Further geometric restrictions on jordan structure in matrix factorization

It is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). It has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C. Furthermore, we show that this generalized geometric multiplicity restriction implies the already known geometric multiplicity restriction, show that the new more restrictive condition is not sufficient in general but is sufficient in a situation that we identify.Fundação para a Ciência e a Tecnologia (FCT), National Science Foundation Grant DMS-03-53510, US

Arbitrariness of Jordan structure in factorization : the geometric multiplicity restriction and the 3 X 3 case

For the problem of which Jordan forms are possible for n × n complex matrices A, B and C, when A = BC, geometric multiplicity restrictions are given for the eigenvalues of the three matrices. Together with the obvious determinantal condition on the eigenvalues, these necessary conditions are shown to be sufficient for the problem when n < 4, but not for n ≥ 4. Some basic observations about the problem are given in the process.National Science Foundation, USA and FCT, Portugal

Investigations into the Influence of Chronic Colitis on Colonic Adenocarcinoma Cell Growth A Progress Report

Graduate Basi

Small Unmanned Aircraft System Off Nominal Operations Reporting System Unmanned Aircraft System: Traffic Management Technical Capability Level 4 Implementation, Data Collection and Analysis

NASA performed research and development of technologies and requirements for traffic management of small Unmanned Aircraft Systems (UAS). In this effort, a small UAS off-nominal situation reporting system was developed to capture information from off-nominal situations to understand their nature and reduce occurrences. This Technical Memorandum (TM) describes the reporting system and analysis of 116 off-nominal situation reports from 352 small UAS operations, which were conducted at two flight test ranges in Summer 2019

Initial Approach to Collect Small Unmanned Aircraft System Off-Nominal Operational Situations Data

NASA is developing the Unmanned Aircraft System Traffic Management research platform to safely integrate small unmanned aircraft operations in large-scale at low-altitudes. As a part of this effort, small unmanned aircraft system off-nominal operational situations data collection process has been developed to take lessons learned and to reinforce operational compliance. In this paper, descriptions of variables used for digital data collection and an online report form for collection of observational data from the operators (contextual data) are provided. They are used to collect off-nominal data from the Unmanned Aircraft System Traffic Management National Campaign in 2017. The digital data show that 2 out of 118 campaign operations (1.7%) encountered loss of navigation. Since the campaign aircraft used Global Positioning System for navigation, it is likely that unobstructed view of the sky at the campaign locations contributed to this small number. Also, 4 out of 47 operations (8.5%) encountered loss of communications. A relatively short distance between ground control system and aircraft, ranging from 2300 feet to 4200 feet, likely contributed to this small number. There was no data to identify the loss of communications condition, aircraft received signal strength, for the remaining 71 operations suggesting that some operators may not be monitoring unmanned aircraft communications system performance or monitoring it with different parameters. For the contextual data, due to the low number of total reports during the campaign, no significant trends emerged. This is an initial attempt to collect contextual data from small unmanned aircraft operators about off-nominal situations, and changes will be made to the future data collection to improve the amount and quality of the information

Radiostereometric Analysis of Tantalum vs. Titanium Acetabular Shells in Young THR Patients

Introduction: In the active total hip replacement (THR) population, maintaining acetabular component stability and limiting polyethylene wear are crucial components to preventing premature implant failure. Titanium with Co/Cr/Mo fiber metal coating is among the most common materials used in cementless THR. Trabecular metal, composed of porous tantalum, has a metallic strut design resembling trabecular bone, designed to improve tissue infiltration and limit migration. This study assesses the stability and clinical outcomes of tantalum versus titanium acetabular shells using radiostereometric analysis (RSA) technology. Methods: In this IRB approved, prospective, randomized, blinded study, 46 patients received a primary THR by a single surgeon (DCA). Each patient was randomized to receive a titanium (23) (Trilogy, Zimmer) or tantalum (23) (Modular tantalum shell, Zimmer) uncemented hemispheric cup and either a highly-crosslinked or conventional polyethylene liner. Tantalum RSA markers were implanted around the liner periphery, femur, and periacetabular bone in each patient. RSA examinations, Harris Hip, UCLA, WOMAC, SF-36 scores were obtained at 10 days, 6 months, and annually with the furthest patients evaluated through 5 years. Results: Median translation was greater at all time points for the tantalum mesh cups except for the 3-year follow-up, however due to large standard errors, there was no significant difference between the two designs (p\u3e0.05). These large standard errors were predominantly caused by two outliers, neither of which had clinical evidence of loosening at 5 years follow-up. Mean UCLA, WOMAC, Harris Hip, and SF-36 PCS and MCS scores improved similarly in both groups. Conclusions: In this young THR population, both titanium and tantalum acetabular shells demonstrated excellent stability at five years follow up. Tantalum shells demonstrated slightly greater micromotion, but there was no statistically significant difference in shell migration. Outstanding clinical outcomes with statistically significant improvements in function and pain relief were observed in both groups

Radiostereometric Analysis of Femoral Head Penetration in Cross-Linked Polyethylene in THR Patients

Background: In the young total hip replacement (THR) population limiting polyethylene liner wear is crucial to preventing premature implant failure. Highly cross-linked ultra-high molecular weight polyethylene (HXLPE) liners were designed to improve wear resistance of polyethylene liners. Radiostereometric analysis (RSA) provides highly precise measurements of liner wear. This study utilized RSA to characterize wear of conventional versus HXLPE liners up to five years following THR. Methods: This IRB-approved, prospective, randomized, blinded study, involved 46 patients with a mean age of 58 and BMI of 30. Each patient was double randomized to receive a conventional or HXLPE liner with an uncemented titanium mesh or tantalum trabecular metal cup. Both liners were prepared from compression-molded GUR 1050 resin without calcium stearate, while HXLPE liners undergo further e-beam irradiation and annealing. At the time of surgery, 1mm tantalum RSA markers were implanted around the liner periphery, femur and periacetabular bone. RSA examinations, Harris Hip, UCLA, WOMAC, SF-36 scores were obtained pre-operatively, post-operatively, at six weeks, six months and annually through five years. Results: All patients had statistically significant improvement in Harris Hip, WOMAC and SF-36 PCS scores following THR with no difference between cohorts. On RSA examination, of titanium shells, HXLPE liners revealed significantly lower femoral head penetration at each follow up except six weeks and six months (p Conclusion: In this young THR population RSA shows significantly less femoral head penetration in the HXLPE liners compared to conventional liners. Novel RSA techniques have been developed to determine polyethylene wear in patients