In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai...In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai 0=1,2,4） are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.展开更多
A feature extraction and fusion algorithm was constructed by combining principal component analysis(PCA) and linear discriminant analysis(LDA) to detect a fault state of the induction motor.After yielding a feature ve...A feature extraction and fusion algorithm was constructed by combining principal component analysis(PCA) and linear discriminant analysis(LDA) to detect a fault state of the induction motor.After yielding a feature vector with PCA and LDA from current signal that was measured by an experiment,the reference data were used to produce matching values.In a diagnostic step,two matching values that were obtained by PCA and LDA,respectively,were combined by probability model,and a faulted signal was finally diagnosed.As the proposed diagnosis algorithm brings only merits of PCA and LDA into relief,it shows excellent performance under the noisy environment.The simulation was executed under various noisy conditions in order to demonstrate the suitability of the proposed algorithm and showed more excellent performance than the case just using conventional PCA or LDA.展开更多
In this paper, a new stability criterion for positive-coefficient polynomial is given. Then the problem about the robust stability for an interval-polynomial is investigated and some new stability criterions for inter...In this paper, a new stability criterion for positive-coefficient polynomial is given. Then the problem about the robust stability for an interval-polynomial is investigated and some new stability criterions for interval-polynomials are obtained. The coefficient perturbation bound for stable interval polynomial can be completely determined by the coefficients of polynomial (1.1). So the conclusions of this paper are simple and useful. Several examples in the end of this paper show that the criterions given in this paper are effective.展开更多
The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the a...The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the above problem are given.展开更多
By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Ni...By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.展开更多
This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on...This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.展开更多
For a(1+3)-dimensional Lorentzian manifold(M,g),the general form of solutions of the Einstein field equations takes that of type I,II,or III.For type I,there is a known result in Gu(2007).In this paper,we try to find ...For a(1+3)-dimensional Lorentzian manifold(M,g),the general form of solutions of the Einstein field equations takes that of type I,II,or III.For type I,there is a known result in Gu(2007).In this paper,we try to find the necessary and sufficient conditions for the Lorentzian metric to take the form of types II and III,and we show how to construct the new coordinate system.展开更多
Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and suffici...Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur factorizations of unbounded operator matrices.Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.展开更多
This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, ...This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.展开更多
We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation wi...We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation with second-order-cone reformulation(SDPR-SOCR) is a tight relaxation. In the more complicated "intersecting" case, which is discussed in this paper, so far there is no result except for a counterexample for the SDPR-SOCR. We present a necessary and sufficient condition for the SDPR-SOCR to be a tight relaxation in both the "nonintersecting" and "intersecting" cases. As an application of this condition, it is verified easily that the "nonintersecting" SDPR-SOCR is a tight relaxation indeed. Furthermore, as another application of the condition, we prove that there exist at least three regions among the four regions in the trust-region ball divided by the two intersecting linear cuts, on which the SDPR-SOCR must be a tight relaxation. Finally, the results of numerical experiments show that the SDPR-SOCR can work efficiently in decreasing or even eliminating the duality gap of the nonconvex extended trust-region subproblem with two intersecting linear inequalities indeed.展开更多
Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE...Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.展开更多
The generalized maximal operator .44 in martingale spaces is considered. For 1 〈 p ≤ q 〈 ∞, the authors give a necessary and sufficient condition on the pair （μ, v） for M to be a bounded operator from martingal...The generalized maximal operator .44 in martingale spaces is considered. For 1 〈 p ≤ q 〈 ∞, the authors give a necessary and sufficient condition on the pair （μ, v） for M to be a bounded operator from martingale space L^P（μ） into L^q（μ） or weak-L^q（μ）, where μ is a measure on Ω × N and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.展开更多
This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous po...This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous polynomials of degree i.Within this class,we identify some new Darboux integrable systems having either a focus or a center at the origin.For such Darboux integrable systems having degrees 5and 9 we give the explicit expressions of their algebraic limit cycles.For the systems having degrees 3,5,7 and 9and restricted to a certain subclass we present necessary and sufficient conditions for being Darboux integrable.展开更多
Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is ...Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is especially the case if the given formula is not an inductive loop invariant,as most automated techniques can only check or generate inductive loop invariants.In this paper,conditions are identified on simple loops and formulas when this check can be performed automatically.A general theorem is proved which gives a necessary and sufficient condition for a formula to be an invariant under certain restrictions on a loop.As a byproduct of this analysis,a new kind of loop invariant inside the loop body,called inside-loop invariant,is proposed.Such an invariant is more general than an inductive loop invariant typically used in the Floyd-Hoare axiomatic approach to program verification.The use of such invariants for program debugging is explored;it is shown that such invariants can be more useful than traditional inductive loop invariants especially when one is interested in checking extreme/side conditions such as underflow,accessing array/collection data structures outside the range,divide by zero,etc.展开更多
In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presen...In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.展开更多
文摘In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai 0=1,2,4） are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.
基金Project supported by the Second Stage of Brain Korea 21 ProjectProject(2010-0020163) supported by Priority Research Centers Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Education,Science and Technology
文摘A feature extraction and fusion algorithm was constructed by combining principal component analysis(PCA) and linear discriminant analysis(LDA) to detect a fault state of the induction motor.After yielding a feature vector with PCA and LDA from current signal that was measured by an experiment,the reference data were used to produce matching values.In a diagnostic step,two matching values that were obtained by PCA and LDA,respectively,were combined by probability model,and a faulted signal was finally diagnosed.As the proposed diagnosis algorithm brings only merits of PCA and LDA into relief,it shows excellent performance under the noisy environment.The simulation was executed under various noisy conditions in order to demonstrate the suitability of the proposed algorithm and showed more excellent performance than the case just using conventional PCA or LDA.
基金Supported by the Fund of China Education Ministry.
文摘In this paper, a new stability criterion for positive-coefficient polynomial is given. Then the problem about the robust stability for an interval-polynomial is investigated and some new stability criterions for interval-polynomials are obtained. The coefficient perturbation bound for stable interval polynomial can be completely determined by the coefficients of polynomial (1.1). So the conclusions of this paper are simple and useful. Several examples in the end of this paper show that the criterions given in this paper are effective.
文摘The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the above problem are given.
基金supported by National Natural Science Foundation of China(Grant Nos.61272481 and 61402352)the China Scholarship Council,Beijing Natural Science Foundation(Grant No.4122089)+1 种基金National Development and Reform Commission(Grant No.20121424)the Norwegian Research Council
文摘By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
基金supported by the National Natural Science Foundation of China under Grant Nos.61034007,61174036,and 61374065the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.
文摘For a(1+3)-dimensional Lorentzian manifold(M,g),the general form of solutions of the Einstein field equations takes that of type I,II,or III.For type I,there is a known result in Gu(2007).In this paper,we try to find the necessary and sufficient conditions for the Lorentzian metric to take the form of types II and III,and we show how to construct the new coordinate system.
基金supported by National Natural Science Foundation of China(Grant Nos.11371185,11101200 and 11361034)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111501110001)+1 种基金Major Subject of Natural Science Foundation of Inner Mongolia of China(Grant No.2013ZD01)Natural Science Foundation of Inner Mongolia of China(Grant No.2012MS0105)
文摘Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur factorizations of unbounded operator matrices.Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61673012,11271194a Project on the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper focuses graph theory method for the problem of decomposition w.r.t. outputs for Boolean control networks(BCNs). First, by resorting to the semi-tensor product of matrices and the matrix expression of BCNs, the definition of decomposition w.r.t. outputs is introduced. Second, by referring to the graphical structure of BCNs, a necessary and sufficient condition for the decomposition w.r.t. outputs is obtained based on graph theory method. Third, an effective algorithm to realize the maximum decomposition w.r.t. outputs is proposed. Finally, some examples are addressed to validate the theoretical results.
基金supported by National Natural Science Foundation of China(Grant Nos.11471052,11171040,11001030 and 61375066)the Grant of China Scholarship Council
文摘We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation with second-order-cone reformulation(SDPR-SOCR) is a tight relaxation. In the more complicated "intersecting" case, which is discussed in this paper, so far there is no result except for a counterexample for the SDPR-SOCR. We present a necessary and sufficient condition for the SDPR-SOCR to be a tight relaxation in both the "nonintersecting" and "intersecting" cases. As an application of this condition, it is verified easily that the "nonintersecting" SDPR-SOCR is a tight relaxation indeed. Furthermore, as another application of the condition, we prove that there exist at least three regions among the four regions in the trust-region ball divided by the two intersecting linear cuts, on which the SDPR-SOCR must be a tight relaxation. Finally, the results of numerical experiments show that the SDPR-SOCR can work efficiently in decreasing or even eliminating the duality gap of the nonconvex extended trust-region subproblem with two intersecting linear inequalities indeed.
基金Project supported by the National Natural Science Foundation of China (No.10371051).
文摘Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.
基金supported by the National Natural Science Foundation of China (Nos. 10671147,11071190)
文摘The generalized maximal operator .44 in martingale spaces is considered. For 1 〈 p ≤ q 〈 ∞, the authors give a necessary and sufficient condition on the pair （μ, v） for M to be a bounded operator from martingale space L^P（μ） into L^q（μ） or weak-L^q（μ）, where μ is a measure on Ω × N and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.
基金supported by National Natural Science Foundation of China (Grant No. 11271252)Ministerio de Economiay Competitidad of Spain (Grant No. MTM2008-03437)+2 种基金 Agència de Gestió d’Ajuts Universitaris i de Recerca of Catalonia (Grant No. 2009SGR410)ICREA Academia,Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110073110054)a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme (Grant Nos. FP7-PEOPLE-2012-IRSES-316338 and 318999)
文摘This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous polynomials of degree i.Within this class,we identify some new Darboux integrable systems having either a focus or a center at the origin.For such Darboux integrable systems having degrees 5and 9 we give the explicit expressions of their algebraic limit cycles.For the systems having degrees 3,5,7 and 9and restricted to a certain subclass we present necessary and sufficient conditions for being Darboux integrable.
基金supported by NSFC-90718041NKBRPC-2005C B321902+1 种基金China Scholarship Council in Chinasupported by the National Science Foundation award CCF-0729097
文摘Checking whether a given formula is an invariant at a given program location(especially,inside a loop) can be quite nontrivial even for simple loop programs,given that it is in general an undecidable property.This is especially the case if the given formula is not an inductive loop invariant,as most automated techniques can only check or generate inductive loop invariants.In this paper,conditions are identified on simple loops and formulas when this check can be performed automatically.A general theorem is proved which gives a necessary and sufficient condition for a formula to be an invariant under certain restrictions on a loop.As a byproduct of this analysis,a new kind of loop invariant inside the loop body,called inside-loop invariant,is proposed.Such an invariant is more general than an inductive loop invariant typically used in the Floyd-Hoare axiomatic approach to program verification.The use of such invariants for program debugging is explored;it is shown that such invariants can be more useful than traditional inductive loop invariants especially when one is interested in checking extreme/side conditions such as underflow,accessing array/collection data structures outside the range,divide by zero,etc.
基金supported partially by the China Scholarship Council and the Science Foundation of Tianjin Polytechnic Universitysupported in part by the Natural Science Foundation Project of Chongqing,China(Grant No.CSTC2011JJA00024)+1 种基金the Research Project of Science and Technology of Chongqing Education Commission,China(Grant No.KJ120625)the Fund of Chongqing Normal University,China(Grant Nos.10XLR017 and 2011XLZ07)
文摘In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.
