Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro...Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.展开更多
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
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equ...In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.展开更多
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
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
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This artic...Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
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.
In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
Surface Mount Technology Manufacturing Grid (SMT-MG) is the application of the grid technology in the SMT product manufacturing.In this paper,as the new manufacturing mode of SMT product,SMT-MG was brought forward.The...Surface Mount Technology Manufacturing Grid (SMT-MG) is the application of the grid technology in the SMT product manufacturing.In this paper,as the new manufacturing mode of SMT product,SMT-MG was brought forward.Then the concept and intention of the SMT-MG were analyzed.And from the three aspects of sufficient condition,necessary condition and stability condition,the static and dynamic conditions under which the SMT-MG was formed were mainly discuss.Finally,it was proved that the formation and development of SMT-MG is feasible and necessary.展开更多
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
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
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
New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE)...New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE). Appropriate algo-rithms for unconstrained minimizing a functional are considered and tested. To construct the algorithms, new form of NCO is used. Such approach demonstrates fast uniform convergence at optimal solution in infinite-dimensional space.展开更多
In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
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
基金supported by the Beijing Natural Science Foundation(1212003)。
文摘Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.
文摘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.
基金supported by an NSERC granta startup fund of University of Albertasupported by the NSF grant DMS1613163
文摘In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
基金Supported by the National Natural Science Foundation of China (No.29976035) and Zhejiang and Fujian Provincial Natural Science Foundation of China.
文摘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.
文摘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.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
文摘Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘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.
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
文摘Surface Mount Technology Manufacturing Grid (SMT-MG) is the application of the grid technology in the SMT product manufacturing.In this paper,as the new manufacturing mode of SMT product,SMT-MG was brought forward.Then the concept and intention of the SMT-MG were analyzed.And from the three aspects of sufficient condition,necessary condition and stability condition,the static and dynamic conditions under which the SMT-MG was formed were mainly discuss.Finally,it was proved that the formation and development of SMT-MG is feasible and necessary.
文摘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.
基金supported by the National Natural Science Foundation of China(61872316)the Natural Science Foundation of Zhejiang Province,China(LY19F020004)
文摘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.
文摘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.
文摘New form of necessary conditions for optimality (NCO) is considered. They can be useful for design the direct infinite- dimensional optimization algorithms for systems described by partial differential equations (PDE). Appropriate algo-rithms for unconstrained minimizing a functional are considered and tested. To construct the algorithms, new form of NCO is used. Such approach demonstrates fast uniform convergence at optimal solution in infinite-dimensional space.
文摘In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
文摘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.
