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Search: All articles in the CMB digital archive with keyword stability

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1. CMB 2011 (vol 56 pp. 44)

Biswas, Indranil; Dey, Arijit
 Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections We show that there is a bijective correspondence between the polystable parabolic principal $G$-bundles and solutions of the Hermitian-Einstein equation. Keywords:ramified principal bundle, parabolic principal bundle, Hitchin-Kobayashi correspondence, polystabilityCategories:32L04, 53C07

2. CMB 2011 (vol 54 pp. 593)

Boersema, Jeffrey L.; Ruiz, Efren
 Stability of Real $C^*$-Algebras We will give a characterization of stable real $C^*$-algebras analogous to the one given for complex $C^*$-algebras by Hjelmborg and RÃ¸rdam. Using this result, we will prove that any real $C^*$-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real $C^*$-algebras satisfying the corona factorization property include AF-algebras and purely infinite $C^*$-algebras. We will also provide an example of a simple unstable $C^*$-algebra, the complexification of which is stable. Keywords:stability, real C*-algebrasCategory:46L05

3. CMB 2010 (vol 54 pp. 364)

Preda, Ciprian; Preda, Petre
 Lyapunov Theorems for the Asymptotic Behavior of Evolution Families on the Half-Line Two theorems regarding the asymptotic behavior of evolution families are established in terms of the solutions of a certain Lyapunov operator equation. Keywords:evolution families, exponential instability, Lyapunov equationCategories:34D05, 47D06

4. CMB 2009 (vol 53 pp. 218)

Biswas, Indranil
 Restriction of the Tangent Bundle of $G/P$ to a Hypersurface Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable. Keywords:tangent bundle, homogeneous space, semistability, hypersurfaceCategories:14F05, 14J60, 14M15

5. CMB 2006 (vol 49 pp. 358)

Khalil, Abdelouahed El; Manouni, Said El; Ouanan, Mohammed
 On the Principal Eigencurve of the $p$-Laplacian: Stability Phenomena We show that each point of the principal eigencurve of the nonlinear problem $$-\Delta_{p}u-\lambda m(x)|u|^{p-2}u=\mu|u|^{p-2}u \quad \text{in } \Omega,$$ is stable (continuous) with respect to the exponent $p$ varying in $(1,\infty)$; we also prove some convergence results of the principal eigenfunctions corresponding. Keywords:$p$-Laplacian with indefinite weight, principal eigencurve, principal eigenvalue, principal eigenfunction, stabilityCategories:35P30, 35P60, 35J70

6. CMB 2000 (vol 43 pp. 418)

Gong, Guihua; Jiang, Xinhui; Su, Hongbing
 Obstructions to $\mathcal{Z}$-Stability for Unital Simple $C^*$-Algebras Let $\cZ$ be the unital simple nuclear infinite dimensional $C^*$-algebra which has the same Elliott invariant as $\bbC$, introduced in \cite{JS}. A $C^*$-algebra is called $\cZ$-stable if $A \cong A \otimes \cZ$. In this note we give some necessary conditions for a unital simple $C^*$-algebra to be $\cZ$-stable. Keywords:simple $C^*$-algebra, $\mathcal{Z}$-stability, weak (un)perforation in $K_0$ group, property $\Gamma$, finitenessCategory:46L05

7. CMB 1998 (vol 41 pp. 49)

Harrison, K. J.; Ward, J. A.; Eaton, L-J.
 Stability of weighted darma filters We study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case. Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuityCategories:47A62, 47B37, 93D25, 42A85, 47N70