Convergence Properties of Certain Minres Algorithms.
Levin (1988) has challenged the convergence properties of the Harman and Jones (1966) method of Minres factor analysis. Levin claimed that convergence of the Harman and Jones method is not guaranteed and that a modified version of this method, with proven convergence, is to be preferred. In the present article it is shown that both claims are invalid. Monotone convergence of the Harman and Jones method is guaranteed whereas the modified version, proposed by Levin, may converge to an incorrect solution. Levin has also claimed that the rank-one version of the Harman and Jones method, as implemented in a method by Zegers and ten Berge (1983) lacks a valid convergence proof, and that a method suggested by Comrey and Ahumada (1964, 1965) should be used instead. It is shown that these claims, too, should be reversed.
A Fast and Simple computational Method of Minimum Residual Factor Analysis.
Some new procedures for minimum residual factor analysis are presented. First a successive method developed by Comrey is modified in order to guarantee convergence and to provide a way to handle Heywood cases. Next, this modified Comrey procedure is extended to a simultaneous procedure which is computationally simpler and faster than the Minres method developed by Harman and Jones. This latter method, however, satisfies a stronger necessary condition for the minimum of the sum of squared off-diagonal residuals. Some empirical results are presented. These are in accordance with the theoretical considerations; that is, the Harman and Jones procedure tends to be slower, but attains in general a lower value for the sum of squared off-diagonal residuals.
A device for uranium series leaching from glass fiber in HEPA filter
For the disposal of a high efficiency particulate air (HEPA) glass filter into the environment, the glass fiber should be leached to lower its radioactive concentration to the clearance level. To derive an optimum method for the removal of uranium series from a HEPA glass fiber, five methods were applied in this study. That is, chemical leaching by a 4.0 M HNO3–0.1 M Ce(IV) solution, chemical leaching by a 5 wt% NaOH solution, chemical leaching by a 0.5 M H2O2–1.0 M Na2CO3 solution, chemical consecutive chemical leaching by a 4.0 M HNO3 solution, and repeated chemical leaching by a 4.0 M HNO3 solution were used to remove the uranium series. The residual radioactivity concentrations of 238U, 235U, 226Ra, and 234Th in glass after leaching for 5 h by the 4.0 M HNO3–0.1 M Ce(IV) solution were 2.1, 0.3, 1.1, and 1.2 Bq/g. The residual radioactivity concentrations of 238U, 235U, 226Ra, and 234Th in glass after leaching for 36 h by 4.0 M HNO3–0.1 M Ce(IV) solution were 76.9, 3.4, 63.7, and 71.9 Bq/g. The residual radioactivity concentrations of 238U, 235U, 226Ra, and 234Th in glass after leaching for 8 h by a 0.5 M H2O2–1.0 M Na2CO3 solution were 8.9, 0.0, 1.91, and 6.4 Bq/g. The residual radioactivity concentrations of 238U, 235U, 226Ra, and 234Th in glass after consecutive leaching for 8 h by the 4.0 M HNO3 solution were 2.08, 0.12, 1.55, and 2.0 Bq/g. The residual radioactivity concentrations of 238U, 235U, 226Ra, and 234Th in glass after three repetitions of leaching for 3 h by the 4.0 M HNO3 solution were 0.02, 0.02, 0.29, and 0.26 Bq/g. Meanwhile, the removal efficiencies of 238U, 235U, 226Ra, and 234Th from the waste solution after its precipitation–filtration treatment with NaOH and alum for reuse of the 4.0 M HNO3 waste solution were 100, 100, 93.3, and 100%.