials but also opens new avenues for quantum device development.Meanwhile,FeB monolayer exhibits robust ferromagnetic properties with a high Curie temperature of~750 K,which is particularly significant for spintronics applications.In addition,NiB and CuB MBenes demonstrate extremely low sodium diffusion barriers(about 30 and 90 meV)and high sodium storage capacities(788 and 734 mAh g1,respectively),making them promising anode materials for sodium-ion batteries(SIBs).This study expands the selection of electrode materials for SIBs and mitigates some existing limitations in battery technology.Overall,these findings underscore the multifunctional potential of MBenes,positioning them as transformative materials for quantum computing,spintronics,and energy storage applications.
基金supported by the National Natural Science Foundation of China(Grant Nos.62175050 and U2341245)the Fundamental Research Funds for the Central Universities(Grant No.HIT.OCEF.2024054).
文摘Diffractive optical neural networks(DONNs)have exhibited the advantages of parallelization,high speed,and low consumption.However,the existing DONNs based on free-space diffractive optical elements are bulky and unsteady.In this study,we propose a planar-waveguide integrated diffractive neural network chip architecture.The three diffractive layers are engraved on the same side of a quartz wafer.The three-layer chip is designed with 32-mm3 processing space and enables a computing speed of 3.1×109 Tera operations per second.The results show that the proposed chip achieves 73.4%experimental accuracy for the Modified National Institute of Standards and Technology database while showing the system’s robustness in a cycle test.The consistency of experiments is 88.6%,and the arithmetic mean standard deviation of the results is~4.7%.The proposed chip architecture can potentially revolutionize high-resolution optical processing tasks with high robustness.
基金supported by the Ministry of Science and Technology SKA Special Project(2020SKA0110202)the Special Project on Building a Science and Technology Innovation Center for South and Southeast Asia–International Joint Innovation Platform in Yunnan Province:"Yunnan Sino-Malaysian International Joint Laboratory of HF-VHF Advanced Radio Astronomy Technology"(202303AP140003)+4 种基金the National Natural Science Foundation of China (NSFC) Joint Fund for Astronomy (JFA) incubator program (U2031133)the International Partnership Program Project of the International Cooperation Bureau of the Chinese Academy of Sciences:"Belt and Road"Cooperation (114A11KYSB20200001)the Kunming Foreign (International) Cooperation Base Program:"Yunnan Observatory of the Chinese Academy of Sciences-University of Malaya Joint R&D Cooperation Base for Advanced Radio Astronomy Technology"(GHJD-2021022)the China-Malaysia Collaborative Research on Space Remote Sensing and Radio Astronomy Observation of Space Weather at Low and Middle Latitudes under the Key Special Project of the State Key R&D Program of the Ministry of Science and Technology for International Cooperation in Science,Technology and Innovation among Governments (2022YFE0140000)the High-precision calibration method for low-frequency radio interferometric arrays for the SKA project of the Ministry of Science and Technology(2020SKA0110300).
文摘Radio antenna arrays have many advantages for astronomical observations,such as high resolution,high sensitivity,multi-target simultaneous observation,and flexible beam formation.Problems surrounding key indices,such as sensitivity enhancement,scanning range extension,and sidelobe level suppression,need to be solved urgently.Here,we propose a sparse optimization scheme based on a genetic algorithm for a 64-array element planar radio antenna array.As optimization targets for the iterative process of the genetic algorithm,we use the maximum sidelobe levels and beamwidth of multiple cross-section patterns that pass through the main beam in three-dimensions,with the maximum sidelobe levels of the patterns at several different scanning angles.Element positions are adjusted for iterations,to select the optimal array configuration.Following sparse layout optimization,the simulated 64-element planar radio antenna array shows that the maximum sidelobe level decreases by 1.79 dB,and the beamwidth narrows by 3°.Within the scan range of±30°,after sparse array optimization,all sidelobe levels decrease,and all beamwidths narrow.This performance improvement can potentially enhance the sensitivity and spatial resolution of radio telescope systems.
