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.

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.

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.

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.

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.

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.

ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS

The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n ＋ a ＋ b.

Necessary and Sufficient Optimality Conditions for Relaxed and Strict Control of Forward-Backward Doubly SDEs with Jumps Under Full and Partial Information

This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.

Necessary and sufficient conditions of the rendezvous between a single spacecraft and three non-coplanar Walker constellation satellites

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.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS

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.

THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE 0F PERIODIC SOLUTIONS OF A TYPE OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

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.

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY

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.

OFDMA系统中最优能效功率分配

该文研究了OFDMA系统中基于能效的功率分配问题。区别于已有研究,该文利用了能效函数关于功率矢量的严格伪凹特性,证明了最优能效功率分配一定具有一种特殊的注水功率结构—能效注水结构。通过该结构,功率分配问题被简化为关于水位线的一元优化问题,进而求得最优能效功率的闭合解。在此基础上,该文进一步提出了一种最优能效功率分配算法,该算法通过顺序搜索有限个水位线区间的方式求得最优解。仿真表明该算法能够快速得到最优能效功率,其计算复杂度远小于已有的能效功率分配算法。

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF LIAPUNOV FUNCTION OF LUR'E FORM WITH■≤0

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).

关于Bertrand曲线和Mannheim曲线推广的一个充要条件

给出了Bertrand曲线和Mannheim曲线推广的一个充要条件.做为其特例,得到了Bertrand曲线和Mannheim曲线的充要条件.

A Note on Diophantine Equation Ax^4+ 1 = By^2 and Erdos’ Conjecture on Combinatorial Number

A necessary and suffcient condition is given for the equation Ax4+ 1 =By2 to have positive integer solution, and an effective method is derived for solving equation a2x4 + 1 = By2 in positive integers x, y for given ho and B completely. Also, using a recently result of Ribet, Darmon and Merel, we proved that Erdos’ conjecture on combinatorial number is right.

拟齐次核半离散Hilbert型逆向不等式的最佳搭配参数条件及算子表示

利用权函数方法和实分析技巧,在l_(p)^(α)(N)和L_(p)^(β)(0,+∞)中讨论拟齐次核的半离散Hilbert型不等式的逆向形式,得到逆向不等式具有最佳常数因子时的最佳搭配参数的充分必要条件,最后给出所得结果的等价算子表示和若干特例。