The phase sensitive NOESY spectrum of oridonin was treated using Full Relaxation Matrix Analysis(FRMA) approach, and the cross relaxation rates of proton pairs were obtained by diagonalizing the NOE matrix of oridonin...The phase sensitive NOESY spectrum of oridonin was treated using Full Relaxation Matrix Analysis(FRMA) approach, and the cross relaxation rates of proton pairs were obtained by diagonalizing the NOE matrix of oridonin. The inter proton distances were calculated according to 1/r6 ij ∝σij. The three-dimensional structure of oridonin in solution was calculated by the combination of WUPH, WUPH-S method with molecular mechanics minimization on the basis of NMR experiment.展开更多
We present a symbolic-numeric hybrid method, based on sum-of-squares （SOS） relaxation and rational vec- tor recovery, to compute inequality invariants and ranking functions for proving total correctness and generati...We present a symbolic-numeric hybrid method, based on sum-of-squares （SOS） relaxation and rational vec- tor recovery, to compute inequality invariants and ranking functions for proving total correctness and generating pre- conditions for programs. The SOS relaxation method is used to compute approximate invariants and approximate rank- ing functions with floating point coefficients. Then Gauss- Newton refinement and rational vector recovery are applied to approximate polynomials to obtain candidate polynomials with rational coefficients, which exactly satisfy the conditions of invariants and ranking functions. In the end, several exam- ples are given to show the effectiveness of our method.展开更多
基金Supported by the National Natural Science Foundation of China
文摘The phase sensitive NOESY spectrum of oridonin was treated using Full Relaxation Matrix Analysis(FRMA) approach, and the cross relaxation rates of proton pairs were obtained by diagonalizing the NOE matrix of oridonin. The inter proton distances were calculated according to 1/r6 ij ∝σij. The three-dimensional structure of oridonin in solution was calculated by the combination of WUPH, WUPH-S method with molecular mechanics minimization on the basis of NMR experiment.
文摘We present a symbolic-numeric hybrid method, based on sum-of-squares （SOS） relaxation and rational vec- tor recovery, to compute inequality invariants and ranking functions for proving total correctness and generating pre- conditions for programs. The SOS relaxation method is used to compute approximate invariants and approximate rank- ing functions with floating point coefficients. Then Gauss- Newton refinement and rational vector recovery are applied to approximate polynomials to obtain candidate polynomials with rational coefficients, which exactly satisfy the conditions of invariants and ranking functions. In the end, several exam- ples are given to show the effectiveness of our method.
