# Clark D.N.'s A similarity problem for Toeplitz operators PDF

By Clark D.N.

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Proofs with out phrases are in general photographs or diagrams that aid the reader see why a selected mathematical assertion might be precise, and the way one can start to pass approximately proving it. whereas in a few proofs with no phrases an equation or might seem to assist advisor that strategy, the emphasis is obviously on delivering visible clues to stimulate mathematical proposal.

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The sensitivity coefficient values for changes in specific yield also are determined for the study area (Fig. 9). The sensitivity coefficient values exhibit a symmetric configuration with respect EXPLANATION <250 B 9 3 50- 750 E D 2 50-350 ■ > 750 Figure 8. Distribution of total dissolved solids in study area (modified from Hathaway and others, 1975), SENSITIVITY ANALYSIS OF GROUNDWATER FLOW SYSTEMS Figure 9. *+5 Sensitivity coefficients for specific yield, S , varia­ y tions, 1972. to boundaries.

The errors in aquifer parameters are calculated by dividing the errors in water levels by the sensitivity coefficients. Two examples to show the usefulness of sensitivity analysis are given. 2 gal/day-ft2 (50 ft/day) is assumed throughout the aquifer. The errors in hydraulic conductivity showed that the area in central Scott County has larger hydraulic conductivities than the first estimate (Gutentag and Stullken, 1974). This also is supported by water-quality data (Hathaway and others, 1975). YUKLER if 8 (2) The interaction between the aquifer and Ladder Creek was assumed to be negligible in the design of the model.

The Oqallala Formation, consist­ ing chiefly of alluvial deposits, is the principal aquifer in the study area. Thin, dissected and isolated deposits of sand and gravel of Pleis­ tocene age occur along the larger streams of the study area. These deposits have been derived from the Ogallala Formation and lithologically are similar to the Ogallala, Because of this similarity it is difficult to distinguish the Pleistocene deposits from the Ogalla­ la. The aquifer considered in the study is the Oqallala Formation.