2006 No. 1
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2006, (1): 1-12.
Abstract(
Abstract:
This paper surveys recent developments in studies of contrast spatial structure solutions of singularly perturbed problems, which have rise since the beginning of 1990's. It mainly introduces a series of work about step-type and spike-type solutions in ODE, including critical and uncritical cases. In themeanwhile, it introduces the latest research progress of contrast spatial structure of variation problems. The outline of contrast spatial structure solutions in PDE is also included.
This paper surveys recent developments in studies of contrast spatial structure solutions of singularly perturbed problems, which have rise since the beginning of 1990's. It mainly introduces a series of work about step-type and spike-type solutions in ODE, including critical and uncritical cases. In themeanwhile, it introduces the latest research progress of contrast spatial structure of variation problems. The outline of contrast spatial structure solutions in PDE is also included.
2006, (1): 23-30.
Abstract:
The periodic solution for a kind of parabolic perturbed equations including transposed item is discussed. The uniqueness of the solution is proved, and the asymptotic expansion of the solution and remainder estimation are also given.
The periodic solution for a kind of parabolic perturbed equations including transposed item is discussed. The uniqueness of the solution is proved, and the asymptotic expansion of the solution and remainder estimation are also given.
2006, (1): 35-39,1.
Abstract:
This paper has proved that the Diophantine equation x3+1=38y2 has only integer solutions(x,y)=(-1, 0),(31,±28).
This paper has proved that the Diophantine equation x3+1=38y2 has only integer solutions(x,y)=(-1, 0),(31,±28).
2006, (1): 35-34.
Abstract:
The growth and development of the research in the singular perturbation theory in the Department of Mathematics at East China Normal University is reviewed, uncovering historical facts in this research area in China. Some outstanding Chinese scientists, such as QIAN Wei-chang, GUO Yong-huai, QIAN Xue-sen and LIN Jia-qiao, have made pioneer contributions in this area.The Chinese Culture Revolution interrupted the research. In the late 1970s, after the end of the Culture Revolution, the section on research and teaching of differential equations in the department of mathematics of ECNU decided to make the theory and application of singular perturbation as a research direction. In the early 1990s the research is thriving under the efforts of themathematicians in China. After then, however, was a recession period because of the lack of new researchers. But now, as a result of Chinese Government's continuously supporting of scientific researches, and outstanding mathematicians such as Ni Ming-kang have returned from abroad, the research of singular perturbation is becoming active again at our university and inChina.
The growth and development of the research in the singular perturbation theory in the Department of Mathematics at East China Normal University is reviewed, uncovering historical facts in this research area in China. Some outstanding Chinese scientists, such as QIAN Wei-chang, GUO Yong-huai, QIAN Xue-sen and LIN Jia-qiao, have made pioneer contributions in this area.The Chinese Culture Revolution interrupted the research. In the late 1970s, after the end of the Culture Revolution, the section on research and teaching of differential equations in the department of mathematics of ECNU decided to make the theory and application of singular perturbation as a research direction. In the early 1990s the research is thriving under the efforts of themathematicians in China. After then, however, was a recession period because of the lack of new researchers. But now, as a result of Chinese Government's continuously supporting of scientific researches, and outstanding mathematicians such as Ni Ming-kang have returned from abroad, the research of singular perturbation is becoming active again at our university and inChina.
2006, (1): 40-44,1.
Abstract:
The existence and multiplicity of periodic solutions are obtained for a class of su-perquadratic resonance nonautonomous second order systems ü(t)+k2ω2u+▽F(t, u(t)) = 0, a.e.t ∈ [0,T] by Z2 version of the Mountain Pass Theorem on the condition that is unbounded.
The existence and multiplicity of periodic solutions are obtained for a class of su-perquadratic resonance nonautonomous second order systems ü(t)+k2ω2u+▽F(t, u(t)) = 0, a.e.t ∈ [0,T] by Z2 version of the Mountain Pass Theorem on the condition that is unbounded.
2006, (1): 45-51.
Abstract:
This paper deals with the case when the α-βgeneralized inverse A(-1)α-β is a linear transformation, in which case we established the characterization of the α-β generalized inverse, and we also give several sufficient conditions that the reverse law holds.
This paper deals with the case when the α-βgeneralized inverse A(-1)α-β is a linear transformation, in which case we established the characterization of the α-β generalized inverse, and we also give several sufficient conditions that the reverse law holds.
2006, (1): 52-56.
Abstract:
The stability of a class of single-input bilinear sampled-data systems with quantization is investigated in this paper. The systems are uniformly globally exponentially stable by proposing a small feedback controller. Based on that，the effect of quantization on the bilinear sampled-data systems are discussed. And under the constrained quantization level， the same stability property of the systems is still concluded.
The stability of a class of single-input bilinear sampled-data systems with quantization is investigated in this paper. The systems are uniformly globally exponentially stable by proposing a small feedback controller. Based on that，the effect of quantization on the bilinear sampled-data systems are discussed. And under the constrained quantization level， the same stability property of the systems is still concluded.
2006, (1): 57-62,7.
Abstract:
In this paper, we investigate the flexibility of a wheel graph on S1 and determine the structures and the number of embeddings of wheel graphs on the torus. As their applications, the structures of embeddings of some generalized halin graphs (may be nonplanar) on the torus are also determined.
In this paper, we investigate the flexibility of a wheel graph on S1 and determine the structures and the number of embeddings of wheel graphs on the torus. As their applications, the structures of embeddings of some generalized halin graphs (may be nonplanar) on the torus are also determined.
2006, (1): 63-71.
Abstract:
This paper proposed a new sampling plan, the sequential mesh test, in order to overcome the disadvantages of the widely used Sequential Probability Ratio Test (SPRT). The main idea of the new plan is to divide a SPRT test problem into a series of subproblems by inserting a number of test points. The paper presented in detail how to realize the new plan, and showed thatthe new plan has a much better control of the sample number than SPRT does. Finally it showed that the new method is also more powerful than IEC 1123 the well-known international standard for sampling inspection.
This paper proposed a new sampling plan, the sequential mesh test, in order to overcome the disadvantages of the widely used Sequential Probability Ratio Test (SPRT). The main idea of the new plan is to divide a SPRT test problem into a series of subproblems by inserting a number of test points. The paper presented in detail how to realize the new plan, and showed thatthe new plan has a much better control of the sample number than SPRT does. Finally it showed that the new method is also more powerful than IEC 1123 the well-known international standard for sampling inspection.
2006, (1): 72-79.
Abstract:
A finite difference method with accuracies of fourth order in space and second order in time is proposed for time-periodic solutions of a nonlinear parabolic boundary value problem. A monotone iterative scheme is developed for proving the existence and uniqueness of the periodic solutions of the nonlinear discrete scheme, and the computational algorithms for the periodic solutions are also provided. The convergence of the discrete scheme is discussed. The numerical results show the advantages of the method.
A finite difference method with accuracies of fourth order in space and second order in time is proposed for time-periodic solutions of a nonlinear parabolic boundary value problem. A monotone iterative scheme is developed for proving the existence and uniqueness of the periodic solutions of the nonlinear discrete scheme, and the computational algorithms for the periodic solutions are also provided. The convergence of the discrete scheme is discussed. The numerical results show the advantages of the method.
2006, (1): 80-86.
Abstract:
A formal definition of proposition formulae was provided by context-free grammar,and the conversion from proposition formulae to polynomials was solved automatically. Using Wu′s Method, the paper presented another solution to the problem of theorem reasoning. In addition, a method for producing logical deduction was introduced.
A formal definition of proposition formulae was provided by context-free grammar,and the conversion from proposition formulae to polynomials was solved automatically. Using Wu′s Method, the paper presented another solution to the problem of theorem reasoning. In addition, a method for producing logical deduction was introduced.
2006, (1): 87-91.
Abstract:
A new method based on numeric computation for automated geometric theorem proving and discovering is shown. And a dynamic searching system of geometric theorem has been implemented,which can solve elementary geometric problems efficiently, including some non-constructive problems.
A new method based on numeric computation for automated geometric theorem proving and discovering is shown. And a dynamic searching system of geometric theorem has been implemented,which can solve elementary geometric problems efficiently, including some non-constructive problems.
2006, (1): 92-99.
Abstract:
Based on the smaller information granularity security, granule technology was presented in this paper, and the information content security architecture model was also given. The model-based prototype system exampled with protecting WORD documents was implemented.
Based on the smaller information granularity security, granule technology was presented in this paper, and the information content security architecture model was also given. The model-based prototype system exampled with protecting WORD documents was implemented.
2006, (1): 100-107.
Abstract:
This paper studies the resource sharing in Tele-learning systems.A community P2P learning resource sharing model is proposed and the resource sharing will be restricted in certain communities. The metadata of digital learning resources is stated by LOM standard. By means of distributed metadata management in structured pure P2P topology, the distributed storage and bandwidth can be taken full advantage. The constitution of community, the publication and retrieval of learning resources are specified in this paper as well as implement of the model.
This paper studies the resource sharing in Tele-learning systems.A community P2P learning resource sharing model is proposed and the resource sharing will be restricted in certain communities. The metadata of digital learning resources is stated by LOM standard. By means of distributed metadata management in structured pure P2P topology, the distributed storage and bandwidth can be taken full advantage. The constitution of community, the publication and retrieval of learning resources are specified in this paper as well as implement of the model.
2006, (1): 108-115.
Abstract:
There are plenty of local copies of pages of remote web sites on local databases on most of web search engine sites. It is necessary to pull remote web pages periodically to refresh local copies of these pages on database in order to keep copies and source pages consistent，and which takes plenty of time and resources.The article proposes serveral policies to synchronize copy and source pages , proposes a Poission model of source page change, define freshness and fresh time, studies on these policies and compares their effectiveness.It is shown that the proposed policies improve the freshness of web pages significantly.
There are plenty of local copies of pages of remote web sites on local databases on most of web search engine sites. It is necessary to pull remote web pages periodically to refresh local copies of these pages on database in order to keep copies and source pages consistent，and which takes plenty of time and resources.The article proposes serveral policies to synchronize copy and source pages , proposes a Poission model of source page change, define freshness and fresh time, studies on these policies and compares their effectiveness.It is shown that the proposed policies improve the freshness of web pages significantly.
2006, (1): 116-119.
Abstract:
Uniform Ag nano-particles was synthesized within nanoscale pores of oxidized porous silicon (OPS) by a simple solution immersion-thermal decomposition approach，forming the compound structure of Ag/OPS/silicon. Ag films deposited on OPS were characterized by X-ray diffraction, and SEM showed the existence of silver nano-particles.
Uniform Ag nano-particles was synthesized within nanoscale pores of oxidized porous silicon (OPS) by a simple solution immersion-thermal decomposition approach，forming the compound structure of Ag/OPS/silicon. Ag films deposited on OPS were characterized by X-ray diffraction, and SEM showed the existence of silver nano-particles.
2006, (1): 120-125.
Abstract:
In this paper, we defined lowering and raising operator of single photon's two polarization states, and used the theory of linear transformation of operator in Fock space to study BS, PBS, wave plate and H transformation. We obtained their representation of operator .On the base of this; we studied some quantum information experiment, e.g. Teleportation, from a new aspect. Using the new representation, we can analyze the probability of photons output states .To do this, we try to find a new method to devise experiments much efficiently.
In this paper, we defined lowering and raising operator of single photon's two polarization states, and used the theory of linear transformation of operator in Fock space to study BS, PBS, wave plate and H transformation. We obtained their representation of operator .On the base of this; we studied some quantum information experiment, e.g. Teleportation, from a new aspect. Using the new representation, we can analyze the probability of photons output states .To do this, we try to find a new method to devise experiments much efficiently.
2006, (1): 126-131.
Abstract:
This paper advances a novel measurement of wave-height — differential algorithm.Compared with electric level method, the differential algorithm has its advantages. This article details its principle,algorithm and demonstrates it with a living example.
This paper advances a novel measurement of wave-height — differential algorithm.Compared with electric level method, the differential algorithm has its advantages. This article details its principle,algorithm and demonstrates it with a living example.