Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defin...Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.展开更多
Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are ...Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.展开更多
The autotetraploid Carassius auratus(4nRR,4n=200,RRRR)is derived from whole-genome duplication of Carassius auratus red var.(RCC,2n=100,RR).In the current study,we demonstrated that chromatophores and pigment changes ...The autotetraploid Carassius auratus(4nRR,4n=200,RRRR)is derived from whole-genome duplication of Carassius auratus red var.(RCC,2n=100,RR).In the current study,we demonstrated that chromatophores and pigment changes directly caused the coloration and variation of 4nRR skin(red in RCC,brownish-yellow in4nRR).To further explore the molecular mechanisms underlying coloration formation and variation in 4nRR,we performed transcriptome profiling and molecular functional verification in RCC and 4nRR.Results revealed that scarb1,associated with carotenoid metabolism,underwent significant down-regulation in 4nRR.Efficient editing of this candidate pigment gene provided clear evidence of its significant role in RCC coloration.Subsequently,we identified four divergent scarb1 homeologs in 4nRR:two original scarb1 homeologs from RCC and two duplicated ones.Notably,three of these homeologs possessed two highly conserved alleles,exhibiting biased and allelespecific expression in the skin.Remarkably,after precise editing of both the original and duplicated scarb1homeologs and/or alleles,4nRR individuals,whether singly or multiply mutated,displayed a transition from brownishyellow skin to a cyan-gray phenotype.Concurrently,the proportional areas of the cyan-gray regions displayed a gene-dose correlation.These findings illustrate the subfunctionalization of duplicated scarb1,with all scarb1genes synergistically and equally contributing to the pigmentation of 4nRR.This is the first report concerning the functional differentiation of duplicated homeologs in an autopolyploidfish,substantiallyenrichingour understanding of coloration formation and change within this group of organisms.展开更多
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function...In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bκ+1^c f(z))′= κBκ^c f(z)-(κ- 1)Bκ+1^c f(z),where b, c, p ∈ C and κ = p +(b + 1)/2 ∈ C / Z0^-(Z0^-= {0,-1,-2, … }). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.展开更多
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessar...In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
In this paper,a new basic method of constructing smooth production functions isgiven,and many ordinary production functions are drawn. It is obvious thatsome more production functions can be obtained from the method.
Numerous authors studied polarities in incidence structures or algebrization of projective geometry <a href="#1">[1]</a> <a href="#2">[2]</a>. The purpose of the present wor...Numerous authors studied polarities in incidence structures or algebrization of projective geometry <a href="#1">[1]</a> <a href="#2">[2]</a>. The purpose of the present work is to establish an algebraic system based on elementary concepts of spherical geometry, extended to hyperbolic and plane geometry. The guiding principle is: “<em>The point and the straight line are one and the same</em>”. Points and straight lines are not treated as dual elements in two separate sets, but identical elements within a single set endowed with a binary operation and appropriate axioms. It consists of three sections. In Section 1 I build an algebraic system based on spherical constructions with two axioms: <em>ab</em> = <em>ba</em> and (<em>ab</em>)(<em>ac</em>) = <em>a</em>, providing finite and infinite models and proving classical theorems that are adapted to the new system. In Section Two I arrange hyperbolic points and straight lines into a model of a projective sphere, show the connection between the spherical Napier pentagram and the hyperbolic Napier pentagon, and describe new synthetic and trigonometric findings between spherical and hyperbolic geometry. In Section Three I create another model of a projective sphere in the Cartesian coordinate system of the plane, and give methods and techniques for using the model in the theory of functions.展开更多
The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the ...The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres...This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.展开更多
Oligopeptide transporters(OPTs) encode integral membrane-localized proteins and have a broad range of substrate transport capabilities. Here, 28 BrrOPT genes were identified in the turnip. Phylogenetic analyses reveal...Oligopeptide transporters(OPTs) encode integral membrane-localized proteins and have a broad range of substrate transport capabilities. Here, 28 BrrOPT genes were identified in the turnip. Phylogenetic analyses revealed two well-supported clades in the OPT family, containing 15 BrrOPTs and 13 BrrYSLs.The exon/intron structure of OPT clade are conserved but the yellow stripe-like(YSL) clade was different.The exon/intron of the YSL clade possesses structural differences, whereas the YSL class motifs structure are conserved. The OPT genes are distributed unevenly among the chromosomes of the turnip genome.Phylogenetic and chromosomal distribution analyses revealed that the expansion of the OPT gene family is mainly attributable to segmental duplication. For the expression profiles at different developmental stages, a comprehensive analysis provided insights into the possible functional divergence among members of the paralog OPT gene family. Different expression levels under a variety of ion deficiencies also indicated that the OPT family underwent functional divergence during long-term evolution.Furthermore. BrrOPT8.1, BrrYSL1.2, BrrYSL1.3, BrrYSL6 and BrrYSL9 responded to Fe(Ⅱ) treatments and BrrYSL7 responded to calcium treatments, BrrYSL6 responded to multiple treatments in root, suggesting that turnip OPTs may be involved in mediating cross-talk among different ion deficiencies. Our data provide important information for further functional dissection of BrrOPTs, especially in transporting metal ions and nutrient deficiency stress adaptation.展开更多
We study the problem of a weighted integral of infinitely differentiable mul-tivariate functions defined on the unit cube with the L∞-norm of partial derivative of all orders bounded by 1.We consider the algorithms t...We study the problem of a weighted integral of infinitely differentiable mul-tivariate functions defined on the unit cube with the L∞-norm of partial derivative of all orders bounded by 1.We consider the algorithms that use finitely many function values as information(called standard information).On the one hand,we obtained that the interpolatory quadratures based on the extended Chebyshev nodes of the second kind have almost the same quadrature weights.On the other hand,by using the Smolyak al-gorithm with the above interpolatory quadratures,we proved that the weighted integral problem is of exponential convergence in the worst case setting.展开更多
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, ...By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.展开更多
A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), so...A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.展开更多
文摘Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.
文摘Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.
基金supported by the National Natural Science Foundation of China (32172972,U19A2040)Science and Technology Innovation Program of Hunan Province (2021RC4028)+4 种基金Earmarked Fund for China Agriculture Research System (CARS-45)Hunan Provincial Science and Technology Department (2019RS5001)Special Funds for Construction of Innovative Provinces in Hunan Province (2021NK1010)Special Science Found of Nansha-South China Agricultural University Fishery Research Institute,Guangzhou (NSYYKY202305,NSYYKY202306)Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province。
文摘The autotetraploid Carassius auratus(4nRR,4n=200,RRRR)is derived from whole-genome duplication of Carassius auratus red var.(RCC,2n=100,RR).In the current study,we demonstrated that chromatophores and pigment changes directly caused the coloration and variation of 4nRR skin(red in RCC,brownish-yellow in4nRR).To further explore the molecular mechanisms underlying coloration formation and variation in 4nRR,we performed transcriptome profiling and molecular functional verification in RCC and 4nRR.Results revealed that scarb1,associated with carotenoid metabolism,underwent significant down-regulation in 4nRR.Efficient editing of this candidate pigment gene provided clear evidence of its significant role in RCC coloration.Subsequently,we identified four divergent scarb1 homeologs in 4nRR:two original scarb1 homeologs from RCC and two duplicated ones.Notably,three of these homeologs possessed two highly conserved alleles,exhibiting biased and allelespecific expression in the skin.Remarkably,after precise editing of both the original and duplicated scarb1homeologs and/or alleles,4nRR individuals,whether singly or multiply mutated,displayed a transition from brownishyellow skin to a cyan-gray phenotype.Concurrently,the proportional areas of the cyan-gray regions displayed a gene-dose correlation.These findings illustrate the subfunctionalization of duplicated scarb1,with all scarb1genes synergistically and equally contributing to the pigmentation of 4nRR.This is the first report concerning the functional differentiation of duplicated homeologs in an autopolyploidfish,substantiallyenrichingour understanding of coloration formation and change within this group of organisms.
基金partly supported by the Natural Science Foundation of China(11271045)the Higher School Doctoral Foundation of China(20100003110004)+2 种基金the Natural Science Foundation of Inner Mongolia of China(2010MS0117)athe Higher School Foundation of Inner Mongolia of China(NJZY13298)the Commission for the Scientific Research Projects of Kafkas Univertsity(2012-FEF-30)
文摘In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bκ+1^c f(z))′= κBκ^c f(z)-(κ- 1)Bκ+1^c f(z),where b, c, p ∈ C and κ = p +(b + 1)/2 ∈ C / Z0^-(Z0^-= {0,-1,-2, … }). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
基金Project supported by the National Natural Science Foundation of China(Nos.51135003 and U1234208)the Major State Basic Research Development Program of China(973 Program)(No.2014CB046303)
文摘In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
文摘In this paper,a new basic method of constructing smooth production functions isgiven,and many ordinary production functions are drawn. It is obvious thatsome more production functions can be obtained from the method.
文摘Numerous authors studied polarities in incidence structures or algebrization of projective geometry <a href="#1">[1]</a> <a href="#2">[2]</a>. The purpose of the present work is to establish an algebraic system based on elementary concepts of spherical geometry, extended to hyperbolic and plane geometry. The guiding principle is: “<em>The point and the straight line are one and the same</em>”. Points and straight lines are not treated as dual elements in two separate sets, but identical elements within a single set endowed with a binary operation and appropriate axioms. It consists of three sections. In Section 1 I build an algebraic system based on spherical constructions with two axioms: <em>ab</em> = <em>ba</em> and (<em>ab</em>)(<em>ac</em>) = <em>a</em>, providing finite and infinite models and proving classical theorems that are adapted to the new system. In Section Two I arrange hyperbolic points and straight lines into a model of a projective sphere, show the connection between the spherical Napier pentagram and the hyperbolic Napier pentagon, and describe new synthetic and trigonometric findings between spherical and hyperbolic geometry. In Section Three I create another model of a projective sphere in the Cartesian coordinate system of the plane, and give methods and techniques for using the model in the theory of functions.
基金Supported by the National Natural Science Foundation of China(11171298)the Zhejiang Natural Science Foundation of China(Y6110425)
文摘The integral representation of differentiable functions in Octonion space is obtained and the explicit solution of the inhomogeneous Cauchy-Riemann equation is given by integral representation. As an application, the Cousin problem analogue of Mittag-Laffier problem is discussed.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
基金Supported by the National Natural Science Foundation of China (10571050 10871062)Hunan Provincial Innovation Foundation For Postgraduate
文摘This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.
基金supported financially by the Major Projects of National Natural Science Foundation of China(No. 31590823)the National Natural Science Foundation of China (No. 31601999)
文摘Oligopeptide transporters(OPTs) encode integral membrane-localized proteins and have a broad range of substrate transport capabilities. Here, 28 BrrOPT genes were identified in the turnip. Phylogenetic analyses revealed two well-supported clades in the OPT family, containing 15 BrrOPTs and 13 BrrYSLs.The exon/intron structure of OPT clade are conserved but the yellow stripe-like(YSL) clade was different.The exon/intron of the YSL clade possesses structural differences, whereas the YSL class motifs structure are conserved. The OPT genes are distributed unevenly among the chromosomes of the turnip genome.Phylogenetic and chromosomal distribution analyses revealed that the expansion of the OPT gene family is mainly attributable to segmental duplication. For the expression profiles at different developmental stages, a comprehensive analysis provided insights into the possible functional divergence among members of the paralog OPT gene family. Different expression levels under a variety of ion deficiencies also indicated that the OPT family underwent functional divergence during long-term evolution.Furthermore. BrrOPT8.1, BrrYSL1.2, BrrYSL1.3, BrrYSL6 and BrrYSL9 responded to Fe(Ⅱ) treatments and BrrYSL7 responded to calcium treatments, BrrYSL6 responded to multiple treatments in root, suggesting that turnip OPTs may be involved in mediating cross-talk among different ion deficiencies. Our data provide important information for further functional dissection of BrrOPTs, especially in transporting metal ions and nutrient deficiency stress adaptation.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11471043,11671271)by the Beijing Natural Science Foundation(Grant No.1172004)。
文摘We study the problem of a weighted integral of infinitely differentiable mul-tivariate functions defined on the unit cube with the L∞-norm of partial derivative of all orders bounded by 1.We consider the algorithms that use finitely many function values as information(called standard information).On the one hand,we obtained that the interpolatory quadratures based on the extended Chebyshev nodes of the second kind have almost the same quadrature weights.On the other hand,by using the Smolyak al-gorithm with the above interpolatory quadratures,we proved that the weighted integral problem is of exponential convergence in the worst case setting.
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
文摘In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
基金sponsored by the National Natural Science Foundation of China(11271197)the Science and Technology Foundation in Ministry of Education of China(207047)the Science Foundation of NUIST of China(20090202 and 2012r101)
文摘By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+1 种基金Liaoning Provincial Natural Science Foundation,China (Grant No 20062018)111 Project (Grant No B08015)
文摘A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.