The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite ...The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.展开更多
A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this p...A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.展开更多
In[6],it is proved that Erceg's pseudo-metric and pointwise pseudo-metric presented by Shi are equivalent.In this paper,it is proved that Theorem 1 in[6]is wrong.Further it is proved that Erceg's pseudo-metric...In[6],it is proved that Erceg's pseudo-metric and pointwise pseudo-metric presented by Shi are equivalent.In this paper,it is proved that Theorem 1 in[6]is wrong.Further it is proved that Erceg's pseudo-metric and pointwise pseudo-metric are not equivalent in the sense of topology.展开更多
For p ：〉 1, many improved or generalized results of the well-known Hardy＇s inequality have been established： In this paper, by means of the weight coefficient method, we establish the following Hardy type inequali...For p ：〉 1, many improved or generalized results of the well-known Hardy＇s inequality have been established： In this paper, by means of the weight coefficient method, we establish the following Hardy type inequality for p = -1：∑^n i=1（1/i∑^i j=1 aj）^-1〈∑^n i=1（1-π^2-9/3i）ai^-1,where ai 〉 0, i = 1,2,... ,n. For any fixed positive integer n 〉 2, we study the best constant Cn such that the inequality ∑^ni=1（1/i∑^ij=1aj）^-1≤cn∑^ni=1ai^-1holds. Moreover, by means ofthe Mathematica software, we givesome examples.展开更多
Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued fu...Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.展开更多
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.展开更多
基金Project (Nos. 60434020 and 60604003) supported by the NationalNatural Science Foundation of China
文摘The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.
文摘A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.
基金Foundation item： the National Natural Science Foundation of China （No. 10371079）.Acknowledgements The authors would like to thank the referees for their valuable comments and suggestions.
文摘In[6],it is proved that Erceg's pseudo-metric and pointwise pseudo-metric presented by Shi are equivalent.In this paper,it is proved that Theorem 1 in[6]is wrong.Further it is proved that Erceg's pseudo-metric and pointwise pseudo-metric are not equivalent in the sense of topology.
基金Foundation item： the National Natural Science Foundation of China （No. 10671136） the Natural Science Foundation of Sichuan Provincial Education Department （No. 2005A201）.
文摘For p ：〉 1, many improved or generalized results of the well-known Hardy＇s inequality have been established： In this paper, by means of the weight coefficient method, we establish the following Hardy type inequality for p = -1：∑^n i=1（1/i∑^i j=1 aj）^-1〈∑^n i=1（1-π^2-9/3i）ai^-1,where ai 〉 0, i = 1,2,... ,n. For any fixed positive integer n 〉 2, we study the best constant Cn such that the inequality ∑^ni=1（1/i∑^ij=1aj）^-1≤cn∑^ni=1ai^-1holds. Moreover, by means ofthe Mathematica software, we givesome examples.
基金the National Natural Science Foundation of China （No. 10771171） the Scientific Research Item of Gansu Education Department （No. 0601-20）.
文摘Absolute integrability and its absolute value inequality for fuzzy-number-valued func- tions are worth to be considered.In this paper,absolute integrability and its absolute value inequality for fuzzy-number-valued functions are discussed by means of the characteristic the- orems of nonabsolute fuzzy integrals and the embedding theorem,i.e.,the fuzzy number space can be embedded into a concrete Banach space.Several necessary and sufficient conditions and examples are given.
基金supported by Fonds National de la Recherche Luxembourg(Grant No.O14/7628746 GEOMREV)the University of Luxembourg(Grant No.IRP R-AGR-0517-10/AGSDE)+1 种基金supported by National Natural Science Foundation of China(Grant No.11501508)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ16A010009)
文摘In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.
