Nonsquare Spectral Factorization for Nonlinear Control Systems

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton–Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.

The Relationship of Left Ventricular Trabeculation to Ventricular Function and Structure Over a 9.5-Year Follow-Up The MESA Study

Left ventricular (LV) trabeculation is highly variable among individuals and is increased in some diseases (e.g., congenital heart disease or cardiomyopathies), but its significance in population-representative individuals is unknown

Effects of Supplementation Strategy and Dormant Season Grazing on Cattle Use of Mixed-Grass Prairie Habitats

Dormant season grazing reduces reliance on harvested feeds, but typically requires protein supplementation to be successful. However, information relating supplementation strategies to individual resource utilization on dormant forage is lacking.  Thus, the intent of this research is to examine cattle resource utilization, residual cover of vegetation and utilization on rangelands grazed during the dormant season under two supplementation strategies. Thirty transects were randomly located within each pasture for measuring vegetation composition, production, canopy cover and visual obstruction readings (VOR) pre and post grazing.  Grazing locations were monitored for seven individuals within each treatment with Lotek GPS collars containing head position sensors that record daily space use. Resource utilization effect size was variable by treatment and time period. Vegetation response to treatment was similar for both cake and protein treatments across time periods (44.2 ± 4.8% vs 41.7 ± 4.5%, 36.7 ± 4.8% vs 30.7 ± 4.3%, 10.4 ± 3.1% vs 16.5 ± 3.5%). VOR was affected by supplementation treatment during time period 1, such that protein treatment significantly decreased VOR in comparison to the Cake treatment (36.6 ± 5.6% vs 15.7 ± 3.6%). Herbaceous and ground cover effects were similar across both supplementation treatments during time periods 1 and 3, while time period 2, cake supplementation had greater percent decrease of litter cover than the protein treatment (28.2 ± 4.4% vs 10.4 ± 2.9%). This research addresses comprehensive agro-ecosystem responses of dormant season grazing while providing multidimensional insight to stakeholders concerning grazing behavior and the ecological impacts on Montana rangelands