This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the ...This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.展开更多
Finite element method is employed to calculate the temperature fields for two kinds of steel concrete composite slabs: composite slab with profiled steel sheeting and LJMB composite slab. The calculated results are in...Finite element method is employed to calculate the temperature fields for two kinds of steel concrete composite slabs: composite slab with profiled steel sheeting and LJMB composite slab. The calculated results are in good agreement with those of tests. Fire resistance of the two kinds of composite slabs is calculated by using a numeric method. The results show that: due to heat absorbing of concrete, the performance of composite slabs under fire is better than that of unprotected steel structure, and fire resistance of composite slabs mentioned in this paper is at least 30 min subjected to standard fire. Parameters related to the fire resistance are discussed. It was found that with increasing of concrete strength and thickness of slab, fire resistance increases, and with increasing of steel strength and steel ratio, fire resistance decreases. Also thickness of fire proof is calculated by a numeric method. The results obtained in this paper may be referenced for practical engineering.展开更多
In order to study the relationship between the main process parameters and the cell size, the mathematical model of cell growth of microcellular foaming injection process is built. Then numeric simulation is employed ...In order to study the relationship between the main process parameters and the cell size, the mathematical model of cell growth of microcellular foaming injection process is built. Then numeric simulation is employed as experimental method, and the Taguchi method is used to analyze significance of effect of process parameters on the cell size. At last the process parameters are focused on melt temperature, injection time, mold temperature and pretidied volume. The significance order from big to small of the effect of each process parameters on cell size is melt temperature, pre-filled volume, injection time, and mold temperature. On the basis of above research, the effect of each process parameter on cell size is further researched. Appropriate reduction of the melt temperature and increase of the pre-filled volume can optimize the cell size effectively, while the effects of injection time and mold temperature on cell size are less significant.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos.10901055,61021004,91118007by NKBRPC 2011CB302802,2011CB70690by the Fundamental Research Funds for the Central Universities under Grant No.78210043
文摘This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments.The authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs.At last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.
文摘Finite element method is employed to calculate the temperature fields for two kinds of steel concrete composite slabs: composite slab with profiled steel sheeting and LJMB composite slab. The calculated results are in good agreement with those of tests. Fire resistance of the two kinds of composite slabs is calculated by using a numeric method. The results show that: due to heat absorbing of concrete, the performance of composite slabs under fire is better than that of unprotected steel structure, and fire resistance of composite slabs mentioned in this paper is at least 30 min subjected to standard fire. Parameters related to the fire resistance are discussed. It was found that with increasing of concrete strength and thickness of slab, fire resistance increases, and with increasing of steel strength and steel ratio, fire resistance decreases. Also thickness of fire proof is calculated by a numeric method. The results obtained in this paper may be referenced for practical engineering.
文摘In order to study the relationship between the main process parameters and the cell size, the mathematical model of cell growth of microcellular foaming injection process is built. Then numeric simulation is employed as experimental method, and the Taguchi method is used to analyze significance of effect of process parameters on the cell size. At last the process parameters are focused on melt temperature, injection time, mold temperature and pretidied volume. The significance order from big to small of the effect of each process parameters on cell size is melt temperature, pre-filled volume, injection time, and mold temperature. On the basis of above research, the effect of each process parameter on cell size is further researched. Appropriate reduction of the melt temperature and increase of the pre-filled volume can optimize the cell size effectively, while the effects of injection time and mold temperature on cell size are less significant.
