In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation netwo...In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.展开更多
Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which sa...Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.展开更多
Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorp...Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assignment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-D0F(degree of freedom)planar KCs.展开更多
Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P...Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).展开更多
The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of man...The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.展开更多
Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ...Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ2, λ3,…, λn, of A(G) are said to be the eigenvalues of the graph G and to form the spectrum of this graph. The number of nonzero eigenvalues and zero eigenvalues in the spectrum of G are called rank and nullity of the graph G, and are denoted by r(G) and η(G), respectively. It follows from the definitions that r(G) + η(G) = n. In this paper, by using the operation of multiplication of vertices, a characterization for graph G with pendant vertices and r(G) = 7 is shown, and then a characterization for graph G with pendant vertices and r(G) less than or equal to 7 is shown.展开更多
Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the...Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the #-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 （2005） 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 （1998） 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann Oakes-Renner relation also holds at finite chemical potential展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network w...In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were s...In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average...In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching ...Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).展开更多
A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote ...A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.展开更多
Chiral nanoporous nanoarchitectures exhibit potential applications in various fields including chiral separation,sensing and catalysis.Two-dimensional(2D)supramolecular chemistry offers novel methods to build chiral n...Chiral nanoporous nanoarchitectures exhibit potential applications in various fields including chiral separation,sensing and catalysis.Two-dimensional(2D)supramolecular chemistry offers novel methods to build chiral nanoporous networks from achiral molecules.Herein,we report a series of chiral nanoporous networks built by an achiral precursor molecule via a stepwise annealing strategy on Ag(100).The nanoporous network morphologies and structural details are characterized by high-resolution scanning tunneling microscopy(STM).It is revealed that all vertices within networks are chiral.These chiral vertices are either dimeric,trimeric,or tetrameric.The connection of these chiral vertices gives rise to diverse chiral nanopores with varying shapes and sizes.A strict chirality correlation between nanopores and their vertices is determined.Specifically,enantiomeric vertices of one-pair nanopore enantiomers are always in identical type but opposite handedness.This work serves as a model to investigate the influence of vertex chirality on nanopore chirality of a supramolecular matrix.The attained chiral nanopores could potentially be utilized as templates for surface reaction,chiral recognition,etc.The mirror-symmetric silver adatoms clusters dictated by chiral nanopore are discerned.展开更多
Schuster, Cai Maocheng and Lin Yixun studied the interpolation theory for the number of end vertices of spanning trees of graph. Zhang Fuji and Guo Xiaofeng obtained the related result of digraph. This paper is devote...Schuster, Cai Maocheng and Lin Yixun studied the interpolation theory for the number of end vertices of spanning trees of graph. Zhang Fuji and Guo Xiaofeng obtained the related result of digraph. This paper is devoted to find the upper and lower bounds of the maximum number of end vertices of spanning (directed) trees for directed or undirected graphs. Our result is connected with some parameters in graph theory such as cyclomatic number and absorption number. For our purpose,展开更多
Optimizing plant architecture for specific cultivation methods is essential for enhancing fruit productivity.Unlike indeterminate growth plants,the total productivity of determinate growth plants relies on cumulative ...Optimizing plant architecture for specific cultivation methods is essential for enhancing fruit productivity.Unlike indeterminate growth plants,the total productivity of determinate growth plants relies on cumulative fruit production and synchronized fruit ripening from both main and axillary shoots.Here,we focused on SlD14and SlMAX1,two key genes involved in the regulation of strigolactone(SL)signaling and biosynthesis,with the goal of maximizing yield and syn chronizing fruit ripening by fine-tuning axillary shoot growth.Using clustered regularly interspaced short palindromic repeats(CRISPR)/CRISPR-associated protein 9(Cas9)technology,we found that the sld14,slmax1,and sld14 slmax1mutant plants exhibited reduced plant height and increased axillary shoot proliferation compared to wild-type plants.However,these mutants showed reduced yield and delayed ripening,likely due to a source-sink imbalance caused by excessive axillary shoot development.A weak sld14 allele displayed a milder phenotype,maintaining total fruit yield and harvest index despite smaller individual fruit size.These findings indicate that allelic variation in SL-related genes can influence plant architecture and yield components.Our results suggest that weak or partial alleles may serve as promising targets for tailoring tomato architecture to space-limited cultivation systems.展开更多
Zinc-air batteries(ZABs)are promising candidates for flexible electronics due to their high energy density and low cost.However,their development is hindered by the sluggish kinetics of the oxygen evolution reaction(O...Zinc-air batteries(ZABs)are promising candidates for flexible electronics due to their high energy density and low cost.However,their development is hindered by the sluggish kinetics of the oxygen evolution reaction(OER)and oxygen reduction reaction(ORR).Herein,we present a novel heterostructured electrocatalyst composed of vertically aligned N-doped graphene(NVG)arrays anchored on Ru-doped ceria(RCO)nanofibers,synthesized via a one-step plasma-enhanced chemical vapor deposition process.Notably,during the plasma-enhanced driven NVG growth,Ru nanoparticles are spontaneously in-situ exsolved from the RCO lattice,forming a unique Ru@RCO-NVG heterostructure.Density functional theory calculations reveal that the Ru@RCO-NVG heterojunction induces interfacial electronic redistribution,thereby significantly lowering the energy barriers for both OER and ORR.Benefiting from the synergistic effects,the Ru@RCO-NVG catalyst exhibits exceptional intrinsic activity towards OER/ORR(an overpotential of 370 mV for OER at 10 mA cm^(−2)and a half-wave potential of 0.86 V for ORR),and higher all-solid-state flexible ZAB performance(peak power density of 286.1 mW cm^(−2)),surpassing commercial Pt/C-IrO_(2)catalysts.This work not only advances the integration of synergistic graphene/ceria composites but also offers a promising strategy for designing efficient electrocatalysts for next-generation energy conversion technologies.展开更多
This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlyin...This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.展开更多
The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly d...The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly defined.The focus of this study is the No.8 coal seam of the Carboniferous Benxi Formation in the Central-Eastern Ordos Basin.By integrating microscopic identification,proximate analysis,gas adsorption(CO_(2),N_(2),and CH_(4)),and the multifractal theory,we quantitatively characterized the nanopore structure(micropores<2 nm and mesopores 2 nm-100 nm)of coal reservoirs with varying ash yields.The results indicate that(1)ash yield is the primary factor that controls the vertical evolution of pore structures in coal seams.In low-ash yield coal seams,the extent of thermal evolution and ash yield jointly constrain the heterogeneity of pore size distribution.In mediumto high-ash yield coal seams,the heterogeneity of pore structure and pore size distribution are predominantly constrained by ash yield.(2)As the ash yield vertically increases,the mesoporous pore volume and specific surface area initially decrease and subsequently increase,while the contribution of micropores to both pore volume and specific surface area continuously diminishes.Consequently,the total pore volume and specific surface area of the coal samples exhibit a two-stage reduction close to an ash yield threshold of approximately 20%.(3)Further,the Langmuir volume for CH_(4)adsorption sharply declines below the 20%threshold,followed by a gradual decrease;in contrast,the Langmuir pressure initially decreases and subsequently increases.Hence,the vertical increase in ash yield constrains the development of pore systems and diminishes pore connectivity,thereby reducing methane adsorption capacity and adversely affecting coalbed methane productivity.(4)Low-ash yield coal reservoirs are characterized by a rapid gas breakthrough and high productivity,whereas medium-ash yield coal reservoirs generally require prolonged depressurization to achieve peak gas production.These findings reveal that in medium-high rank coal,ash yield―and not thermal evolution―is the main factor that controls vertical pore evolution and methane adsorption efficiency.The quantitative ash yield threshold(20%)established in this study provides a practical criterion for evaluating reservoir quality and predicting vertical variations in gas storage potential in the Ordos Basin.展开更多
Permeable electronics promise improved physiological comfort,but remain constrained by limited functional integration and poor mechanical robustness.Here,we report a three-dimensional(3D)permeable electronic system th...Permeable electronics promise improved physiological comfort,but remain constrained by limited functional integration and poor mechanical robustness.Here,we report a three-dimensional(3D)permeable electronic system that overcomes these challenges by combining electrospun SEBS nanofiber mats,high-resolution liquid metal conductors patterned via thermal imprinting(50μm),and a strain isolators(SIL)that protects vertical interconnects(VIAs)from stress concentration.This architecture achieves ultrahigh air permeability(>5.09 m L cm^(-2)min^(-1)),exceptional stretchability(750%fracture strain),and reliable conductivity maintained through more than 32,500 strain cycles.Leveraging these advances,we have integrated multilayer circuits,strain sensors,and a three-axis accelerometer to achieve a fully integrated,stretchable,permeable wireless real-time gesture recognition glove.The system enables accurate sign language interpretation(98%)and seamless robotic hand control,demonstrating its potential for assistive technologies.By uniting comfort,durability,and high-density integration,this work establishes a versatile platform for nextgeneration wearable electronics and interactive human-robot interfaces.展开更多
This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shea...This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shear(VWS),using idealized numerical experiments.Results reveal that the SE develops greater radial extent when surface winds align with VWS compared to counter-aligned conditions.In alignment configurations,shear-enhanced surface winds on the right flank amplify surface enthalpy fluxes,thereby elevating boundary-layer entropy within the downshear outer-core region.Subsequently,more vigorous outer rainbands develop,inducing marked acceleration of tangential winds in the outer core preceding SE formation.The resultant radial expansion of supergradient winds near the boundary-layer top triggers widespread convective activity immediately beyond the inner core.Progressive axisymmetrization of this convective forcing ultimately generates an expansive SE structure.展开更多
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the relationship between the average degree and the average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 was studied.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the airline as the edge of the network.On the basis of the statistical data,the average degree and average path length of edge vertices of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Through regression analysis,it was found that the average degree had a logarithmic relationship with the average path length of edge vertices and the two parameters of the logarithmic relationship had linear evolutionary trace.
基金Project(RTI04-01-03) supported by the Regional Technology Innovation Program of the Ministry of Knowledge Economy (MKE) of Korea
文摘Factors for determining the spindle size are the shaft diameter, positions of bearing and motor, and entire length of the spindle. Then, it is important to find the assembling of the optimal design variables, which satisfy the stiffimss and rotational speed required to the spindle. A general full factorial design method was used to verify some factors that affect the natural frequency of a spindle. It is verified that the shorter shaft length and bearing span length represent the higher natural frequency, and there are some effects according to the change in the levels of factors. The detailed spindle dimension is determined by applying an EVD method, which can define the optimal bearing position through considering the limiting condition. Based on the estimated regression model, the optimal spindle size and bearing distance that can improve the primary natural frequency are obtained, and the influence of design factors on the natural frequency is also analyzed.
基金Supported by National Natural Science Foundation of China(Grant Nos.51675488,51975534)Zhejiang Provincial Natural Science Foundation of China(Grant No.LY19E050021)。
文摘Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assignment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-D0F(degree of freedom)planar KCs.
基金the National Natural Science Foundation of China(11702094)the Fundamental Research Funds for the Central University(3142015045)。
文摘Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).
基金the National Key R&D Program of China(Grant No.2017YFA0303800)the National Natural Science Foundation of China(Grant Nos.91850205 and 11974046)。
文摘The quantum search on the graph is a very important topic.In this work,we develop a theoretic method on searching of single vertex on the graph[Phys.Rev.Lett.114110503(2015)],and systematically study the search of many vertices on one low-connectivity graph,the joined complete graph.Our results reveal that,with the optimal jumping rate obtained from the theoretical method,we can find such target vertices at the time O(√N),where N is the number of total vertices.Therefore,the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.
文摘Let G be a graph of order n with vertex set V(G) = {v1, v2,…, vn}. the adjacency matrix of G is an n × n matrix A(G) = (aij)n×n, where aij is the number edges joining vi and vj in G. The eigenvalues λ1, λ2, λ3,…, λn, of A(G) are said to be the eigenvalues of the graph G and to form the spectrum of this graph. The number of nonzero eigenvalues and zero eigenvalues in the spectrum of G are called rank and nullity of the graph G, and are denoted by r(G) and η(G), respectively. It follows from the definitions that r(G) + η(G) = n. In this paper, by using the operation of multiplication of vertices, a characterization for graph G with pendant vertices and r(G) = 7 is shown, and then a characterization for graph G with pendant vertices and r(G) less than or equal to 7 is shown.
基金supported in part by National Natural Science Foundation of China under Grant No.10575050the Research Fund for the Doctoral Program of Higher Education under Grant No.20060284020
文摘Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the #-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 （2005） 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 （1998） 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann Oakes-Renner relation also holds at finite chemical potential
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of average degree of edge vertices of China aviation network were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the average degrees of edge vertices in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the average degree of edge vertices had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of arithmetic average of edge vertices nearest neighbor average degree values of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the arithmetic averages of edge vertices nearest neighbor average degree values of China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the arithmetic average of edge vertices nearest neighbor average degree values had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
基金supported in part by the National Natural Science Foundation of China(Grant No.11871398)the Natural Science Foundation of Shaanxi Province(Nos.2020JQ-107,2020JQ-696)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(Nos.ZZ2018171,CX2020190).
文摘Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).
基金Partially supported by National Natural Science Foundation of China(No.11771172)key scientific and technological project of higher education of Henan Province(No.19A110019)+1 种基金Science and technology innovation fund of Henan Agricultural University(No.KJCX2019A15)Partially supported by the Ph D Research Foundation of Henan Agricultural University(No.30500614)
文摘A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.21773222,U1732272,and U1932214)the National Key R&D Program of China(Nos.2017YFA0403402,2017YFA0403403,and 2019YFA0405601)+1 种基金Users with Excellence Program of Hefei Science Center CAS(No.2020HSC-UE004)the DNL Cooperation Fund,CAS(No.DNL180201).
文摘Chiral nanoporous nanoarchitectures exhibit potential applications in various fields including chiral separation,sensing and catalysis.Two-dimensional(2D)supramolecular chemistry offers novel methods to build chiral nanoporous networks from achiral molecules.Herein,we report a series of chiral nanoporous networks built by an achiral precursor molecule via a stepwise annealing strategy on Ag(100).The nanoporous network morphologies and structural details are characterized by high-resolution scanning tunneling microscopy(STM).It is revealed that all vertices within networks are chiral.These chiral vertices are either dimeric,trimeric,or tetrameric.The connection of these chiral vertices gives rise to diverse chiral nanopores with varying shapes and sizes.A strict chirality correlation between nanopores and their vertices is determined.Specifically,enantiomeric vertices of one-pair nanopore enantiomers are always in identical type but opposite handedness.This work serves as a model to investigate the influence of vertex chirality on nanopore chirality of a supramolecular matrix.The attained chiral nanopores could potentially be utilized as templates for surface reaction,chiral recognition,etc.The mirror-symmetric silver adatoms clusters dictated by chiral nanopore are discerned.
文摘Schuster, Cai Maocheng and Lin Yixun studied the interpolation theory for the number of end vertices of spanning trees of graph. Zhang Fuji and Guo Xiaofeng obtained the related result of digraph. This paper is devoted to find the upper and lower bounds of the maximum number of end vertices of spanning (directed) trees for directed or undirected graphs. Our result is connected with some parameters in graph theory such as cyclomatic number and absorption number. For our purpose,
基金funded by the National Research Foundation of Korea(NRF)grant from the Ministry of Science and ICT(MSIT),Republic of Korea(Nos.RS-2024-00407469 and RS-2025-00517964)the BK21 FOUR program of Graduate School,Kyung Hee University(GS-1-JO-NON-20240417)。
文摘Optimizing plant architecture for specific cultivation methods is essential for enhancing fruit productivity.Unlike indeterminate growth plants,the total productivity of determinate growth plants relies on cumulative fruit production and synchronized fruit ripening from both main and axillary shoots.Here,we focused on SlD14and SlMAX1,two key genes involved in the regulation of strigolactone(SL)signaling and biosynthesis,with the goal of maximizing yield and syn chronizing fruit ripening by fine-tuning axillary shoot growth.Using clustered regularly interspaced short palindromic repeats(CRISPR)/CRISPR-associated protein 9(Cas9)technology,we found that the sld14,slmax1,and sld14 slmax1mutant plants exhibited reduced plant height and increased axillary shoot proliferation compared to wild-type plants.However,these mutants showed reduced yield and delayed ripening,likely due to a source-sink imbalance caused by excessive axillary shoot development.A weak sld14 allele displayed a milder phenotype,maintaining total fruit yield and harvest index despite smaller individual fruit size.These findings indicate that allelic variation in SL-related genes can influence plant architecture and yield components.Our results suggest that weak or partial alleles may serve as promising targets for tailoring tomato architecture to space-limited cultivation systems.
基金supported by the National Natural Science Foundation of China(Grant No.22479133,and No.22469008)the Natural Science Foundation of Guangdong Province(Grant No.2024A1515012235).
文摘Zinc-air batteries(ZABs)are promising candidates for flexible electronics due to their high energy density and low cost.However,their development is hindered by the sluggish kinetics of the oxygen evolution reaction(OER)and oxygen reduction reaction(ORR).Herein,we present a novel heterostructured electrocatalyst composed of vertically aligned N-doped graphene(NVG)arrays anchored on Ru-doped ceria(RCO)nanofibers,synthesized via a one-step plasma-enhanced chemical vapor deposition process.Notably,during the plasma-enhanced driven NVG growth,Ru nanoparticles are spontaneously in-situ exsolved from the RCO lattice,forming a unique Ru@RCO-NVG heterostructure.Density functional theory calculations reveal that the Ru@RCO-NVG heterojunction induces interfacial electronic redistribution,thereby significantly lowering the energy barriers for both OER and ORR.Benefiting from the synergistic effects,the Ru@RCO-NVG catalyst exhibits exceptional intrinsic activity towards OER/ORR(an overpotential of 370 mV for OER at 10 mA cm^(−2)and a half-wave potential of 0.86 V for ORR),and higher all-solid-state flexible ZAB performance(peak power density of 286.1 mW cm^(−2)),surpassing commercial Pt/C-IrO_(2)catalysts.This work not only advances the integration of synergistic graphene/ceria composites but also offers a promising strategy for designing efficient electrocatalysts for next-generation energy conversion technologies.
基金supported by the National Natural Science Foundation of China(Grant No.42261134532,42405059,and U2342212)。
文摘This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.
基金sponsored by the National Natural Science Foundation of China(Grant No.42202205)Natural Science Foundation of Shandong Province,China(Grant No.ZR2021QD072).-。
文摘The vertical heterogeneity of the pore structure in deep coal seams with varying ash yields is a key control for coalbed methane storage and producibility;however,its specific impact on gas adsorption is not clearly defined.The focus of this study is the No.8 coal seam of the Carboniferous Benxi Formation in the Central-Eastern Ordos Basin.By integrating microscopic identification,proximate analysis,gas adsorption(CO_(2),N_(2),and CH_(4)),and the multifractal theory,we quantitatively characterized the nanopore structure(micropores<2 nm and mesopores 2 nm-100 nm)of coal reservoirs with varying ash yields.The results indicate that(1)ash yield is the primary factor that controls the vertical evolution of pore structures in coal seams.In low-ash yield coal seams,the extent of thermal evolution and ash yield jointly constrain the heterogeneity of pore size distribution.In mediumto high-ash yield coal seams,the heterogeneity of pore structure and pore size distribution are predominantly constrained by ash yield.(2)As the ash yield vertically increases,the mesoporous pore volume and specific surface area initially decrease and subsequently increase,while the contribution of micropores to both pore volume and specific surface area continuously diminishes.Consequently,the total pore volume and specific surface area of the coal samples exhibit a two-stage reduction close to an ash yield threshold of approximately 20%.(3)Further,the Langmuir volume for CH_(4)adsorption sharply declines below the 20%threshold,followed by a gradual decrease;in contrast,the Langmuir pressure initially decreases and subsequently increases.Hence,the vertical increase in ash yield constrains the development of pore systems and diminishes pore connectivity,thereby reducing methane adsorption capacity and adversely affecting coalbed methane productivity.(4)Low-ash yield coal reservoirs are characterized by a rapid gas breakthrough and high productivity,whereas medium-ash yield coal reservoirs generally require prolonged depressurization to achieve peak gas production.These findings reveal that in medium-high rank coal,ash yield―and not thermal evolution―is the main factor that controls vertical pore evolution and methane adsorption efficiency.The quantitative ash yield threshold(20%)established in this study provides a practical criterion for evaluating reservoir quality and predicting vertical variations in gas storage potential in the Ordos Basin.
基金supported in part by the National Key R&D Program of China under Grant 2024YFB4405300 and 2022YFA1204300the Natural Science Foundation of Hunan Province under Grant 2023JJ20016+2 种基金the National Natural Science Foundation of China under Grants of 52221001 and 62090035the Key Research and Development Plan of Hunan Province under grants of 2022GK3002 and 2023GK2012the Key Program of Science and Technology Department of Hunan Province under grant of 2020XK2001。
文摘Permeable electronics promise improved physiological comfort,but remain constrained by limited functional integration and poor mechanical robustness.Here,we report a three-dimensional(3D)permeable electronic system that overcomes these challenges by combining electrospun SEBS nanofiber mats,high-resolution liquid metal conductors patterned via thermal imprinting(50μm),and a strain isolators(SIL)that protects vertical interconnects(VIAs)from stress concentration.This architecture achieves ultrahigh air permeability(>5.09 m L cm^(-2)min^(-1)),exceptional stretchability(750%fracture strain),and reliable conductivity maintained through more than 32,500 strain cycles.Leveraging these advances,we have integrated multilayer circuits,strain sensors,and a three-axis accelerometer to achieve a fully integrated,stretchable,permeable wireless real-time gesture recognition glove.The system enables accurate sign language interpretation(98%)and seamless robotic hand control,demonstrating its potential for assistive technologies.By uniting comfort,durability,and high-density integration,this work establishes a versatile platform for nextgeneration wearable electronics and interactive human-robot interfaces.
基金jointly supported by the National Natural Science Foundation of China[grant numbers U2342202,42175005,and 42175016]the Qing Lan Project[grant number R2023Q06]。
文摘This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shear(VWS),using idealized numerical experiments.Results reveal that the SE develops greater radial extent when surface winds align with VWS compared to counter-aligned conditions.In alignment configurations,shear-enhanced surface winds on the right flank amplify surface enthalpy fluxes,thereby elevating boundary-layer entropy within the downshear outer-core region.Subsequently,more vigorous outer rainbands develop,inducing marked acceleration of tangential winds in the outer core preceding SE formation.The resultant radial expansion of supergradient winds near the boundary-layer top triggers widespread convective activity immediately beyond the inner core.Progressive axisymmetrization of this convective forcing ultimately generates an expansive SE structure.
