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...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.展开更多
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 condit...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.展开更多
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...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.展开更多
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 appre...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.展开更多
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 tech...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.展开更多
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...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.展开更多
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 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.展开更多
By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differenti...By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].展开更多
The construction industry has been in continuous progress. The rapid development of economy also provides more opportunities for the development of construction. At the same time, various technologies have been relati...The construction industry has been in continuous progress. The rapid development of economy also provides more opportunities for the development of construction. At the same time, various technologies have been relatively developed and achieved good results. Electromechanical installation technology has also made progress and development. The construction industry has made good achievements in construction technology and methods, resulting in prefabricated buildings. For buildings, the embedding of on-site pipelines and the production requirements of prefabricated components are also very high. At the same time, there are problems in the distance and location between lines, which are the difficulties of electromechanical installation of prefabricated buildings. However, its unique function still plays a very important role. If we master this technology, we can make more progress.展开更多
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 gettin...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.展开更多
In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series...In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.展开更多
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. Li...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.展开更多
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 ...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.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
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...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.展开更多
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 h...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.展开更多
基金supported by the National Science Foundation of Shandong Province(ZR2009AM004)
文摘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.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China.
文摘By making use of the differential inequalities, in this paper we study the uniqueness of solutions of the two kinds of the singularly perturbed boundary value problems for the nonlinear third order ordinary differential equation with a small parameter ε>0: where i=1, 2; a(?)(ε), β(ε) and γ(ε) are functions defined on (0, ε_o], while ε_o>0 is a constant.This paper is the continuation of our works [4, 6].
文摘The construction industry has been in continuous progress. The rapid development of economy also provides more opportunities for the development of construction. At the same time, various technologies have been relatively developed and achieved good results. Electromechanical installation technology has also made progress and development. The construction industry has made good achievements in construction technology and methods, resulting in prefabricated buildings. For buildings, the embedding of on-site pipelines and the production requirements of prefabricated components are also very high. At the same time, there are problems in the distance and location between lines, which are the difficulties of electromechanical installation of prefabricated buildings. However, its unique function still plays a very important role. If we master this technology, we can make more progress.
基金This work is supported partly by the Meteorological Office of Air Command
文摘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.
文摘In the present paper, an equation of nonlinear chromatography is derived from the physical chemistry A recursion formula of the symmetries of the equation as well as an infinite number of symmetries is found. A series of Backlund transformations of the equation are constructed by means of the symmetries. The exact solutions of two boundary-initial value problems on the half straight line for the equation are given m terms of the solutions of the corresponding linear problems.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 51477039 and 51207041the Program of Hefei Normal University under Grant Nos 2014136KJA04 and 2015TD01the Key Project of Provincial Natural Science Research of University of Anhui Province of China under Grant No KJ2015A174
文摘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.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
文摘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.
文摘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.
