It is easy to see that (Upsilon^{S}(mathcal{A})) captures exactly all singular values of (mathcal{A}) from Figure 2. Figure 2 The singular value inclusion set (pmb{Upsilon ^{S}(mathcal{A})}) and the exact singular values.
When there are no control constraints, abnormal extremals project exactly onto singular trajectories.
Equation (3.4) happens with a continuous transition at ( u, λ ) = ( 0, T c ), namely there is an attractor bifurcation, and it bifurcates exactly into two singular points v i ( i = 1, 2 ), which attract two open subsets of U separately.
Theorem 4.5 If − δ < μ < η 2 ( μ ≠ 0 ), we have the following conclusions for (3.4): (1) Equation (3.4) happens with a continuous transition at ( u, λ ) = ( 0, T c ), namely there is an attractor bifurcation, and it bifurcates exactly into two singular points v i ( i = 1, 2 ), which attract two open subsets of U separately.
It just has a singular focus on building products exactly the way users need them in order to be the most productive, and frankly, to have the most fun.
Inserting the Laurent series w z)=sum_{lambda=-q}^{infty}beta_{lambda}z^{lambda},quad beta _{-q}neq0, q>0, (17) into equation (16), we can determine exactly p different Laurent singular parts: sum_{lambda=-q}^{-1}beta_{lambda}z^{lambda}, then equation (16) is said to satisfy the weak (langle p,q rangle) condition.
The diversity and street life that draw residents and tourists to thriving urban neighborhoods is exactly what gets erased by singular centers of activity.
His most common experience, he recalls, went something like this: Some eager producer would discover his work and decide that Leyner's strange and singular vision was exactly what a project needed.
The Riemannian geometry of (Sym_^{d}) can be exploited when the extracted feature descriptors are covariance matrices, e.g., region covariance [15], since the SPD cone is exactly the set of non-singular covariance matrices [16].
How to pay for the NHS The Albanian mess Single market, singular irony ReprintsBut what exactly should the Americans do?
