Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an...Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.展开更多
A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this p...A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.展开更多
An effective method for eddy current calculation has been developed for EAST’s new divertor by using ANSYS.A 3D model of a double null divertor for the EAST device was built to evaluate eddy currents and electromagne...An effective method for eddy current calculation has been developed for EAST’s new divertor by using ANSYS.A 3D model of a double null divertor for the EAST device was built to evaluate eddy currents and electromagnetic(EM)forces on these components.The main input to the model is the plasma current and poloidal field coil currents,which are loaded into the model using experimental data measured from the EAST discharges.These currents generate magnetic fields that match those producing an EAST discharge,and the time variation of these fields produces the eddy currents in the divertors,along with from the resulting EM forces.In addition,the first 10 time steps were discussed for the eddy current generation and changing trend.It indicates that a static analysis before a transient mode start can solve the eddy current origination in the initial time steps.With this method,the EM transient response of EAST’s new divertor can be predicted based on ANSYS simulations.Furthermore,the method is also an effective approach to estimate the EM results for the in-vessel components of a fusion reactor during a disruption.展开更多
This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.展开更多
基金Supported by the National Natural Science Foundation of China(No.61772031)the Special Energy Saving Foundation of Changsha,Hunan Province in 2017
文摘Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.
文摘A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.
基金supported by the National Basic Research Program of China("973"Program)(Grant No.2013GB10200)
文摘An effective method for eddy current calculation has been developed for EAST’s new divertor by using ANSYS.A 3D model of a double null divertor for the EAST device was built to evaluate eddy currents and electromagnetic(EM)forces on these components.The main input to the model is the plasma current and poloidal field coil currents,which are loaded into the model using experimental data measured from the EAST discharges.These currents generate magnetic fields that match those producing an EAST discharge,and the time variation of these fields produces the eddy currents in the divertors,along with from the resulting EM forces.In addition,the first 10 time steps were discussed for the eddy current generation and changing trend.It indicates that a static analysis before a transient mode start can solve the eddy current origination in the initial time steps.With this method,the EM transient response of EAST’s new divertor can be predicted based on ANSYS simulations.Furthermore,the method is also an effective approach to estimate the EM results for the in-vessel components of a fusion reactor during a disruption.
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.
