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One of the motivations for analyzing stable vector bundles is their nice behavior in families. In fact, Moduli spaces of stable vector bundles can be constructed using the Quot scheme in many cases, whereas the stack of vector bundles is an Artin stack whose underlying set is a single point.
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [1] [2]In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is
In the former case, the orbit is called stable; in the latter case, it is called asymptotically stable and the given orbit is said to be attracting. An equilibrium solution f e {\displaystyle f_{e}} to an autonomous system of first order ordinary differential equations is called:
ρ r and ρ w are the densities of rock and (sea)water (kg/m 3) D n50 is the nominal median diameter of armor blocks = (W 50 /ρ r) 1/3 (m) K D is a dimensionless stability coefficient, deduced from laboratory experiments for different kinds of armor blocks and for very small damage (a few blocks removed from the armor layer) (-):
Stable polynomials arise in control theory and in mathematical theory of differential and difference equations. A linear, time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output. A linear system is BIBO stable if its characteristic polynomial is stable.
Drinking coffee could extend your life up to two years, new research finds. Regular coffee consumption was found to be associated with increased health span (time spent living free from serious ...
Alabama A&M linebacker Medrick Burnett Jr. has died, approximately five weeks after suffering an injury in a head-to-head collision during the Bulldogs' game against Alabama State on Oct. 29. He ...
The stability radius of a continuous function f (in a functional space F) with respect to an open stability domain D is the distance between f and the set of unstable functions (with respect to D). We say that a function is stable with respect to D if its spectrum is in D. Here, the notion of spectrum is defined on a case-by-case basis, as ...