Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplifie

Extremal classical interpolation problems (matrix case)

AbstractIn this paper, we try to find amongst the solutions w(z) of the corresponding interpolation problem the solution which satisfies an additional extremal condition. We show that degenerate interpolation problems play an important role in the theory of extremal interpolation problems. At the end of the paper we accomplish a comparison of our approach with former known approaches

Technical Work Plan for: Additional Multoscale Thermohydrologic Modeling

The primary objective of Revision 04 of the MSTHM report is to provide TSPA with revised repository-wide MSTHM analyses that incorporate updated percolation flux distributions, revised hydrologic properties, updated IEDs, and information pertaining to the emplacement of transport, aging, and disposal (TAD) canisters. The updated design information is primarily related to the incorporation of TAD canisters, but also includes updates related to superseded IEDs describing emplacement drift cross-sectional geometry and layout. The intended use of the results of Revision 04 of the MSTHM report, as described in this TWP, is to predict the evolution of TH conditions (temperature, relative humidity, liquid-phase saturation, and liquid-phase flux) at specified locations within emplacement drifts and in the adjoining near-field host rock along all emplacement drifts throughout the repository. This information directly supports the TSPA for the nominal and seismic scenarios. The revised repository-wide analyses are required to incorporate updated parameters and design information and to extend those analyses out to 1,000,000 years. Note that the previous MSTHM analyses reported in Revision 03 of Multiscale Thermohydrologic Model (BSC 2005 [DIRS 173944]) only extend out to 20,000 years. The updated parameters are the percolation flux distributions, including incorporation of post-10,000-year distributions, and updated calibrated hydrologic property values for the host-rock units. The applied calibrated hydrologic properties will be an updated version of those available in Calibrated Properties Model (BSC 2004 [DIRS 169857]). These updated properties will be documented in an Appendix of Revision 03 of UZ Flow Models and Submodels (BSC 2004 [DIRS 169861]). The updated calibrated properties are applied because they represent the latest available information. The reasonableness of applying the updated calibrated' properties to the prediction of near-fieldin-drift TH conditions will be evaluated and justified. Some of this evaluation will be conducted in conjunction with the post-model development validation activity involving comparisons of predicted TH conditions with measured TH conditions in the DST. The expected result is that, consistent with what was found in Revision 03 of Multiscale Thermohydrologic Model (BSC 2005 [DIRS 173944], Section 6.3.9), near-field/in-drift TH behavior is insensitive to a wide range of host-rock hydrologic property values. It is the intention of the work described in this TWP to propagate the new infiltration fluxes from the replacement infiltration model, by using the percolation fluxes from the revised site-scale unsaturated zone (UZ) flow model that has applied those new infiltration fluxes. The percolation flux distributions will be obtained from the updated site-scale UZ flow model, which has applied updated infiltration flux maps. Another objective of the work scope is to develop, implement, and validate a revised TH submodel-construction approach. This revised approach utilizes interpolation among a set of generic LDTH submodels that are run for a range of percolation flux histories that cover a sufficiently broad range of infiltration flux uncertainty, as well as for four host-rock units (two lithophysal units and two nonlithophysal units), and for three thermal property sets (low, mean, and high). A key motivation for this revised LDTH submodel-construction approach is to enable the MSTHM to be more flexible in addressing a broad range of infiltration flux cases. This approach allows the generic LDTH submodel simulations to be conducted prior to receiving percolation flux maps