Inversion and III-Posed Problem Solutions in Atmospheric Remote Sensing

With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is getting more and more importance.It is known that since a remote sensing equation falls into an integral equation of the first kind,thus leading to the fact that it is ill-posed and particularly the solution is unsteady,tremendous difficulties arise from the retrieval.This paper will present a simple review on the inversion techniques with some necessary remarks,before introducing the successful efforts with respect to such equations and the encouraging solutions achieved in recent decades by researchers of the world.

SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS

We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0, x′（0）-∑i=1^m2 βi x′（ηi） = 0, x′（1）=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f（t, x, y）may be singular at x, y, t = 0 and/or t = 1.

A Tentative Probe into the Solution of the Listening Problems

Many students often raise questions, "Why it is so difficult to improve the listening comprehension?" This cannot be solved easily, because listening is a kind of complex and perceptual knowledge process. Listening does not only mean the ability to hear, it is also the ability to capture the information that the language carries through hearing organs and the ability of head. As far as I am concerned, such a problem is related to the complexity of various factors: listening itself covers, the language knowledge proficiency listeners possess, and also it is closely connected with the traditional foreign language style.

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.

A Solution to Old Problems

I work in the Dalian Development Zone. Although the central government did not invest a penny, the zone’s annual revenue is some 5 billion yuan. In 2003, it surpassed 6 billion yuan. There are many solely foreign-invested enterprises in the development zone-more than 300 are Japanese, and there are many Sino-foreign joint ventures. The annual profits of 70 million yuan come mostly from these joint ventures.I think the development zone will play an important role in the revital-ization of industries in the Northeast.

ASYMPTOTIC SOLUTION OF SINGULAR PERTURBATION PROBLEMS FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k is-an-element-of N union {0}.

POSITIVE SOLUTIONS FOR SOME 1-DIMENSIONAL BOUNDARY VALUE PROBLEMS OF LAPLACE-TYPE

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.

GENERAL SOLUTION FOR DYNAMICAL PROBLEM OF INFINITE BEAM ON AN ELASTIC FOUNDATION

Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.

Fundamental solution method for inverse source problem of plate equation

The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method （FSM） and the Tikhonov regularization technique axe used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.

THERMOELASTIC PROBLEMS IN THE HALF SPACE—AN APPLICATION OF THE GENERAL SOLUTION IN ELASTICITY

In this paper, some thermoelastic problems in the half space are studied by using the general solutions of the elastic equations. The method presented here is extremely effective for the axisymmetric problems of the half space as well as the half plane problems.

Problems and Solutions in Implementing Modern Apprenticeship in Higher Vocational Institutions

With the furthering of educational reform in higher vocational institutions, China＇s vocational education has given a new connotation to modem apprenticeship. The government makes efforts in promoting the modem apprenticeship and this is met with active response of the higher vocational institutions. However, in the practical situation of the higher vocational institutions, the implementation of modem apprenticeship is still faced with lots of problems. It is the author＇s opinion that the government and higher vocational institutions should overall integrate the planning for scientific and systematic designing of the implementation of modem apprenticeship to create an integrated environment for the enterprises to actively participate in the higher vocational education. The institutions and enterprises should join hands in the management of higher vocational education, strengthen the pilot institutionsand promote the apprenticeship to solve the problems in the implementation and enhance the development of the higher vocational education of China.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

An Elasticity Solution of a Nonhomogeneous Half-Plane Problem

We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.

THE SOLUTION OF RANDOM EIGENVALUE PROBLEM WITH SMALL STOCHASTIC PROCESSES

This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.

Problems with Mobile IP and Their Solutions

The Mobile IP technology is the core technology to implement NGN applications in traditional networks.It is a new domain for the development of IP technologies and the convergence of wireless communication and IP technologies.This paper discusses the main problems of Mobile IP in triangle routing,handoff, micro-movement and QoS,and gives their solutions respectively.It also analyzes Mobile IP applications for mobile communications,and concludes that the Mobile IP technology will play an important role in mobile communications and provide new opportunities to develop novel applications in the future.

A GENERAL SOLUTION AND THE APPLICATION OF SPACE AXISYMMETRIC PROBLEM IN PIEZOELECTRIC MATERIAL

According to the structure feature of the governing equations of spaceaxisymmetric problem in transversely, isotropic piezoelectric material. using the methodof introducing potential .function one by. one, in this paper we obtain the so-calledgeneral solution of displacement and eleclric potential function denoied by uniquepoiential.function which satisfies specific partiality equations. As an applying exampleof the general solution, we solve problem of semi-infinile boodt. made of piezoelectricmaterial, on the surface of the semi-infinite body a concentrative .force is applied, andget the analytic .formulations of stress and electric displacement comiponenis. Thegeneral solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity inclusion. penny-shape crack. and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between twopiezoelectric bodies or piezoelectric body. and elastic body .

Religion Conflicts in Indonesia Problems and Solutions

Religious perspectives which place religion as a source of conflict have initiated various attempts to reinterpret and accordingly find some common ground at a certain level which hopefully may reduce conflicts among religious communities due to the existence of mutual tolerance. At the exoteric level, religions are different, but at the esoteric level, religions are not similar. All religions are viewed as equally valid paths toward God. However, in many ways, the reality shows that the tension among religious communities is closely related to the factors that are beyond the scope of religion. It is important for all religious believers to keep the peace among them. As far as the record of religious conflicts in Indonesia is concerned, it shows three major patterns： conflicts among adherents of different religions, conflicts between one religion with a group accused as heretical, and internal conflicts of the same people of faith with those who have different understanding of the religion. In any point of views, however, such conditions would be so detrimental to the human race in general, and society and the state of Indonesia in particular. This paper examines intensively about the issues and attempts to uncover the nature of the root-causes underlying them.

ON THE METHOD OF RECIPROCAL THEOREM TO FIND SOLUTIONS OF THE PLANE PROBLEMS OF ELASTICITY

In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist, obtaining displacement expressions by means of the method of reciprocal theorem is actual. But in other conditions, when static force edge conditions or mixed ones exist, the obtained displacements are admissible. In order to find actual displacement, the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple, convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions. Evidently, it is a new method.