Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defec...Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.展开更多
Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear ...Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.展开更多
By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic ...By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.展开更多
The grass spikelet is a unique inflorescence structure that determines grain size.Although many genetic factors have been well characterized for grain size and glume development,the underlying molecular mechanisms in ...The grass spikelet is a unique inflorescence structure that determines grain size.Although many genetic factors have been well characterized for grain size and glume development,the underlying molecular mechanisms in rice are far from established.Here,we isolated rice gene,AGL1 that controlled grain size and determines the fate of the sterile lemma.Loss of function of AGL1 produced larger grains and reduced the size of the sterile lemma.Larger grains in the agl1 mutant were caused by a larger number of cells that were longer and wider than in the wild type.The sterile lemma in the mutant spikelet was converted to a rudimentary glume-like organ.Our findings showed that the AGL1(also named LAX1)protein positively regulated G1 expression,and negatively regulated NSG1 expression,thereby affecting the fate of the sterile lemma.Taken together,our results revealed that AGL1 played a key role in negative regulation of grain size by controlling cell proliferation and expansion,and supported the opinion that rudimentary glume and sterile lemma in rice are homologous organs.展开更多
A review of the history of human development shows that every major technological revolution brings new challenges to national security.With the advent of the information technology revolution represented by the Inter...A review of the history of human development shows that every major technological revolution brings new challenges to national security.With the advent of the information technology revolution represented by the Internet,cybersecurity has become an issue of paramount importance,and the digital intelligence revolution with digital technology innovations such as big data and cloud computing has further expanded the connotation and extension of cybersecurity.展开更多
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo...This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.展开更多
This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple ex...This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.展开更多
In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. Th...In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.展开更多
On the basis of Hill's lemma for classical Cauchy continuum, a version of Hill's lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. T...On the basis of Hill's lemma for classical Cauchy continuum, a version of Hill's lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.展开更多
Let B2,p:= {z ∈ C2: |z1|2+ |z2|p< 1}(0 < p < 1). Then, B2,p(0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ...Let B2,p:= {z ∈ C2: |z1|2+ |z2|p< 1}(0 < p < 1). Then, B2,p(0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈ ?B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2,p, where z0 is any smooth boundary point of B2,p.展开更多
The Q gene in common wheat encodes an APETALA2(AP2) transcription factor that causes the free threshing attribute. Wheat spikelets bearing several florets are subtended by a pair of soft glumes that allow free liberat...The Q gene in common wheat encodes an APETALA2(AP2) transcription factor that causes the free threshing attribute. Wheat spikelets bearing several florets are subtended by a pair of soft glumes that allow free liberation of seeds. In wild species, the glumes are tough and rigid,making threshing difficult. However, the nature of these "soft glumes", caused by the domestication allele Q is not clear. Here, we found that over expression of Q in common wheat leads to homeotic florets at glume positions. We provide phenotypic, microscopy, and marker genes evidence to demonstrate that the soft glumes of common wheat are in fact lemma-like organs, or so-called sterile-lemmas. By comparing the structures subtending spikelets in wheat and other crops such as rice and maize, we found that AP2 genes may play conserved functions in grasses by manipulating vestigial structures, such as floret-derived soft glumes in wheat and empty glumes in rice. Conversion of these seemingly vegetative organs to reproductive organs may be useful in yield improvement of crop species.展开更多
The strict bounded real lemma for linear system with finite discrete jumps was considered. Especially, the case where D matrices in the system are not assumed to be zero was dealt. Several versions of the bounded real...The strict bounded real lemma for linear system with finite discrete jumps was considered. Especially, the case where D matrices in the system are not assumed to be zero was dealt. Several versions of the bounded real lemma are presented in terms of solution to Riccati differential equations or inequalities with finite discrete jumps. Both the finite and infinite horizon cases are considered. These results generalize the existed bounded real lemma for linear systems.展开更多
In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
Rice florets are subtended by two sterile lemmas,whose origin and biological functions have not been studied extensively.Here we demonstrate that two putative transcription factors,LAX PANICLE1(LAX1)and FRIZZY PANICLE...Rice florets are subtended by two sterile lemmas,whose origin and biological functions have not been studied extensively.Here we demonstrate that two putative transcription factors,LAX PANICLE1(LAX1)and FRIZZY PANICLE(FZP),synergistically control the development of sterile lemmas.Both LAX1 and FZP are previously known for their roles in panicle and floret development.Disruption of either LAX1 or FZP greatly reduces the number of floret development.We generated new lax1 mutants(lax1-c)using CRISPR/Cas9 gene editing technology.In addition to the expected lax panicle phenotypes,we noticed that a significant number of spikelets of lax1-c developed elongated sterile lemmas.Moreover,our characterization of lax1-RNAi plants also revealed sterile lemma phenotypes similar to lax1-c mutants.We isolated a weak allele of fzp(fzp-14)in a genetic screen for lax1–1 enhancers.The fzp-14 lax1–1 double mutants completely eliminated flower development.Interestingly,the isolated fzp-14 produced spikelets with elongated sterile lemmas.Furthermore,fzp-14 was haploid-insufficient in the lax1–1 background whereas fzp-14 heterozygous plants were indistinguishable from wild type plants.The lax1–1 fzp-14+/−also developed elongated sterile lemma as observed in lax1-c,lax1-RNAi,and fzp-14,suggesting that LAX1 and FZP synergistically control sterile lemma development.展开更多
Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception o...Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.展开更多
Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with exp...Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.展开更多
A. Robinson's sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^*R is its corollary. As its application, the paper proves a property about topology of uniform conv...A. Robinson's sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^*R is its corollary. As its application, the paper proves a property about topology of uniform convergence.展开更多
We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.
Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including ...Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.展开更多
In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimens...In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(Dn, BN) is C1+α at z0 ∈ ErDn with f(0) = 0 and f(z0) = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =(λ1,0,…,λr,0,…,0)T∈R2 nsatisfying λi≥1/(22 n-1) for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.展开更多
基金supported in part by the National Science Fund for Distinguished Young Scholarship of China (62025602)the National Natural Science Foundation of China (11931915, U22B2036)+2 种基金Fok Ying-Tong Education Foundationm China (171105)Technological lmnovation Team of Shaanxi Province (2020TD013)the Tencent Foundation and XPLORER PRIZE。
文摘Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.
基金Supported by the National Natural Science Foundation of China(12001142).
文摘Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.
基金supported by the National Natural Science Foundation of China(12071161,11971165)supported by the National Natural Science Foundation of China(11971042)the Natural Science Foundation of Zhejiang Province(Z24A010005)。
文摘By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.
基金supported by the National Natural Science Foundation of China(32372118,32188102,32071993)the Qian Qian Academician Workstation,Specific Research Fund of the Innovation Platform for Academicians in Hainan Province(YSPTZX202303)+1 种基金Key Research and Development Program of Zhejiang Province(2021C02056)Hainan Seed Industry Laboratory,China(B21HJ0220)。
文摘The grass spikelet is a unique inflorescence structure that determines grain size.Although many genetic factors have been well characterized for grain size and glume development,the underlying molecular mechanisms in rice are far from established.Here,we isolated rice gene,AGL1 that controlled grain size and determines the fate of the sterile lemma.Loss of function of AGL1 produced larger grains and reduced the size of the sterile lemma.Larger grains in the agl1 mutant were caused by a larger number of cells that were longer and wider than in the wild type.The sterile lemma in the mutant spikelet was converted to a rudimentary glume-like organ.Our findings showed that the AGL1(also named LAX1)protein positively regulated G1 expression,and negatively regulated NSG1 expression,thereby affecting the fate of the sterile lemma.Taken together,our results revealed that AGL1 played a key role in negative regulation of grain size by controlling cell proliferation and expansion,and supported the opinion that rudimentary glume and sterile lemma in rice are homologous organs.
文摘A review of the history of human development shows that every major technological revolution brings new challenges to national security.With the advent of the information technology revolution represented by the Internet,cybersecurity has become an issue of paramount importance,and the digital intelligence revolution with digital technology innovations such as big data and cloud computing has further expanded the connotation and extension of cybersecurity.
基金by Dr Kemp from National Mathematics and Science College.
文摘This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.
基金supported by National Natural Science Foundation of China(No.60710002,60974044)Program for Changjiang Scholars and Innovative Research Team in University
文摘This note presents a set of new versions of Barbalat's lemma combining with positive (negative) definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.
基金supported by National Natural Science Foundations of China(11011373,11201199,11271333)Zhejiang Provincial Natural Science Foundation of China(LY14A010008)
文摘In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.
基金supported by the National Natural Science Foundation of China (90715011, 10672033 and 10590354) the National Key Basic Research and Development Program (2002CB412709) the Australia Research Council through the ARC International Fellowship Offered at University of Newcastle (LX0666274)
文摘On the basis of Hill's lemma for classical Cauchy continuum, a version of Hill's lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.
基金The project supported in part by the National Natural Science Foundation of China(11671306)
文摘Let B2,p:= {z ∈ C2: |z1|2+ |z2|p< 1}(0 < p < 1). Then, B2,p(0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈ ?B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2,p, where z0 is any smooth boundary point of B2,p.
基金supported by the National Key Program for Transgenic Crop Cultivation (2016ZX09001-001)The CAAS Agricultural Science and Technology Innovation Program Cooperation and Innovation Mission (CAAS-XTCX2016)
文摘The Q gene in common wheat encodes an APETALA2(AP2) transcription factor that causes the free threshing attribute. Wheat spikelets bearing several florets are subtended by a pair of soft glumes that allow free liberation of seeds. In wild species, the glumes are tough and rigid,making threshing difficult. However, the nature of these "soft glumes", caused by the domestication allele Q is not clear. Here, we found that over expression of Q in common wheat leads to homeotic florets at glume positions. We provide phenotypic, microscopy, and marker genes evidence to demonstrate that the soft glumes of common wheat are in fact lemma-like organs, or so-called sterile-lemmas. By comparing the structures subtending spikelets in wheat and other crops such as rice and maize, we found that AP2 genes may play conserved functions in grasses by manipulating vestigial structures, such as floret-derived soft glumes in wheat and empty glumes in rice. Conversion of these seemingly vegetative organs to reproductive organs may be useful in yield improvement of crop species.
基金National Natural Science Foundation of China(No.60274058)
文摘The strict bounded real lemma for linear system with finite discrete jumps was considered. Especially, the case where D matrices in the system are not assumed to be zero was dealt. Several versions of the bounded real lemma are presented in terms of solution to Riccati differential equations or inequalities with finite discrete jumps. Both the finite and infinite horizon cases are considered. These results generalize the existed bounded real lemma for linear systems.
基金supported by the National Natural Science Foundation of China(11201199)the Scientific Research Foundation of Jinling Institute of Technology(Jit-b-201221)Qing Lan Project
文摘In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.
基金supported by the National Transgenic Research Program of China(2016ZX08010002)
文摘Rice florets are subtended by two sterile lemmas,whose origin and biological functions have not been studied extensively.Here we demonstrate that two putative transcription factors,LAX PANICLE1(LAX1)and FRIZZY PANICLE(FZP),synergistically control the development of sterile lemmas.Both LAX1 and FZP are previously known for their roles in panicle and floret development.Disruption of either LAX1 or FZP greatly reduces the number of floret development.We generated new lax1 mutants(lax1-c)using CRISPR/Cas9 gene editing technology.In addition to the expected lax panicle phenotypes,we noticed that a significant number of spikelets of lax1-c developed elongated sterile lemmas.Moreover,our characterization of lax1-RNAi plants also revealed sterile lemma phenotypes similar to lax1-c mutants.We isolated a weak allele of fzp(fzp-14)in a genetic screen for lax1–1 enhancers.The fzp-14 lax1–1 double mutants completely eliminated flower development.Interestingly,the isolated fzp-14 produced spikelets with elongated sterile lemmas.Furthermore,fzp-14 was haploid-insufficient in the lax1–1 background whereas fzp-14 heterozygous plants were indistinguishable from wild type plants.The lax1–1 fzp-14+/−also developed elongated sterile lemma as observed in lax1-c,lax1-RNAi,and fzp-14,suggesting that LAX1 and FZP synergistically control sterile lemma development.
文摘Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.
基金This work was supported by the National Natural Science Foundation of China (No. 60274058).
文摘Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.
基金the Basic Research Foundation of Xi'an University Architecture Technology(JC0620)the Youth Science and Technology Foundation of Xi'an University of Architecture and Technology(QN0736)
文摘A. Robinson's sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^*R is its corollary. As its application, the paper proves a property about topology of uniform convergence.
基金Research supported by the National Natural Science Foundation of China(1120119911071083+1 种基金11671361)Jiangsu Overseas Visiting Scholar Program for University Prominent Young&Middle-aged Teachers and Presidents
文摘We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(2013R1A1A2005402)National Science Foundation(DMS-1109063)
文摘Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.
基金Supported by the Natural and Science Foundation of China(61379001,61771001)
文摘In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(Dn, BN) is C1+α at z0 ∈ ErDn with f(0) = 0 and f(z0) = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =(λ1,0,…,λr,0,…,0)T∈R2 nsatisfying λi≥1/(22 n-1) for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.