A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-...A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-degree-of-freedom optimization (CMMO) problem, the commonly used quadratic programming model is converted into a two-level optimization problem solved by the tolerant lexicographic method and the varying-domain optimization method. In contrast to previous works, the proposed approach allows the decision-maker to determine a desirable achievement degree for each goal to reflect explicitly the relative importance of these goals. The resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum. The power of the proposed approach is demonstrated with an example.展开更多
Let p(z)=be a polynomial degree n and let Then accord-ing to Bernstein's inequality ||p'||<n||p||.It is a well known open problem to obtain inequality analogous to Bernstein's inequality for the class I...Let p(z)=be a polynomial degree n and let Then accord-ing to Bernstein's inequality ||p'||<n||p||.It is a well known open problem to obtain inequality analogous to Bernstein's inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z)Here we obtain an inequality analogous to Bernstein's inequality for a subclass of IIn Our results include several of the known results as special cases.展开更多
Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（with...Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.展开更多
If G satisfies the permutizer condition, we call G a pc-group; clearly, all the super-solvable groups are pc-groups. It was shown in [1] that pc-groups of odd order were supersolvable. It is easy to verify that the sy...If G satisfies the permutizer condition, we call G a pc-group; clearly, all the super-solvable groups are pc-groups. It was shown in [1] that pc-groups of odd order were supersolvable. It is easy to verify that the symmetric group of degree four is a solvable pc-group, but it is not supersolvable. In general, solvable展开更多
In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebe...In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincare inequalities for vector fields satisfying Hormander＇s condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p（x）-subLaplacian. Our results are only stated and proved for vector fields satisfying Hormander＇s condition, but they also hold for Grushin vector fields as well with obvious modifications.展开更多
Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subal...Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.展开更多
Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists ...Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists a positive constant M>0 such that |φ(x)-φ(y)|(?)Mψ(|x-y|) for all x,y∈R^1. For ψ(x)=x^r,0<r(?)1, the condition Lip-x^r reduces to the usual rth order Lipschitz condition, a fact that will be denoted by Lip-r instead of Lip-x^r. Let J be the set of all those one-dimension-展开更多
In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in t...In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in the construction of Q processes which satisfy the backward equations, the nonconservative case may be reduced to展开更多
In order to make a decision in the face of multiple objectives, it is necessary to know the relative importance of the different objectives. Yet, it is often very difficult to specify a set of precise weights before p...In order to make a decision in the face of multiple objectives, it is necessary to know the relative importance of the different objectives. Yet, it is often very difficult to specify a set of precise weights before possible alternatives solutions are known. In this paper, we present an improved weighted method, which is based on a modified definition by the membership function of fuzzy theory; an interactive, iterative method for arriving at an acceptable solution. The decision maker gradually discerns what is achievable and adjusts his aspirations and implicitly the specification of weights and trade-offs between his objectives, in the light of what he learns. To aid the decision maker＇s cognition and to allow him to express his wishes in a natural way, we present decision maker with grey relational degree to select the best solution from the finite solutions.展开更多
In 1959,the talk of Richard P.Feynman“There's plenty of room at the bottom”inspired us to explore the very,very small world where a lot of new things would happen that represent completely new designing opportun...In 1959,the talk of Richard P.Feynman“There's plenty of room at the bottom”inspired us to explore the very,very small world where a lot of new things would happen that represent completely new designing opportunities.Atoms on a small scale behave like nothing on a large scale,for they satisfy the laws of quantum mechanics.As we go down and fiddle around with the atoms there,we work with different laws,which enables us to realize different tasks and manufacture in different ways.展开更多
Chinese Chemical Letters(CCL)(ISSN 1001-8417) was founded in July 1990. The journal publishes preliminary accounts in the whole field of chemistry, including inorganic chemistry, organic chemistry, analytical chemistr...Chinese Chemical Letters(CCL)(ISSN 1001-8417) was founded in July 1990. The journal publishes preliminary accounts in the whole field of chemistry, including inorganic chemistry, organic chemistry, analytical chemistry, physical chemistry, polymer chemistry, applied chemistry, etc., satisfying a real and urgent need for the dissemination of research results, especially hot topics. The journal does not accept articles previously published or scheduled to be published. To verify originality, your article may be checked by the originality detection service CrossCheck.展开更多
设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(...设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。展开更多
My childhood and adolescence1were a joyous outpouring2 of energy,a ceaseless3 quest for expression,skill,and experience.School was only a background to the supreme delight of lessons in music,dance,and dramatics,and t...My childhood and adolescence1were a joyous outpouring2 of energy,a ceaseless3 quest for expression,skill,and experience.School was only a background to the supreme delight of lessons in music,dance,and dramatics,and the thrill of sojourns4 in the country,theaters,and concerts.And books,展开更多
Dielectronic-recombination cross sections of hydrogen-like argon are calculated conveniently by our simplified relativistic configuration-interaction method.The results for the KLL,KLM,KLN,and KLO resonances are in go...Dielectronic-recombination cross sections of hydrogen-like argon are calculated conveniently by our simplified relativistic configuration-interaction method.The results for the KLL,KLM,KLN,and KLO resonances are in good agreement with experimental measurement within a few percent.Our methods can provide various dielectronic-recombination rates which can satisfy the need for relevant applications.展开更多
For bipartite angle consensus tracking and vibration suppression of multiple Timoshenko manipulator systems with time-varying actuator faults,parameter and modeling uncertainties,and unknown disturbances,a novel distr...For bipartite angle consensus tracking and vibration suppression of multiple Timoshenko manipulator systems with time-varying actuator faults,parameter and modeling uncertainties,and unknown disturbances,a novel distributed boundary event-triggered control strategy is proposed in this work.In contrast to the earlier findings,time-varying consensus tracking and actuator defects are taken into account simultaneously.In addition,the constructed event-triggered control mechanism can achieve a more flexible design because it is not required to satisfy the input-to-state condition.To achieve the control objectives,some new integral control variables are given by using back-stepping technique and boundary control.Moreover,adaptive neural networks are applied to estimate system uncertainties.With the proposed event-triggered scheme,control inputs can reduce unnecessary updates.Besides,tracking errors and vibration states of the closed-looped network can be exponentially convergent into some small fields,and Zeno behaviors can be excluded.At last,some simulation examples are given to state the effectiveness of the control algorithms.展开更多
文摘A hierarchical satisfying optimal algorithm incorporating different importance and preemptive priorities is formulated. With the priority structure given by the decision-maker in the constrained multi-objective multi-degree-of-freedom optimization (CMMO) problem, the commonly used quadratic programming model is converted into a two-level optimization problem solved by the tolerant lexicographic method and the varying-domain optimization method. In contrast to previous works, the proposed approach allows the decision-maker to determine a desirable achievement degree for each goal to reflect explicitly the relative importance of these goals. The resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum. The power of the proposed approach is demonstrated with an example.
文摘Let p(z)=be a polynomial degree n and let Then accord-ing to Bernstein's inequality ||p'||<n||p||.It is a well known open problem to obtain inequality analogous to Bernstein's inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z)Here we obtain an inequality analogous to Bernstein's inequality for a subclass of IIn Our results include several of the known results as special cases.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117134311426121)+1 种基金the Science Foundation of Jiangxi University of Science and Technology(Grant Nos.NSFJ2014–K12NSFJ2015–G24)
文摘Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.
文摘If G satisfies the permutizer condition, we call G a pc-group; clearly, all the super-solvable groups are pc-groups. It was shown in [1] that pc-groups of odd order were supersolvable. It is easy to verify that the symmetric group of degree four is a solvable pc-group, but it is not supersolvable. In general, solvable
基金supported by NSFC(Grant No.11371056)supported by a US NSF grant
文摘In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincare inequalities for vector fields satisfying Hormander＇s condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p（x）-subLaplacian. Our results are only stated and proved for vector fields satisfying Hormander＇s condition, but they also hold for Grushin vector fields as well with obvious modifications.
基金Supported by the National Natural Science Foundation of China (Grant No.11071040)the Natural Science Foundation of Fujian Province (Grant No. 2009J05005)
文摘Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.
文摘Let ψ(x) be a continuous and strictly increasing function defined on [0,∞) with ψ(0)=0 and ψ(x)/x is nonincreasing. A function φ(x) is said to satisfy the condition Lip-ψ (denoted byφ ∈Lip-ψ) if there exists a positive constant M>0 such that |φ(x)-φ(y)|(?)Mψ(|x-y|) for all x,y∈R^1. For ψ(x)=x^r,0<r(?)1, the condition Lip-x^r reduces to the usual rth order Lipschitz condition, a fact that will be denoted by Lip-r instead of Lip-x^r. Let J be the set of all those one-dimension-
文摘In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in the construction of Q processes which satisfy the backward equations, the nonconservative case may be reduced to
基金This research is supported by National Natural Science Foundation of China（70471019）
文摘In order to make a decision in the face of multiple objectives, it is necessary to know the relative importance of the different objectives. Yet, it is often very difficult to specify a set of precise weights before possible alternatives solutions are known. In this paper, we present an improved weighted method, which is based on a modified definition by the membership function of fuzzy theory; an interactive, iterative method for arriving at an acceptable solution. The decision maker gradually discerns what is achievable and adjusts his aspirations and implicitly the specification of weights and trade-offs between his objectives, in the light of what he learns. To aid the decision maker＇s cognition and to allow him to express his wishes in a natural way, we present decision maker with grey relational degree to select the best solution from the finite solutions.
文摘In 1959,the talk of Richard P.Feynman“There's plenty of room at the bottom”inspired us to explore the very,very small world where a lot of new things would happen that represent completely new designing opportunities.Atoms on a small scale behave like nothing on a large scale,for they satisfy the laws of quantum mechanics.As we go down and fiddle around with the atoms there,we work with different laws,which enables us to realize different tasks and manufacture in different ways.
文摘Chinese Chemical Letters(CCL)(ISSN 1001-8417) was founded in July 1990. The journal publishes preliminary accounts in the whole field of chemistry, including inorganic chemistry, organic chemistry, analytical chemistry, physical chemistry, polymer chemistry, applied chemistry, etc., satisfying a real and urgent need for the dissemination of research results, especially hot topics. The journal does not accept articles previously published or scheduled to be published. To verify originality, your article may be checked by the originality detection service CrossCheck.
文摘设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。
文摘My childhood and adolescence1were a joyous outpouring2 of energy,a ceaseless3 quest for expression,skill,and experience.School was only a background to the supreme delight of lessons in music,dance,and dramatics,and the thrill of sojourns4 in the country,theaters,and concerts.And books,
基金Supported by Chinese Association of Atomic and Molecular Data,Chinese Science and Technology Commissionthe National Natural Science Foundation of ChinaScience and Technology Funds of CAEP.
文摘Dielectronic-recombination cross sections of hydrogen-like argon are calculated conveniently by our simplified relativistic configuration-interaction method.The results for the KLL,KLM,KLN,and KLO resonances are in good agreement with experimental measurement within a few percent.Our methods can provide various dielectronic-recombination rates which can satisfy the need for relevant applications.
基金supported in part by the National Key R&D Program of China(2021YFB3202200)the Natural Science Foundation of China(62203141)the Guangdong Basic and Applied Basic Research Foundation(2021B1515120017)。
文摘For bipartite angle consensus tracking and vibration suppression of multiple Timoshenko manipulator systems with time-varying actuator faults,parameter and modeling uncertainties,and unknown disturbances,a novel distributed boundary event-triggered control strategy is proposed in this work.In contrast to the earlier findings,time-varying consensus tracking and actuator defects are taken into account simultaneously.In addition,the constructed event-triggered control mechanism can achieve a more flexible design because it is not required to satisfy the input-to-state condition.To achieve the control objectives,some new integral control variables are given by using back-stepping technique and boundary control.Moreover,adaptive neural networks are applied to estimate system uncertainties.With the proposed event-triggered scheme,control inputs can reduce unnecessary updates.Besides,tracking errors and vibration states of the closed-looped network can be exponentially convergent into some small fields,and Zeno behaviors can be excluded.At last,some simulation examples are given to state the effectiveness of the control algorithms.
