Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minim...Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.展开更多
Different criteria and factors are used in different methods of soft soil foundation settlement calculation and engineering geological zoning.The methods used are not universally suitable for complex geological enviro...Different criteria and factors are used in different methods of soft soil foundation settlement calculation and engineering geological zoning.The methods used are not universally suitable for complex geological environments.The post-construction settlement of soft soil foundations are especially large and difficult to calculate.In addition,there are many deficiencies in the current methods used for engineering geological zoning.Focusing on the need of establishing engineering geological zoning for areas with soft soil foundations in the Tianjin Marine Economic Area,combination weighting and extension methods were introduced.An evaluation model for the settlement of soft soil foundations was established using multiple factors and large amounts of data.This evaluation model is accurate and objective for delineating engineering geological zoning.These methods eliminate deficiencies by considering both objective and subjective factors,and help obtain an objective and accurate result.展开更多
Based on the resent research about the planting structure of slope farmland in northern Shaanxi,in order to increase the native's income,we use the theory of the extension methods to analyze the planting structure...Based on the resent research about the planting structure of slope farmland in northern Shaanxi,in order to increase the native's income,we use the theory of the extension methods to analyze the planting structure of slope farmland,so that we can get the extensive strategy,and put them into use for planting of slope farmland to make the native's income higher.展开更多
In this paper, we propose an accelerated search-extension method (ASEM) based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple...In this paper, we propose an accelerated search-extension method (ASEM) based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.展开更多
In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the ...In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.展开更多
In this paper,we present the simplification of Sachs formulas for the measurement and calculation of the residual stresses of the cylinder only with the plane stresses. Furthermore, we present the method for the measu...In this paper,we present the simplification of Sachs formulas for the measurement and calculation of the residual stresses of the cylinder only with the plane stresses. Furthermore, we present the method for the measurement and calculation of the residual stresses of the cylinder not only with the finite length but with the longitudinal stress. These can be applied to the investigation on the residual stresses of the autofretted gun tube.展开更多
The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or obse...The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.展开更多
By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x...By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x+y)/x][(a+b)/2] y, for 0<a<b,0<x<1,y>0,x+y≤2. These inequalities are the extensions of inequalities of Qi Feng, Xu Senlin and Zheng Lin. And a conjection of Qi Feng is proved not true.展开更多
The importance of rural highway maintenance is self-evident, and it is also a basic work of the highway operation department. Selecting an appropriate evaluation method can timely and accurately find the pavement dise...The importance of rural highway maintenance is self-evident, and it is also a basic work of the highway operation department. Selecting an appropriate evaluation method can timely and accurately find the pavement diseases, and improve the timeliness of pavement repair. To improve the accuracy of pavement quality comprehensive evaluation, based on the game theory, the improved extension evaluation method was combined with subjective and objective weight determination methods in this paper, to propose a comprehensive weight determination method with a good operability.<span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The results</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">show that the improved extension evaluation method provid</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">es</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> a feasible scheme for rural highway maintenance quality evaluation</span></span></span>展开更多
To achieve de novo protein structure determination of challenging cases, multi-wavelength anomalous diffraction(MAD) and multiple isomorphous replacement(MIR) phasing can be powerful tools to obtain low-resolution ini...To achieve de novo protein structure determination of challenging cases, multi-wavelength anomalous diffraction(MAD) and multiple isomorphous replacement(MIR) phasing can be powerful tools to obtain low-resolution initial phases from heavy-atom derivative datasets, then phase extension is needed against high-resolution data to obtain accurate structures.In this context, we propose a direct-methods procedure here that could improve the initial low-resolution MAD/MIR phase quality.And accordingly, an automated process for extending initial phases to high resolution is also described.These two procedures are both implanted in the newly released IPCAS pipeline.Three cases are used to perform the test, including one set of 4.17 ? MAD data from a membrane protein and two sets of MAD/MIR data with derivatives truncated down to 6.80 ? and 6.90 ?, respectively.All the results have shown that the initial phases generated from the direct-methods procedure are better than that from the conventional MAD/MIR methods.The automated phase extensions for the latter two cases starting from 6.80 ? to 3.00 ? and 6.90 ? to 2.80 ? are proved to be successful, leading to complete models.This may provide convenient and reliable tools for phase improvement and phase extension in difficult low-resolution tasks.展开更多
Extension strategy tactics planning (ESTP), based upon the science of Extenics, is established for the purpose of solving contradictory problems. In this paper, the fundamental thoughts, theories and methods of ESTP a...Extension strategy tactics planning (ESTP), based upon the science of Extenics, is established for the purpose of solving contradictory problems. In this paper, the fundamental thoughts, theories and methods of ESTP are introduced concisely. The highlights of ESTP are that the techniques, used in the case of tackling such problems as how to generate the ideas of strategy tactics planning, how to completely analyze the resources, how to exploit extension resources, how to transfer the incompatible into the compati ble, and how to transfer the opposite into the co existent, are developed in a formalized way. And regarding the practices of ESTP, the applications of ESTP in resource integration, project, market development, and the prevention and handling crises are presented.展开更多
文摘Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.
基金National Natural Science Foundations of China(Nos.41172236,41402243)
文摘Different criteria and factors are used in different methods of soft soil foundation settlement calculation and engineering geological zoning.The methods used are not universally suitable for complex geological environments.The post-construction settlement of soft soil foundations are especially large and difficult to calculate.In addition,there are many deficiencies in the current methods used for engineering geological zoning.Focusing on the need of establishing engineering geological zoning for areas with soft soil foundations in the Tianjin Marine Economic Area,combination weighting and extension methods were introduced.An evaluation model for the settlement of soft soil foundations was established using multiple factors and large amounts of data.This evaluation model is accurate and objective for delineating engineering geological zoning.These methods eliminate deficiencies by considering both objective and subjective factors,and help obtain an objective and accurate result.
基金Supported by The Special Research Projects of Education Department of Shaanxi Province (09JK556)The Special Fund-susten-tation Project of Key Disciplines of Shaanxi Province~~
文摘Based on the resent research about the planting structure of slope farmland in northern Shaanxi,in order to increase the native's income,we use the theory of the extension methods to analyze the planting structure of slope farmland,so that we can get the extensive strategy,and put them into use for planting of slope farmland to make the native's income higher.
基金supported by the National Natural Science Foundation of China (10571053, 10871066, 10811120282)Programme for New Century Excellent Talents in University(NCET-06-0712)
文摘In this paper, we propose an accelerated search-extension method (ASEM) based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.
文摘In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.
文摘In this paper,we present the simplification of Sachs formulas for the measurement and calculation of the residual stresses of the cylinder only with the plane stresses. Furthermore, we present the method for the measurement and calculation of the residual stresses of the cylinder not only with the finite length but with the longitudinal stress. These can be applied to the investigation on the residual stresses of the autofretted gun tube.
文摘The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
文摘By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x+y)/x][(a+b)/2] y, for 0<a<b,0<x<1,y>0,x+y≤2. These inequalities are the extensions of inequalities of Qi Feng, Xu Senlin and Zheng Lin. And a conjection of Qi Feng is proved not true.
文摘The importance of rural highway maintenance is self-evident, and it is also a basic work of the highway operation department. Selecting an appropriate evaluation method can timely and accurately find the pavement diseases, and improve the timeliness of pavement repair. To improve the accuracy of pavement quality comprehensive evaluation, based on the game theory, the improved extension evaluation method was combined with subjective and objective weight determination methods in this paper, to propose a comprehensive weight determination method with a good operability.<span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The results</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">show that the improved extension evaluation method provid</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">es</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> a feasible scheme for rural highway maintenance quality evaluation</span></span></span>
基金Project supported by the National Basic Research Program of China(Grant No.2011CB911100)of the Ministry of Science and Technology of China
文摘To achieve de novo protein structure determination of challenging cases, multi-wavelength anomalous diffraction(MAD) and multiple isomorphous replacement(MIR) phasing can be powerful tools to obtain low-resolution initial phases from heavy-atom derivative datasets, then phase extension is needed against high-resolution data to obtain accurate structures.In this context, we propose a direct-methods procedure here that could improve the initial low-resolution MAD/MIR phase quality.And accordingly, an automated process for extending initial phases to high resolution is also described.These two procedures are both implanted in the newly released IPCAS pipeline.Three cases are used to perform the test, including one set of 4.17 ? MAD data from a membrane protein and two sets of MAD/MIR data with derivatives truncated down to 6.80 ? and 6.90 ?, respectively.All the results have shown that the initial phases generated from the direct-methods procedure are better than that from the conventional MAD/MIR methods.The automated phase extensions for the latter two cases starting from 6.80 ? to 3.00 ? and 6.90 ? to 2.80 ? are proved to be successful, leading to complete models.This may provide convenient and reliable tools for phase improvement and phase extension in difficult low-resolution tasks.
基金TheNationalNaturalScienceFoundationofChina (No .70 14 0 0 0 3 )GuangdongNaturalScienceFoundation (No .0 10 0 49)
文摘Extension strategy tactics planning (ESTP), based upon the science of Extenics, is established for the purpose of solving contradictory problems. In this paper, the fundamental thoughts, theories and methods of ESTP are introduced concisely. The highlights of ESTP are that the techniques, used in the case of tackling such problems as how to generate the ideas of strategy tactics planning, how to completely analyze the resources, how to exploit extension resources, how to transfer the incompatible into the compati ble, and how to transfer the opposite into the co existent, are developed in a formalized way. And regarding the practices of ESTP, the applications of ESTP in resource integration, project, market development, and the prevention and handling crises are presented.