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Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity 被引量:1
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作者 孙清滢 叶留青 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第4期33-37,共5页
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un... Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. 展开更多
关键词 necessary and sufficient conditions generalized convexity nonlinear programming multiobjective programming type functions
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Necessary and Sufficient Conditions for Reactive Azeotropes in Multi-reaction Mixtures in Terms of Elemental Composition 被引量:1
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作者 林金清 李浩然 韩世钧 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2000年第4期361-365,共5页
Necessary and sufficient conditions for azeotropy in reactive mixtures are derived in terms of elemental composition, which shows that in the space of elemental compositions, they take the same functional form as the ... Necessary and sufficient conditions for azeotropy in reactive mixtures are derived in terms of elemental composition, which shows that in the space of elemental compositions, they take the same functional form as the conditions for azeotropy in non-reactive mixtures. The production of methyl tert-butyl ether (MTBE) is taken as an example. It is found that there are a 'pseudo' intermediate-boiling ternary reactive azeotrope at p = 101.325kPa and two 'real' ternary reactive azeotropes at p = 101.325 Pa. The introduced elemental compositions also reduce the dimensionality of the phase diagrams and provide a natural set of variables for visualization of phase behavior. 展开更多
关键词 reactive azeotropy necessary and sufficient condition multi-reactive mixture phase and chemical equilibrium
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NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM 被引量:1
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作者 刘德明 《Acta Mathematica Scientia》 SCIE CSCD 1991年第1期65-71,共7页
In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We ... In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles. 展开更多
关键词 necessary and sufficient conditionS OF EXISTENCE and UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM LIM
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A NECESSARY AND SUFFICIENT CONDITION FOR THEOSCILLATION OF SOLUTIONS OF LIENARD TYPE SYSTEM WITH MULTIPLE SINGULAR POINTS
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作者 孙继涛 张银萍 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第12期0-0,0-0+0-0,共6页
In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also ex... In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper. 展开更多
关键词 Liénard type system oscillating solution necessary and sufficient condition
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A necessary and sufficient condition for positive solutions of singular fourth order boundary value problems
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作者 YU Xiaoyao PANG Bangyan 《商丘师范学院学报》 CAS 2010年第3期46-53,共8页
This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the mo... This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained. 展开更多
关键词 singular boundary value problem iterative solution necessary and sufficient condition
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Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations 被引量:6
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作者 XU XiaoMing 《Science China Mathematics》 SCIE 2011年第2期301-310,共10页
Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 ... Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z. 展开更多
关键词 comparison theorem multidimensional anticipated backward stochastic differential equation necessary and sufficient condition
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Necessary and sufficient conditions of the rendezvous between a single spacecraft and three non-coplanar Walker constellation satellites 被引量:2
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作者 ZHANG Jing WU MeiPing 《Science China(Technological Sciences)》 SCIE EI CAS 2011年第9期2254-2262,共9页
The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduc... The probability of the rendezvous between a single spacecraft and three non-coplanar constellation satellites is studied,and the necessary and sufficient conditions of the rendezvous without orbital maneuver are deduced.The rendezvous orbit design can be transformed into the patching of two spacecraft orbits,either of which can achieve the rendezvous with two satellites.Firstly,due to the precious quality of spherical geometry,the unique existence of the rendezvous orbit for two constellation satellites is proved.Then,according to the difference between equispaced and non-equispaced orbital planes of three satellites,the necessary and sufficient conditions are given respectively,and the calculating method of the spacecraft orbit is proposed.At last,the constraint conditions between two different rendezvous orbits is derived,while the relative position of two groups of objects are under specific distribution.The results can be applied to the rendezvous between a single spacecraft and multiple constellation satellites without orbital maneuver. 展开更多
关键词 Walker constellation necessary and sufficient conditions orbital design rendezvous with multiple satellites patchedorbit constraint conditions
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A Mean-Field Necessary and Sufficient Conditions for Optimal Singular Stochastic Control 被引量:1
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作者 Mokhtar Hafayed 《Communications in Mathematics and Statistics》 SCIE 2013年第4期417-435,共19页
This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of... This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example. 展开更多
关键词 Stochastic optimal singular control Mean-field stochastic maximum principle Mean-field necessary and sufficient conditions of optimality McKean-Vlasov SDEs Convex perturbation
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A NECESSARY AND SUFFICIENT CONDITION FOR ASYMPTOTIC STABILITY OF A FIRST ORDER DELAY EQUATION WITH TWO DELAYS 被引量:2
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作者 任洪善 《Annals of Differential Equations》 2004年第1期59-69,共11页
Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which i... Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply. 展开更多
关键词 asymptotic stability delay equation necessary and sufficient condition characteristic equation
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A NECESSARY AND SUFFICIENT CONDITION FOR A POINT TO BE A GLOBAL MAXIMIZER OF ACONSTRAINED OPTIMIZATION
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作者 SUN Churen(Department of Systems Engineering and Engineering Management, The Chinese Universityof Hong Kong, Hong Kong International Business School, The Instituteof Foreign Trade of Shanghai, Shanghai 201600, China. 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第1期111-118,共8页
It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary an... It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm. 展开更多
关键词 global optimization global maximizer necessary and sufficient condition auxiliary function
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The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method
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作者 LIN Hong-wei XIONG Yun-yang +2 位作者 HU Hui YAN Jia-cong HU Qian-qian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2022年第2期272-289,共18页
Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical... Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method. 展开更多
关键词 isogeometric collocation CONSISTENCY necessary and sufficient condition convergence rate
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NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS
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作者 郜奉欣 侯占元 张振国 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1989年第3期219-233,共15页
In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the cha... In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y^2+b(t)y+c(t)+δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved. 展开更多
关键词 TH PS necessary and sufficient conditionS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI’S EQUATION WITH PERIODIC COEFFICIENTS exp
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THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE 0F PERIODIC SOLUTIONS OF A TYPE OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
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作者 张毅 章毅 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1991年第1期74-79,共6页
In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence o... In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions. 展开更多
关键词 OD OP PER THE necessary and sufficient conditionS FOR THE EXISTENCE 0F PERIODIC SOLUTIONS OF A TYPE OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
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NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY
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作者 刘安平 王国庆 +1 位作者 刘婷 肖莉 《Annals of Differential Equations》 2003年第3期337-342,共6页
In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-del... In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay. 展开更多
关键词 DELAY PARABOLIC OSCILLATION necessary and sufficient condition
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Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property
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作者 MAI Jiehua and GU Rongbao1.Institute of Mathematics, Shantou University, Shantou 515063, China 2. Department of Mathematics, Anhui University, Hefei 230039, China 《Chinese Science Bulletin》 SCIE EI CAS 1997年第3期259-260,共2页
IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, ever... IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows. 展开更多
关键词 necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property
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NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF LIAPUNOV FUNCTION OF LUR'E FORM WITH■≤0
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作者 仵永先 赵素霞 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1990年第3期245-250,共6页
This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e f... This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semi--definite derivative (i.e. V≤0). 展开更多
关键词 necessary and sufficient conditionS FOR THE EXISTENCE OF LIAPUNOV FUNCTION OF LUR’E FORM WITH
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A necessary and sufficient condition for ternary majority functions being monotonic functions
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《Chinese Science Bulletin》 SCIE CAS 1998年第23期2018-2019,共2页
关键词 A necessary and sufficient condition for ternary majority functions being monotonic functions
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A NECESSARY AND SUFFICIENT CONDITION FOR SINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS 被引量:1
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作者 ZHAO ZENGQIN 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第1期15-24,共10页
In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v,... In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B. 展开更多
关键词 Second order boundary value problems singular differential equation necessary and sufficient condition.
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Equivalence between the Dependent Right Censorship Model and the Independent Right Censorship Model
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作者 Qiqing Yu Kai Yu 《Open Journal of Statistics》 2016年第2期209-219,共11页
Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and L... Yu et al. (2012) considered a certain dependent right censorship model. We show that this model is equivalent to the independent right censorship model, extending a result with continuity restriction in Williams and Lagakos (1977). Then the asymptotic normality of the product limit estimator under the dependent right censorship model follows from the existing results in the literature under the independent right censorship model, and thus partially solves an open problem in the literature. 展开更多
关键词 Constant-Sum Models Right-Censoring Dependent Censoring necessary and sufficient condition
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SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS 被引量:5
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作者 王丽娟 何培杰 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期729-734,共6页
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
关键词 necessary and sufficient optimality conditions optimal control Navier-Stokes equation periodic state constraint
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