Ⅰ. BUILDING OF THE MODEL The economic equilibrium equation of the expanded reproduction may be written as X_t=A_tX_t+I_t+H_t, (1)where X_t is the gross social product, which is an n-dimensional vector, A_t is an inpu...Ⅰ. BUILDING OF THE MODEL The economic equilibrium equation of the expanded reproduction may be written as X_t=A_tX_t+I_t+H_t, (1)where X_t is the gross social product, which is an n-dimensional vector, A_t is an input-coefficient matrix of (n×n)-dimensions, I_t is an n-dimensional investment vector展开更多
Ⅰ. INTRODUCTION Recently, mathematicians have been very much interested in differential equations with infinite delays. A lot of papers have appeared, among which J. K. Hale and J. Kato’s and F. Kappel and W. Schapp...Ⅰ. INTRODUCTION Recently, mathematicians have been very much interested in differential equations with infinite delays. A lot of papers have appeared, among which J. K. Hale and J. Kato’s and F. Kappel and W. Schappacher’s are the representatives. Most展开更多
A fluoro-alkyl-bonded phase as HPLC packing has been prepared from silica (5μ) with 1, 2,-tetra-hydro 7-trifluoro methyl-fluoro-octyltrichlorosilane, (CF3)2CF(CF2CF2)2CH2CH2SiCl3.
In the last ten years, a series of new organosilicon compounds known as 'silatranes' with highly specific biological actvity have received much attention from scientists. In 1966, Voronkov announced that these...In the last ten years, a series of new organosilicon compounds known as 'silatranes' with highly specific biological actvity have received much attention from scientists. In 1966, Voronkov announced that these compounds possess transannular structure between penta-coordinated silicon and tetracoordinated nitrogen, such展开更多
In the present paper, we have obtained several random fixed-point theorems for random set-valued mapping which generalize S. Itoh’s results. The method used in this paper differs from those used by other authors. Our...In the present paper, we have obtained several random fixed-point theorems for random set-valued mapping which generalize S. Itoh’s results. The method used in this paper differs from those used by other authors. Our main result consists of Theorems 1, 2, 3. Theorem 1 improves Theorem 1 of Itoh. The measurability of展开更多
Suppose that the control delay system with external disturbance w (k)is where x(0), u(-1), u(-2),…, u(-M<sub>q</sub>) are given, and 0=M<sub>0</sub>【M, 【…【M<sub>q</sub&g...Suppose that the control delay system with external disturbance w (k)is where x(0), u(-1), u(-2),…, u(-M<sub>q</sub>) are given, and 0=M<sub>0</sub>【M, 【…【M<sub>q</sub>, x∈R<sup>n</sup>,u∈R<sup>r</sup>,w∈R<sup>m</sup>.展开更多
Let f (x) ∈ C [-1, 1], p<sub>n</sub><sup>*</sup> (x) be the best approximation polynomial of degree n tof (x). G. Iorentz conjectured that if for all n, p<sub>2n</sub><sup...Let f (x) ∈ C [-1, 1], p<sub>n</sub><sup>*</sup> (x) be the best approximation polynomial of degree n tof (x). G. Iorentz conjectured that if for all n, p<sub>2n</sub><sup>*</sup> (x) = p<sub>2n+1</sub><sup>*</sup> (x), then f is even; and ifp<sub>2n+1</sub><sup>*</sup> (x) = p<sub>2n+2</sub><sup>*</sup> (x), p<sub>o</sub><sup>*</sup> (z) = 0, then f is odd. In this paper, it is proved that, under the L<sub>1</sub>-norm, the Lorentz conjecture is validconditionally, i. e. if (i) (1-x<sup>2</sup>) f (x) can be extended to an absolutely convergentTehebyshev sories; (ii) for every n, f (x) - p<sub>2n+1</sub><sup>*</sup> (x) has exactly 2n + 2 zeros (or, in thearcond situation, f (x) - p<sub>2n+2</sub><sup>*</sup> (x) has exaetly 2n+3 zeros), then Lorentz conjecture isvalid.展开更多
In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in t...In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in the construction of Q processes which satisfy the backward equations, the nonconservative case may be reduced to展开更多
文摘Ⅰ. BUILDING OF THE MODEL The economic equilibrium equation of the expanded reproduction may be written as X_t=A_tX_t+I_t+H_t, (1)where X_t is the gross social product, which is an n-dimensional vector, A_t is an input-coefficient matrix of (n×n)-dimensions, I_t is an n-dimensional investment vector
文摘Ⅰ. INTRODUCTION Recently, mathematicians have been very much interested in differential equations with infinite delays. A lot of papers have appeared, among which J. K. Hale and J. Kato’s and F. Kappel and W. Schappacher’s are the representatives. Most
文摘A fluoro-alkyl-bonded phase as HPLC packing has been prepared from silica (5μ) with 1, 2,-tetra-hydro 7-trifluoro methyl-fluoro-octyltrichlorosilane, (CF3)2CF(CF2CF2)2CH2CH2SiCl3.
文摘In the last ten years, a series of new organosilicon compounds known as 'silatranes' with highly specific biological actvity have received much attention from scientists. In 1966, Voronkov announced that these compounds possess transannular structure between penta-coordinated silicon and tetracoordinated nitrogen, such
文摘In the present paper, we have obtained several random fixed-point theorems for random set-valued mapping which generalize S. Itoh’s results. The method used in this paper differs from those used by other authors. Our main result consists of Theorems 1, 2, 3. Theorem 1 improves Theorem 1 of Itoh. The measurability of
基金Project supported by the National Natural Science Foundation of China
文摘Suppose that the control delay system with external disturbance w (k)is where x(0), u(-1), u(-2),…, u(-M<sub>q</sub>) are given, and 0=M<sub>0</sub>【M, 【…【M<sub>q</sub>, x∈R<sup>n</sup>,u∈R<sup>r</sup>,w∈R<sup>m</sup>.
文摘Let f (x) ∈ C [-1, 1], p<sub>n</sub><sup>*</sup> (x) be the best approximation polynomial of degree n tof (x). G. Iorentz conjectured that if for all n, p<sub>2n</sub><sup>*</sup> (x) = p<sub>2n+1</sub><sup>*</sup> (x), then f is even; and ifp<sub>2n+1</sub><sup>*</sup> (x) = p<sub>2n+2</sub><sup>*</sup> (x), p<sub>o</sub><sup>*</sup> (z) = 0, then f is odd. In this paper, it is proved that, under the L<sub>1</sub>-norm, the Lorentz conjecture is validconditionally, i. e. if (i) (1-x<sup>2</sup>) f (x) can be extended to an absolutely convergentTehebyshev sories; (ii) for every n, f (x) - p<sub>2n+1</sub><sup>*</sup> (x) has exactly 2n + 2 zeros (or, in thearcond situation, f (x) - p<sub>2n+2</sub><sup>*</sup> (x) has exaetly 2n+3 zeros), then Lorentz conjecture isvalid.
文摘In Refs. [2], [4]—[6] on the construction of Q processes it is assumed that matrix Q is conservative. The nonconservative case was dealt with only in a few papers, such as Refs. [3], [7], (8)If we are interested in the construction of Q processes which satisfy the backward equations, the nonconservative case may be reduced to