Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin...Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.展开更多
In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed poin...In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.展开更多
A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of el...A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.展开更多
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this un...This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.展开更多
The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, te...The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, temperature and press in the filming process. The concrete technique of filming is showed by establishing the fuzzy mumbership function of above three indexes, which improves the precision of the materials of nanometer electro-thermal in hot-working. At the same time, the principles of the fuzzy relationship mapping inversion （FRMI） is put forward, Therefore, the standardization and continuity can be met.展开更多
In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form...In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.展开更多
Volcanic hazard zoning is an effective way to reduce and mitigate volcanic risks.Due to its frequent magmatic unrest and potential for catastrophic eruption,the Changbaishan-Tianchi Volcano is currently the focus of a...Volcanic hazard zoning is an effective way to reduce and mitigate volcanic risks.Due to its frequent magmatic unrest and potential for catastrophic eruption,the Changbaishan-Tianchi Volcano is currently the focus of attention for volcanic disaster prevention in China.This study uses past eruption data obtained from geological surveys and geochronological studies,to construct simulations of tephra fall,pyroclastic flows,lava flows,and lahars.Several widely accepted numerical models were adopted to simulate each hazard at different eruption scales.Hazard zoning was then conducted,producing a comprehensive hazards map of the Changbaishan-Tianchi Volcano.The map identifies areas of high,medium,and low hazard,mostly at 0-15,15-60,60-100 km from the edifice.This work serves as the scientific basis for the authorities and general public in the areas around the Changbaishan-Tianchi Volcano in planning for future response,as well as provides a reference for hazard zoning in other areas potentially affected by volcanic hazards.展开更多
Background: The multiple sequence alignment (MSA) algorithms are the traditional ways to compare and analyze DNA sequences. However, for large DNA sequences, these algorithms require a long time computationally. Objec...Background: The multiple sequence alignment (MSA) algorithms are the traditional ways to compare and analyze DNA sequences. However, for large DNA sequences, these algorithms require a long time computationally. Objective: Here we will propose a new numerical method to characterize and compare DNA sequences quickly. Method: Based on a new 2-dimensional (2D) graphical representation of DNA sequences, we can obtain an 8-dimensional vector using two basic concepts of probability, the mean and the variance. Results: We perform similarity/dissimilarity analyses among two real DNA data sets, the coding sequences of the first exon of beta-globin gene of 11 species and 31 mammalian mitochondrial genomes, respectively. Conclusion: Our results are in agreement with the existing analyses in our literatures. We also compare our approach with other methods and find that ours is more effective.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
Tephra fallout is an important type of hazard caused by explosive volcanic eruption, and numerical simulation has become a fast and effective approach to assess the dispersion and deposition of tephra fallout. Accordi...Tephra fallout is an important type of hazard caused by explosive volcanic eruption, and numerical simulation has become a fast and effective approach to assess the dispersion and deposition of tephra fallout. According to the improved 2D diffusion model of Suzuki （ 1983）, we edited a tephra diffusion program that can run in the Windows system. Based on previous data, we simulated the diffusion scope of the Jinlongdingzi volcanic eruption, which is the latest eruption in the Longgang volcanic cluster. The simulated results are in good agreement with the results from measurement in situ, indicating that the model is reliable and the parameters used in the model are suitable. By using wind profiles of ten years, 7, 021 simulations under different wind profiles were carried out, and then probabilistic hazard maps of tephra fallout were constructed for tephra thickness thresholds, lcm and 0.5cm. This study can provide an important scientific basis for volcanic hazard analysis, risk mitigation plans and countermeasures in the Longgang volcanic area.展开更多
The method of numerical solving of nonlinear model problems of theory of a complex quasi-potential in doubly-connected nonlinear-layered curvilinear domains considering inverse influence function of flow on a conducti...The method of numerical solving of nonlinear model problems of theory of a complex quasi-potential in doubly-connected nonlinear-layered curvilinear domains considering inverse influence function of flow on a conductivity coefficient of medium was developed on the basis of synthesis of numerical methods of the quasi-conformal mappings and summary representations in conjunction with domain decomposition by method Schwartz. The proposed algorithm allows finding the potential of the quasiideals field, construction a motion grid （fluid-flow grid） simultaneously defining the flow lines that separate of sub-domains constancy of coefficient conductivity and identification the piecewise-constant values of coefficient conductivity, the local flows for the known measurements on boundary of domain.展开更多
In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach ...In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficie...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann op...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.展开更多
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.
文摘In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.
基金the National Natural Science Foundation of China(No.51005180)the Ao-Xiang Star Project of NPU(Northwestern Polytechnical University)+2 种基金the Research Fund of the State Key Laboratory of Solidification Processing(NPU,China)(No.69-QP- 2011)the Program for New Century Excellent Talents in University by the Ministry of Education of China (No.NECT-08-0463)the 111 Project(No.B08040)
文摘A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.
基金supported by the National Natural Science Foundation of China (NSFC) (10872155)
文摘This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.
文摘The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, temperature and press in the filming process. The concrete technique of filming is showed by establishing the fuzzy mumbership function of above three indexes, which improves the precision of the materials of nanometer electro-thermal in hot-working. At the same time, the principles of the fuzzy relationship mapping inversion （FRMI） is put forward, Therefore, the standardization and continuity can be met.
基金supported by the Ministry Of Higher Education Malaysia for the Fundamental Research Grant scheme,project No. 01-04-10-897FRthe NSF scholarship
文摘In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.
基金supported by the National Natural Science Foundation of China(Nos.42042034,41861144025)the National Nonprofit Fundamental Research,Institute of Geology,China Earthquake Administration(No.IGCEA1603)。
文摘Volcanic hazard zoning is an effective way to reduce and mitigate volcanic risks.Due to its frequent magmatic unrest and potential for catastrophic eruption,the Changbaishan-Tianchi Volcano is currently the focus of attention for volcanic disaster prevention in China.This study uses past eruption data obtained from geological surveys and geochronological studies,to construct simulations of tephra fall,pyroclastic flows,lava flows,and lahars.Several widely accepted numerical models were adopted to simulate each hazard at different eruption scales.Hazard zoning was then conducted,producing a comprehensive hazards map of the Changbaishan-Tianchi Volcano.The map identifies areas of high,medium,and low hazard,mostly at 0-15,15-60,60-100 km from the edifice.This work serves as the scientific basis for the authorities and general public in the areas around the Changbaishan-Tianchi Volcano in planning for future response,as well as provides a reference for hazard zoning in other areas potentially affected by volcanic hazards.
文摘Background: The multiple sequence alignment (MSA) algorithms are the traditional ways to compare and analyze DNA sequences. However, for large DNA sequences, these algorithms require a long time computationally. Objective: Here we will propose a new numerical method to characterize and compare DNA sequences quickly. Method: Based on a new 2-dimensional (2D) graphical representation of DNA sequences, we can obtain an 8-dimensional vector using two basic concepts of probability, the mean and the variance. Results: We perform similarity/dissimilarity analyses among two real DNA data sets, the coding sequences of the first exon of beta-globin gene of 11 species and 31 mammalian mitochondrial genomes, respectively. Conclusion: Our results are in agreement with the existing analyses in our literatures. We also compare our approach with other methods and find that ours is more effective.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
基金unded by the National Natural Science Foundation Project(40972209)the Special Projects for China Earthquake Research(201208005)
文摘Tephra fallout is an important type of hazard caused by explosive volcanic eruption, and numerical simulation has become a fast and effective approach to assess the dispersion and deposition of tephra fallout. According to the improved 2D diffusion model of Suzuki （ 1983）, we edited a tephra diffusion program that can run in the Windows system. Based on previous data, we simulated the diffusion scope of the Jinlongdingzi volcanic eruption, which is the latest eruption in the Longgang volcanic cluster. The simulated results are in good agreement with the results from measurement in situ, indicating that the model is reliable and the parameters used in the model are suitable. By using wind profiles of ten years, 7, 021 simulations under different wind profiles were carried out, and then probabilistic hazard maps of tephra fallout were constructed for tephra thickness thresholds, lcm and 0.5cm. This study can provide an important scientific basis for volcanic hazard analysis, risk mitigation plans and countermeasures in the Longgang volcanic area.
文摘The method of numerical solving of nonlinear model problems of theory of a complex quasi-potential in doubly-connected nonlinear-layered curvilinear domains considering inverse influence function of flow on a conductivity coefficient of medium was developed on the basis of synthesis of numerical methods of the quasi-conformal mappings and summary representations in conjunction with domain decomposition by method Schwartz. The proposed algorithm allows finding the potential of the quasiideals field, construction a motion grid （fluid-flow grid） simultaneously defining the flow lines that separate of sub-domains constancy of coefficient conductivity and identification the piecewise-constant values of coefficient conductivity, the local flows for the known measurements on boundary of domain.
文摘In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.
