We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSS...We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.展开更多
The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We ...The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.展开更多
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoreti...As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.展开更多
The expressions for calculating the values of the workspace areas of 2-DOF parallel planar manipulators (PPM) is derived. By the aid of computer, the values are calculated and plotted on the physical model o...The expressions for calculating the values of the workspace areas of 2-DOF parallel planar manipulators (PPM) is derived. By the aid of computer, the values are calculated and plotted on the physical model of the solution space of the 2-DOF PPMs,so the workspaee-area-property atlas is obtained. The atlas delineates the relationship between the workspace areas and the link lengths of the 2-DOF PPMs all-sidedly. It is very useful for designers overalI to understand and know welI the relationship.展开更多
The input impedance of the post-matching network(PMN)is configured as a complex value.The parameter solution space is determined based on the fundamental principles of the Doherty power amplifier(DPA),enabling the DPA...The input impedance of the post-matching network(PMN)is configured as a complex value.The parameter solution space is determined based on the fundamental principles of the Doherty power amplifier(DPA),enabling the DPA to achieve high efficiency at the output power back-off(OBO).The parameter solution space comprises three variables:the phase parameter of the output matching network for the carrier power amplifier(carrier PA),the phase parameter of the output matching network for the peaking power amplifier(peaking PA),and the input impedance of PMN.These parameters are optimized to enable the DPA to achieve high efficiency at the OBO.In this paper,a one-to-one mapping relationship is established between the frequency and the parameter solution space,allowing for a precise optimization of the DPA across a broad frequency range.Leveraging this mapping relationship,an asymmetric DPA designed to operate over the 1.8–2.6 GHz frequency band is designed and fabricated,demonstrating the feasibility and effectiveness of the proposed approach.Under continuous wave excitation,the test results show that the drain efficiency(DE)is 42.7%–56.4%at 9.5 dB OBO and the saturated DE is 45.8%–71.1%.The saturated output power of this DPA is 46.9–48.8 dBm with a gain of 5.5–8.0 dB at saturation.A 20-MHz long-term-evolution modulated signal with a peak-to-average power ratio of 8 dB is also applied to the fabricated DPA at 1.8,2.1,and 2.6 GHz.Under these conditions,at 8 dB OBO,the DPA shows an adjacent channel power ratio always lower than 48 dBc after digital pre-distortion linearization.展开更多
The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota...The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.展开更多
This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted...This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.展开更多
Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an e...Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.展开更多
Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform a...Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.展开更多
We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spac...In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y, f(t, y): [0, T] x Y --> Y, and G(t, y): [0, T] X Y --> L(H, Y), y0: OMEGA --> Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].展开更多
It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. ...It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for展开更多
On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi...On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.展开更多
In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parame...In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.展开更多
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-pl...We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-ployed.The first method is similar to the classic mesh-based discretization method requiring n centers per dimension or a total ndpoints.The second method is based upon n randomly generated points in dℜrequiring far fewer data centers than the classic mesh method.Instead of having a crisp boundary,we form a“fuzzy”boundary.Using the analytic or numerical in-verse interior and boundary operators,we find the local and global minima and maxima to cull discretization points.We also find that the GMQ-RBF“flatness”can be controlled by increasing the GMQ exponential,β.We per-form a search to find the smallest root mean squared error(RMSE)by varying the exponent,the maximum,the minimum range of the GMQ shape parame-ter,and boundary influence,with the exponential having the most influence.Because the GMQ-RBFs are essentially nonlinear,it follows that the starting point of the simple search influences the end result.The optimal algorithm for high dimensional PDEs is still the subject of much research and may wait for the common place availability of massively parallel quantum computers for even higher dimensional PDEs and integral equations(IEs).展开更多
In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and aut...In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and authority on partial differential equation, starting from heatconduction equation, obtained some results of properly posed of certain initialboundary value problems of Navier-Stokes equation. Professor R. Temam of University de Paris XI and other experts in this field also brought up the possibility ofcomparing these two classes of equations. This paper attempts to describe and provethe .fundamental difference between these two.展开更多
In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and aut...In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and authority on partial differential equation, starting from heatconduction equation, obtained some results of properly posed of certain initialboundary value problems of Navier-Stokes equation. Professor R. Temam of University de Paris XI and other experts in this field also brought up the possibility ofcomparing these two classes of equations. This paper attempts to describe and provethe .fundamental difference between these two.展开更多
This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
This paper presents an uncoupled state space solution to three-dimensional consolidation of layered poroelastic medium with anisotropic permeability and compressible pore fluid.Starting from the basic equations of por...This paper presents an uncoupled state space solution to three-dimensional consolidation of layered poroelastic medium with anisotropic permeability and compressible pore fluid.Starting from the basic equations of poroelastic medium,and introducing intermediate variables,the state space equation usually comprising eight coupled state vectors is uncoupled into two sets of equations of six and two state vectors in the Laplace-Fourier transform domain.Combined with the continuity conditions between adjacent layers and boundary conditions,the uncoupled state space solution of a layered poroelastic medium is obtained by using the transfer matrix method.Numerical results show that the anisotropy of permeability and the compressibility of pore fluid have remarkable influence on the consolidation behavior of poroelastic medium.展开更多
文摘We develop a 3D bounded slice-surface grid （3D-BSSG） structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences under Grant No.KJCX2-EW-J02the Natural National Science Foundation of China under Grant Nos.11121403 and 11225526
文摘The random K-satisfiability （K-SAT） problem is very diffcult when the clause density is close to the satisfiability threshold. In this paper we study this problem from the perspective of solution space coupling. We divide a given difficult random K-SAT formula into two easy sub-formulas and let the two corresponding solution spaces to interact with each other through a coupling field x. We investigate the statistical mechanical property of this coupled system by mean field theory and computer simulations. The coupled system has an ergodicity-breaking （clustering） transition at certain critical value Xd of the coupling field. At this transition point, the mean overlap value between the solutions of the two solution spaces is very close to 1. The mean energy density of the coupled system at its clustering transition point is less than the mean energy density of the original K-SAT problem at the temperature-induced clustering transition point. The implications of this work for designing new heuristic K-SAT solvers are discussed.
基金NationalNaturalScienceFoundationof China underGrant No .60173054
文摘As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
文摘The expressions for calculating the values of the workspace areas of 2-DOF parallel planar manipulators (PPM) is derived. By the aid of computer, the values are calculated and plotted on the physical model of the solution space of the 2-DOF PPMs,so the workspaee-area-property atlas is obtained. The atlas delineates the relationship between the workspace areas and the link lengths of the 2-DOF PPMs all-sidedly. It is very useful for designers overalI to understand and know welI the relationship.
基金supported by the National Key Laboratory of Science and Technology on Space Microwave,China(No.HTKJ2023KL504005)the Funds in the Field of Technology of the Enhanced Program of National Basic Research,China(No.2022-JCJQ-JJ-0637)。
文摘The input impedance of the post-matching network(PMN)is configured as a complex value.The parameter solution space is determined based on the fundamental principles of the Doherty power amplifier(DPA),enabling the DPA to achieve high efficiency at the output power back-off(OBO).The parameter solution space comprises three variables:the phase parameter of the output matching network for the carrier power amplifier(carrier PA),the phase parameter of the output matching network for the peaking power amplifier(peaking PA),and the input impedance of PMN.These parameters are optimized to enable the DPA to achieve high efficiency at the OBO.In this paper,a one-to-one mapping relationship is established between the frequency and the parameter solution space,allowing for a precise optimization of the DPA across a broad frequency range.Leveraging this mapping relationship,an asymmetric DPA designed to operate over the 1.8–2.6 GHz frequency band is designed and fabricated,demonstrating the feasibility and effectiveness of the proposed approach.Under continuous wave excitation,the test results show that the drain efficiency(DE)is 42.7%–56.4%at 9.5 dB OBO and the saturated DE is 45.8%–71.1%.The saturated output power of this DPA is 46.9–48.8 dBm with a gain of 5.5–8.0 dB at saturation.A 20-MHz long-term-evolution modulated signal with a peak-to-average power ratio of 8 dB is also applied to the fabricated DPA at 1.8,2.1,and 2.6 GHz.Under these conditions,at 8 dB OBO,the DPA shows an adjacent channel power ratio always lower than 48 dBc after digital pre-distortion linearization.
基金Supported by the Teaching Steering Committee Research Project of Higher-Learning Institutions of Ministry of Education(JZW-16-DD-15)
文摘The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.
文摘This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.
文摘Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.
文摘Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are obtained by the application of a double Fourier transform and an order reduction method based on the Cayley-Hamilton theorem. Combining the solutions and the constitutive equations which connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.
文摘We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
基金This work is supported by the National Science Foundation of China.
文摘In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y, f(t, y): [0, T] x Y --> Y, and G(t, y): [0, T] X Y --> L(H, Y), y0: OMEGA --> Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].
基金This paper is supported by the National Foundations.
文摘It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
文摘In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.
文摘In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
文摘We solve numerically an eigenvalue elliptic partial differential equation(PDE)ranging from two to six dimensions using the generalized multiquadric(GMQ)radial basis functions(RBFs).Two discretization methods are em-ployed.The first method is similar to the classic mesh-based discretization method requiring n centers per dimension or a total ndpoints.The second method is based upon n randomly generated points in dℜrequiring far fewer data centers than the classic mesh method.Instead of having a crisp boundary,we form a“fuzzy”boundary.Using the analytic or numerical in-verse interior and boundary operators,we find the local and global minima and maxima to cull discretization points.We also find that the GMQ-RBF“flatness”can be controlled by increasing the GMQ exponential,β.We per-form a search to find the smallest root mean squared error(RMSE)by varying the exponent,the maximum,the minimum range of the GMQ shape parame-ter,and boundary influence,with the exponential having the most influence.Because the GMQ-RBFs are essentially nonlinear,it follows that the starting point of the simple search influences the end result.The optimal algorithm for high dimensional PDEs is still the subject of much research and may wait for the common place availability of massively parallel quantum computers for even higher dimensional PDEs and integral equations(IEs).
文摘In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and authority on partial differential equation, starting from heatconduction equation, obtained some results of properly posed of certain initialboundary value problems of Navier-Stokes equation. Professor R. Temam of University de Paris XI and other experts in this field also brought up the possibility ofcomparing these two classes of equations. This paper attempts to describe and provethe .fundamental difference between these two.
文摘In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those .for heat conduction equation.In his study of Navier-Stokes equation .Professor J.Leray. a Frenehmathematician and authority on partial differential equation, starting from heatconduction equation, obtained some results of properly posed of certain initialboundary value problems of Navier-Stokes equation. Professor R. Temam of University de Paris XI and other experts in this field also brought up the possibility ofcomparing these two classes of equations. This paper attempts to describe and provethe .fundamental difference between these two.
文摘This paper, applying the stratification theory, proves the instability of certain initial (boundary) Value problem of forced dissipative nonlinear system in atmospheric dynamies. An example in given.
基金supported by the National Natural Science Foundation of China(Grant No.50578121).
文摘This paper presents an uncoupled state space solution to three-dimensional consolidation of layered poroelastic medium with anisotropic permeability and compressible pore fluid.Starting from the basic equations of poroelastic medium,and introducing intermediate variables,the state space equation usually comprising eight coupled state vectors is uncoupled into two sets of equations of six and two state vectors in the Laplace-Fourier transform domain.Combined with the continuity conditions between adjacent layers and boundary conditions,the uncoupled state space solution of a layered poroelastic medium is obtained by using the transfer matrix method.Numerical results show that the anisotropy of permeability and the compressibility of pore fluid have remarkable influence on the consolidation behavior of poroelastic medium.
