Beginning with the method of whole path iterative ray-tracing and according to the positive definiteness of the coefficient matrix of the systems of linear equations, a symmetry olock tridiagonal matrix was decomposed...Beginning with the method of whole path iterative ray-tracing and according to the positive definiteness of the coefficient matrix of the systems of linear equations, a symmetry olock tridiagonal matrix was decomposed into the product of block bidiagonal triangular matrix and its transpose by means of Cholesky decomposition. Then an algorithm for solving systems of block bidiagonal triangular linear equations was given, which is not necessary to treat with the zero elements out of banded systems. A fast algorithm for solving the systems of symmetry block tridiagonal linear equations was deduced, which can quicken the speed of ray-tracing. Finally, the simulation based on this algorithm for ray-tracing in three dimensional media was carried out. Meanwhile, the segmentally-iterative ray-tracing method and banded method for solving the systems of block tridiagonal linear equations were compared in the same model mentioned above. The convergence condition was assumed that the L-2 norm summation for mk, 1 and mk. 2 in the whole ray path was limited in 10-6. And the calculating speeds of these methods were compared. The results show that the calculating speed of this algorithm is faster than that of conventional method and the calculated results are accurate enough. In addition, its precision can be controlled according to the requirement of ray-tracing.展开更多
Determination of dissolution rate of alumina is one of the classical problems in aluminum electrolysis. A novel method which can measure the dissolution rate of alumina was presented. Effect of factors on dissolution ...Determination of dissolution rate of alumina is one of the classical problems in aluminum electrolysis. A novel method which can measure the dissolution rate of alumina was presented. Effect of factors on dissolution rate of alumina was studied intuitively and roundly using transparent quartz electrobath and image analysis techniques. Images about dissolution process of alumina were taken at an interval of fixed time from transparent quartz electrobath of double rooms. Gabor wavelet transforms were used for extracting and describing the texture features of each image. After subsampling several times, the dissolution rate of alumina was computed using these texture features in local neighborhood of samples. Regression equation of the dissolution rate of alumina was obtained using these dissolution rates. Experiments show that the regression equation of the dissolution rate of alumina is y=-0.000 5x^3＋0.024 0x^2-0.287 3x＋ 1.276 7 for Na3AIF6-AIF3-Al2O3-CaF2-LiF- MgF2 system at 920 ℃.展开更多
A discriminant method for optimizing activity in nuclear medicine studies is validated by comparison with ROC （received operating characteristic）-curves. The method is tested in 21 single photon emission computerize...A discriminant method for optimizing activity in nuclear medicine studies is validated by comparison with ROC （received operating characteristic）-curves. The method is tested in 21 single photon emission computerized tomography （SPECT）, performed with a cardiac phantom. Three different lesions （Lb L2 and L3） were placed in the myocardium-wall by pairs fbr each SPECT. Three activities （84, 37 or 18.5 MBq） of 99mTc were used as background. Linear discriminant analysis was used to select the parameters that characterize image quality among the measured variables in the images [（Background-to-Lesion （B/Li） and Signal-to-Noise （S/N） ratios）]. Two clusters with different image quality （P=0.021 ） were obtained. The ratios B/Lj, B/L2 and B/L3 are the parameters used to construct the function with 100% of cases correctly classified into the clusters. The value of 37 MBq was the lowest tested activity for which good results for the B/Li ratios were obtained. The result coincides with the applied ROC-analysis （r=0.89）.展开更多
基金Project(40674071) supported by the National Natural Science Foundation of ChinaProject(KFAS2002-2003) supported by the Korea Foundation for Advanced Studies
文摘Beginning with the method of whole path iterative ray-tracing and according to the positive definiteness of the coefficient matrix of the systems of linear equations, a symmetry olock tridiagonal matrix was decomposed into the product of block bidiagonal triangular matrix and its transpose by means of Cholesky decomposition. Then an algorithm for solving systems of block bidiagonal triangular linear equations was given, which is not necessary to treat with the zero elements out of banded systems. A fast algorithm for solving the systems of symmetry block tridiagonal linear equations was deduced, which can quicken the speed of ray-tracing. Finally, the simulation based on this algorithm for ray-tracing in three dimensional media was carried out. Meanwhile, the segmentally-iterative ray-tracing method and banded method for solving the systems of block tridiagonal linear equations were compared in the same model mentioned above. The convergence condition was assumed that the L-2 norm summation for mk, 1 and mk. 2 in the whole ray path was limited in 10-6. And the calculating speeds of these methods were compared. The results show that the calculating speed of this algorithm is faster than that of conventional method and the calculated results are accurate enough. In addition, its precision can be controlled according to the requirement of ray-tracing.
基金Projects(51101104,51072121) supported by the National Natural Science Foundation of ChinaProject(LS2010109) supported by the Key Laboratory Foundation of Liaoning Province,China
文摘Determination of dissolution rate of alumina is one of the classical problems in aluminum electrolysis. A novel method which can measure the dissolution rate of alumina was presented. Effect of factors on dissolution rate of alumina was studied intuitively and roundly using transparent quartz electrobath and image analysis techniques. Images about dissolution process of alumina were taken at an interval of fixed time from transparent quartz electrobath of double rooms. Gabor wavelet transforms were used for extracting and describing the texture features of each image. After subsampling several times, the dissolution rate of alumina was computed using these texture features in local neighborhood of samples. Regression equation of the dissolution rate of alumina was obtained using these dissolution rates. Experiments show that the regression equation of the dissolution rate of alumina is y=-0.000 5x^3＋0.024 0x^2-0.287 3x＋ 1.276 7 for Na3AIF6-AIF3-Al2O3-CaF2-LiF- MgF2 system at 920 ℃.
基金Project supported by the Third World Academy of Sciences (TWAS), Cuba
文摘A discriminant method for optimizing activity in nuclear medicine studies is validated by comparison with ROC （received operating characteristic）-curves. The method is tested in 21 single photon emission computerized tomography （SPECT）, performed with a cardiac phantom. Three different lesions （Lb L2 and L3） were placed in the myocardium-wall by pairs fbr each SPECT. Three activities （84, 37 or 18.5 MBq） of 99mTc were used as background. Linear discriminant analysis was used to select the parameters that characterize image quality among the measured variables in the images [（Background-to-Lesion （B/Li） and Signal-to-Noise （S/N） ratios）]. Two clusters with different image quality （P=0.021 ） were obtained. The ratios B/Lj, B/L2 and B/L3 are the parameters used to construct the function with 100% of cases correctly classified into the clusters. The value of 37 MBq was the lowest tested activity for which good results for the B/Li ratios were obtained. The result coincides with the applied ROC-analysis （r=0.89）.
