No abstract

Summary. The iterative method for solving system of linear equations, due to Kaczmarz [2], is investigated. It is shown that the method works well for both singulax and non-singular systems and it determines the affine space formed by the solutions if they exist. The method also provides an iterative procedure for computing a generalized inverse of a matrix.

No abstract

Immediate diagnosis of human specimen is an essential prerequisites in medical routines. This study aimed to establish a novel cancer diagnostics system based on probe electrospray ionization-mass spectrometry (PESI-MS) combined with statistical data processing. PESI-MS uses a very fine acupuncture needle as a probe for sampling as well as for ionization. To demonstrate the applicability of PESI-MS for cancer diagnosis, we analyzed nine cases of clear cell renal cell carcinoma (ccRCC) by PESI-MS and processed the data by principal components analysis (PCA). Our system successfully delineated the differences in lipid composition between non-cancerous and cancerous regions. In this case, triacylglycerol (TAG) was reproducibly detected in the cancerous tissue of nine different individuals, the result being consistent with well-known profiles of ccRCC. Moreover, this system enabled us to detect the boundaries of cancerous regions based on the expression of TAG. These results strongly suggest that PESI-MS will be applicable to cancer diagnosis, especially when the number of data is augmented.