SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

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.

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

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.

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

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.

Necessary and Sufficient Conditions for Reactive Azeotropes in Multi-reaction Mixtures in Terms of Elemental Composition

Necessary and sufficient conditions for azeotropy in reactive mixtures axe 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=101.325 kPa 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.

A NECESSARY AND SUFFICIENT CONDITION FOR THEOSCILLATION OF SOLUTIONS OF LIENARD TYPE SYSTEM WITH MULTIPLE SINGULAR POINTS

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.

The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method

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.

A necessary and sufficient condition for positive solutions of singular fourth order boundary value problems

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.

Necessary Conditions and Situational Variables of Payments for Ecosystem Services

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.

Some Necessary and Sufficient Condition of Multivariate Random Variabl

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A NECESSARY AND SUFFICIENT CONDITION FOR SINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS

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.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

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.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

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.

Study on Intention and Forming Conditions of SMT-MG

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.

Optimality Conditions and Algorithms for Direct Optimizing the Partial Differential Equations

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.

ON NECESSARY CONDITIONS FOR RESONANCE IN TURNING POINT PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

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.

平台型企业商业模式创新组态研究——基于共创生态视角

文章基于共生理论构建了涵盖“共创主体—共创网络—共创环境”的平台型企业商业模式创新前因条件联动模型,并结合NCA和fsQCA方法探讨了多维前因条件与平台型企业商业模式创新的必要性和充分性关系。结果表明:单个前因条件并不构成平台型企业商业模式创新的必要条件,但强化共创网络结构嵌入能够发挥较为普适的作用;存在“共创精神-生态联动”等3种引发高水平商业模式创新的组态模式,并且高管企业家精神、用户共创参与以及环境动态性存在互补关系;存在4种引发非高水平商业模式创新的组态模式,表明前因条件与商业模式创新之间属于非对称因果关系。研究结论能够为平台型企业商业模式创新提供实践指导,从而促进平台经济的健康发展。

具有周期系数的线性微分方程的Hyers-Ulam稳定性

本文研究了具有周期系数的一阶和二阶线性微分方程的Hyers-Ulam稳定性.利用常数变易法,获得了其Hyers-Ulam稳定性的充分必要条件,推广了具有周期系数的一阶齐次线性微分方程Hyers-Ulam稳定性的相关结果.

制度组态视角下数字生态激发创业活跃度的多元路径——基于NCA与fsQCA的研究

如何优化数字生态环境激发区域创业活跃度是亟待解决的重要管理问题。本文基于制度逻辑理论,采用必要条件分析(NCA)与模糊集定性比较分析(fsQCA)方法,以中国31个省区市为案例,检验了数字政府、数字基础、数字经济、数字能力与数字社会5个条件对区域创业活跃度的组态效应。研究结果表明:数字政府、数字基础、数字经济是区域创业活跃度的必要条件,其重要性程度依次为数字政府、数字基础与数字经济。存在“政府统筹—市场决定型”“政府赋能—市场调节型”“市场调节—社会助力型”“政府统筹—社会助力型”4类产生高创业活跃度的制度组态。存在3类产生非高创业活跃度的制度组态,呈现出以下2个特征:数字生态中各要素均表现不佳;在缺少政府统筹或赋能的情况下,即使市场发挥调节作用,也不能产生高区域创业活跃度。研究揭示了数字生态影响创业活跃度的多元路径,对优化地区数字生态环境,更好激发市场主体创业活力具有重要的实践启示。

一类反应扩散SIQR传染病模型的最优控制

为探究疾病发生时如何更快地控制疾病、避免疾病的扩散和流行,研究了一类反应扩散的易感-感染-隔离-恢复(susceptible-infectious-quarantined-recovered,SIQR)传染病模型的最优控制问题。首先利用截断方法证明状态方程解y=(S,I,Q,R)^(T)的存在性,其次利用极小化序列证明最优控制对(S^(*),I^(*),Q^(*),R^(*),u^(*))的存在性,最后利用拉格朗日方法得到一阶必要条件以及最优控制u^(*)的表达形式。结果表明:当控制u=u^(*)为最优控制时,给定的目标泛函达到最小值。该研究在偏微分方程传染病模型的最优控制方面具有重要意义。

开放政府数据生态系统中的数据利用:瓶颈与组态

当前中国开放政府数据利用水平普遍较低,揭示高开放政府数据利用水平生成的必要条件和组态条件对释放数据价值、促进数字经济发展有重要意义。基于创新生态系统理论构建开放政府数据生态系统分析框架,并运用NCA和QCA混合方法,基于中国27个省域的数据检验高开放政府数据利用水平生成的必要条件和组态条件。研究发现,开放者、开放平台和技术环境是生成高开放政府数据利用水平的必要条件,其分别在74.70%、77.00%和45.00%的水平上构成瓶颈。高开放政府数据利用水平有供给主导型、供需联动型和综合驱动型3种生成类型。要提高开放政府数据利用水平,各地政府既要补好“漏水桶”,又要打好“组合拳”,并注重发挥需求侧的拉动作用。