The expressions of the internal forces of the webs under the vertical loads of the simply supported beam type trusses with vertical and horizontal webs and without vertical webs are studied through the mathematical fo...The expressions of the internal forces of the webs under the vertical loads of the simply supported beam type trusses with vertical and horizontal webs and without vertical webs are studied through the mathematical formula method. The variations of internal forces under different angles and spacings of the webs are simulated. The law of the optimal arrangement of the webs of the parallel-string simple-beam truss is obtained: under the condition that the rigidity of the rod is allowed, the form of no vertical web-type truss and reducing the span distance and inclination of the side span are advisable, which can save materials and reduce the weight as well. This method can be applied to the calculation of internal forces for arbitrary loads and truss forms.展开更多
In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found ...In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.展开更多
A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some resul...A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.展开更多
The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s met...The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.展开更多
Estimation of water content is the foundation of natural gas processing and designing,and a formula calculation method provides a solution simple and easy to be programmed by computers.In this regard,several main form...Estimation of water content is the foundation of natural gas processing and designing,and a formula calculation method provides a solution simple and easy to be programmed by computers.In this regard,several main formula calculation methods of water content in sweet natural gas were reviewed and evaluated individually.There are formulas fitted with nomographic data(e.g.Sloan formula,Ning Yingnan formula,Khaled formula and Bahadori formula),empirical formulas fitted with experimental data(e.g.Zhu Lin formula,Behr formula and Kazim formula)and formulas generated based on water-hydrocarbon phases equilibrium(e.g.Saturated Vapor Pressure Model,Modified Ideal Model,Simplified Thermodynamic Model and Bukacek formula).The comparison of calculated and experimental values of each above formula calculation method indicates that,the Khaled formula provided the minimum average absolute deviation(AAD)–2.5240%,while the Behr method achieved the maximum AAD–19.255%.After the analysis of the AAD results calculated by the methods at different temperature ranges,the Zhu Lin formula is recommended for−50 to−40℃,the Sloan formula for−40 to 0℃,the Simplified Thermodynamic Model for 0 to 37.78°C,the Khaled formula for 37.78 to 171.11℃,and the Bukacek formula for 171.11 to 237.78℃.展开更多
This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and s...This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).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
This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introd...This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introduces the three formulas obtained from the cubic equation of a hearth by Murase (Ref. [1]). We find that Murase’s three formulas lead to a Horner’s method (Ref. [2]) and extension of a Newton’s method (2009) at the same time. This shows originality of Wasan (mathematics developed in Japan) in the Edo era (1603-1868). Suzuki (Ref. [3]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 2 gives the relations between Newton’s method, Horner’s method and Murase’s three formulas. Section 3 gives a new function defined such as .展开更多
This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homoge...This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.展开更多
In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models...In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.展开更多
文摘The expressions of the internal forces of the webs under the vertical loads of the simply supported beam type trusses with vertical and horizontal webs and without vertical webs are studied through the mathematical formula method. The variations of internal forces under different angles and spacings of the webs are simulated. The law of the optimal arrangement of the webs of the parallel-string simple-beam truss is obtained: under the condition that the rigidity of the rod is allowed, the form of no vertical web-type truss and reducing the span distance and inclination of the side span are advisable, which can save materials and reduce the weight as well. This method can be applied to the calculation of internal forces for arbitrary loads and truss forms.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161278)
文摘In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.
文摘A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
文摘The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.
基金National Natural Science Foundation of China(No.u1262111).
文摘Estimation of water content is the foundation of natural gas processing and designing,and a formula calculation method provides a solution simple and easy to be programmed by computers.In this regard,several main formula calculation methods of water content in sweet natural gas were reviewed and evaluated individually.There are formulas fitted with nomographic data(e.g.Sloan formula,Ning Yingnan formula,Khaled formula and Bahadori formula),empirical formulas fitted with experimental data(e.g.Zhu Lin formula,Behr formula and Kazim formula)and formulas generated based on water-hydrocarbon phases equilibrium(e.g.Saturated Vapor Pressure Model,Modified Ideal Model,Simplified Thermodynamic Model and Bukacek formula).The comparison of calculated and experimental values of each above formula calculation method indicates that,the Khaled formula provided the minimum average absolute deviation(AAD)–2.5240%,while the Behr method achieved the maximum AAD–19.255%.After the analysis of the AAD results calculated by the methods at different temperature ranges,the Zhu Lin formula is recommended for−50 to−40℃,the Sloan formula for−40 to 0℃,the Simplified Thermodynamic Model for 0 to 37.78°C,the Khaled formula for 37.78 to 171.11℃,and the Bukacek formula for 171.11 to 237.78℃.
文摘This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).
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This paper gives the extension of Newton’s method, and a variety of formulas to compare the convergences for the extension of Newton’s method (Section 4). Section 5 gives the numerical calculations. Section 1 introduces the three formulas obtained from the cubic equation of a hearth by Murase (Ref. [1]). We find that Murase’s three formulas lead to a Horner’s method (Ref. [2]) and extension of a Newton’s method (2009) at the same time. This shows originality of Wasan (mathematics developed in Japan) in the Edo era (1603-1868). Suzuki (Ref. [3]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 2 gives the relations between Newton’s method, Horner’s method and Murase’s three formulas. Section 3 gives a new function defined such as .
基金Hunan Provincial Natural Science Foundation Under Grant No.02JJY2085
文摘This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.
基金National Basic Research Program of China Under Grant No. 2007CB714200National Natural Science Foundation of China Under Grant No. 90715038
文摘In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.
