For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversio...For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.展开更多
During the desing of channel transect,the paper brings forward golden section method,which is 0.618 methods.In order to reduce the calculation volume of the natural depth of water h 0 and bottomˉwidth b which apply ...During the desing of channel transect,the paper brings forward golden section method,which is 0.618 methods.In order to reduce the calculation volume of the natural depth of water h 0 and bottomˉwidth b which apply trial calculation method and graphic method,and improve the calculate precision,the mathematical model has been built up,the writer combines example to explain the train of thought,the result shows that the calculation precision is high,the correctness is tested and verified by the result which is calculated by hand.It can be referred to the hydroelectric works.展开更多
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest m...The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest masses of the decay particles are assigned to the points-velocities).Two points-velocities of the decay particles can be connected by a line segment and an arc of a line of constant curvature 0,called the oricycle.Archimedes’leverage laws define a 3rd point on the arc of the oricycle to which an additive mass(sum of rest masses of particles)is assigned.Connecting 3 points-velocities by line segments,we obtain isosceles triangles of decays of resonances in the Beltrami model of the Lobachevsky velocity space.In the decay triangles of resonances,the golden section is found and the Stewart,Brettschneider theorems on oricyclic arcs are satisfied.Near the decay triangles of scalar,strange mesons andΔ,N baryons,isosceles triangles-satellites with integer values of their characteristics were found.On the satellite triangles,the Lorentz invariant function—the product of the length of the arc of the oricycle subtending the base and the cotangent of half the angle at the vertex opposite the base—takes integer values.The function is called the oricyclic cotangent of a triangle(OCT).In addition to the integer values of OCT,these satellite triangles also have the sum of the hyperbolic cosines of the lengths of the lateral sides and the hyperbolic cosines of the base lengths equal to integers.These satellite triangles are called Heron triangles.On Heron triangles,the generalized cosines of the angles between the tangent to the oricycle at the point-velocity of the additive mass and the tan-gent at the point-velocity of the base of the triangle take multiples of 1/2 values.展开更多
Splines are important in both mathematics and mechanics. We investigate the relationships between bivariate splines and mechanics in this paper. The mechanical meanings of some univariate splines were viewed based on ...Splines are important in both mathematics and mechanics. We investigate the relationships between bivariate splines and mechanics in this paper. The mechanical meanings of some univariate splines were viewed based on the analysis of bending beams. For the 2D case, the relationships between a class of quintic bivariate splines with smoothness 3 and bending of thin plates are presented constructively. Furthermore, the variational property of bivariate splines and golden section in splines are also discussed.展开更多
To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluatio...To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.展开更多
基金supported by Specialized Research Fund for the Doctoral Program of Higher Education of China(20110022120004)the Fundamental Research Funds for the Central Universities
文摘For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.
文摘During the desing of channel transect,the paper brings forward golden section method,which is 0.618 methods.In order to reduce the calculation volume of the natural depth of water h 0 and bottomˉwidth b which apply trial calculation method and graphic method,and improve the calculate precision,the mathematical model has been built up,the writer combines example to explain the train of thought,the result shows that the calculation precision is high,the correctness is tested and verified by the result which is calculated by hand.It can be referred to the hydroelectric works.
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金financed by the LLP“Industry 4.0”,Almaty,Kazakhstan.
文摘The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest masses of the decay particles are assigned to the points-velocities).Two points-velocities of the decay particles can be connected by a line segment and an arc of a line of constant curvature 0,called the oricycle.Archimedes’leverage laws define a 3rd point on the arc of the oricycle to which an additive mass(sum of rest masses of particles)is assigned.Connecting 3 points-velocities by line segments,we obtain isosceles triangles of decays of resonances in the Beltrami model of the Lobachevsky velocity space.In the decay triangles of resonances,the golden section is found and the Stewart,Brettschneider theorems on oricyclic arcs are satisfied.Near the decay triangles of scalar,strange mesons andΔ,N baryons,isosceles triangles-satellites with integer values of their characteristics were found.On the satellite triangles,the Lorentz invariant function—the product of the length of the arc of the oricycle subtending the base and the cotangent of half the angle at the vertex opposite the base—takes integer values.The function is called the oricyclic cotangent of a triangle(OCT).In addition to the integer values of OCT,these satellite triangles also have the sum of the hyperbolic cosines of the lengths of the lateral sides and the hyperbolic cosines of the base lengths equal to integers.These satellite triangles are called Heron triangles.On Heron triangles,the generalized cosines of the angles between the tangent to the oricycle at the point-velocity of the additive mass and the tan-gent at the point-velocity of the base of the triangle take multiples of 1/2 values.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 6053306060373093+4 种基金10726068)the Natural Science Foundation of Hebei Province (Grant Nos. A2009000735A2010000908)Research Projectof Hebei Educational Committee (Grant No.2009448)Shanghai Key Laboratory for Contemporary AppliedMathamtics (Grant No.09FG067)
文摘Splines are important in both mathematics and mechanics. We investigate the relationships between bivariate splines and mechanics in this paper. The mechanical meanings of some univariate splines were viewed based on the analysis of bending beams. For the 2D case, the relationships between a class of quintic bivariate splines with smoothness 3 and bending of thin plates are presented constructively. Furthermore, the variational property of bivariate splines and golden section in splines are also discussed.
文摘To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.
