417 research outputs found
The Lyapunov Matrix Equation Sa+a*s=s*b*bs
No full textThe matrix equation SA+A*S=S*B*BS is studied, under the assumption that (A, B*) is controllable, but allowing nonhermitian S. An inequality is given relating the dimensions of the eigenspaces of A and of the null space of S. In particular, if B has rank 1 and S is nonsingular, then S is hermitian, and the inertias of A and S are equal. Other inertial results are obtained, the role of the controllability of (A*, B*S*) is studied, and a class of D-stable matrices is determined. © 1979.28C4352D. Carlson and B.N. Datta, On the effective computation of the inertia of a nonhermitian matrix, submitted for publicationD. Carlson and B.N. Datta, Controllability, inertia and the root-location problem, submitted for publicationCarlson, Loewy, On ranges of Lyapunov transformations (1974) Linear Algebra and Appl., 8, pp. 237-248Carlson, Schneider, Inertia theorems for matrices: the semidefinite case (1963) J. Math. Anal. Appl., 6, pp. 430-446Chen, A generalization of the inertia theorem (1973) SIAM Journal on Applied Mathematics, 25, pp. 158-161Datta, Stability and D-stability (1978) Linear Algebra and Appl., 21, pp. 135-141Hautus, Controllability and observability conditions for linear autonomous systems (1969) Nederl. Akad. Wetensch. Proc. Ser. A, 72, pp. 443-448Hearon, Nonsingular solutions of TA−BT=C (1977) Linear Algebra and Appl., 16, pp. 57-65Kalman, Lyapunov functions for the problem of Lur'e in automatic control (1963) Proceedings of the National Academy of Sciences, 49, pp. 201-205MacDuffee, (1956) The Theory of Matrices, , Chelsea, New YorkOstrowski, Schneider, Some theorems on the inertia of general matrices (1962) J. Math. Anal. Appl., 4, pp. 72-84Taussky, A remark on a theorem of Lyapunov (1961) J. Math. Anal. Appl., 2, pp. 105-107Taussky, A generalization of a theorem of Lyapunov (1961) Journal of the Society for Industrial and Applied Mathematics, 9, pp. 640-643Wimmer, Inertia theorems for matrices, controllability, and linear vibrations (1974) Linear Algebra and Appl., 8, pp. 337-343Wimmer, An inertia theorem for tridiagonal matrices and a criterion of Wall on continued fractions (1974) Linear Algebra and Appl., 9, pp. 41-4
An elementary proof of the stability criterion of Liénard and Chipart
No full textAbstractAn alternative proof, via matrix equations, is given for the stability criterion of Liénard and Chipart. The proof is simple and elementary
Effects Of A Nearby Mn Delta Layer On The Optical Properties Of An Ingaas/gaas Quantum Well
Full text linkWe investigated the effects of nearby Mn ions on the confined states of a InGaAs/GaAs quantum well through circularly polarized and magneto-optical measurements. The addition of a Mn delta-doping layer at the barrier close to the well gives rise to surprisingly narrow absorption peaks in the photoluminescence excitation spectra. The peaks become increasingly stronger for decreasing spacer-layer thicknesses between the quantum well and the Mn layer. Most of the peaks were identified based on self-consistent calculations; however, we observed additional peaks that cannot be identified with quantum well transitions, which origin we attribute to an enhanced exciton-phonon coupling. Finally, we discuss possible effects related to the exciton magneto-polaron complex in the reinforcement of the photoluminescence excitation peaks.11620Žutić, I., Fabian, J., Sarma, S.D., (2004) Rev. Mod. Phys., 76, p. 323Dielt, T., Ohno, H., (2014) Rev. Mod. Phys., 86, p. 187Tanaka, M., Ohya, S., Hai, P.N., (2014) Appl. Phys. Rev., 1, p. 011102Krebs, O., Benjamin, E., Lemaître, A., (2009) Phys. Rev. B, 80, p. 165315Gazoto, A.L., Brasil, M.J.S.P., Iikawa, F., Brum, J.A., Ribeiro, E., Danilov, Y.A., Vikhrova, O.V., Zvonkov, B.N., (2011) Appl. Phys. Lett., 98, p. 251901Ohno, H., (1998) Science, 281, p. 951Nazmul, A.M., Amemiya, T., Shuto, Y., Sugahara, S., Tanaka, M., (2005) Phys. Rev. Lett., 95, p. 017201Korenev, V.L., Akimov, I.A., Zaitsev, S.V., Sapega, V.F., Langer, L., Yakovlev, D.R., Danilov, Y.A., Bayer, M., (2012) Nat. Commun., 3, p. 959Bobrov, A.I., Vikhrova, O.V., Danilov, Y.A., Dorokhin, M.V., Drozdov, Y.N., Drozdov, M.N., Zvonkov, B.N., Pavlova, E.D., (2014) Bull. Russ. Acad. Sci. Phys., 78 (1), pp. 6-8Wurstbauer, U., Soda, M., Jakiela, R., Schuh, D., Weiss, D., Zweck, J., Wegscheider, W., (2009) J. Cryst. Growth, 311 (7), p. 2160Poggio, M., Myers, R.C., Stern, N.P., Gossard, A.C., Awschalom, D.D., (2005) Phys. Rev. B, 72, p. 235313Balanta, M.A.G., Brasil, M.J.S.P., Iikawa, F., Mendes, U.C., Brum, J.A., Maialle, M.Z., Danilov, Y.A., Zvonkov, B.N., (2013) J. Phys. D: Appl. Phys., 46, p. 215103Lee, K.-S., Lee, C.-D., Kim, Y., Noh, S.K., (2003) Solid State Commun., 128, p. 177Hou, H.Q., Staguhn, W., Takeyama, S., Miura, N., Segawa, Y., Aoyagi, Y., Namba, S., (1991) Phys. Rev. B, 43, p. 4152Wu, J.-W., Nurmikko, A.V., Quinn, J.J., (1986) Phys. Rev. B, 34, p. 1080(1986) Solid State Commun., 57, p. 853Gonc¸alves Da Silva, C.E.T., (1985) Phys. Rev. B, 32, p. 6962Zhang, X.-C., Chang, S.-K., Nurmikko, A.V., Kolodziejski, L.A., Gunshor, R.L., Datta, S., (1985) Phys. Rev. B, 31, p. 4056Zhang, X.-C., Chang, S.-K., Nurmikko, A.V., Kolodziejski, L.A., Gunshor, R.L., Datta, S., (1985) Solid State Commun., 56, p. 255Zhang, X.-C., Chang, S.-K., Nurmikko, A.V., Kolodziejski, L.A., Gunshor, R.L., Datta, S., (1985) Appl. Phys. Lett., 47, p. 59Yakovlev, D.R., Ossau, W., (2010) Introduction to the Physics of Diluted Magnetic Semiconductors, p. 221. , edited by J. Kosut and J. A. Gaj Springer, Chap. 7Preisler, V., Grange, T., Ferreira, R., De Vaulchier, L.A., Guldner, Y., Teran, F.J., Potemski, M., Lemaitre, A., (2006) Phys. Rev. B, 73, p. 075320Verzelen, O., Bastard, G., Ferreira, R., (2000) Phys. Rev. B, 62, p. R4809Verzelen, O., Bastard, G., Ferreira, R., (2002) Phys. Rev. B, 66, p. 081308RDickmann, S., Tartakovskii, A.I., Timofeev, V.B., Zhilin, V.M., Zeman, J., Martinez, G., Hvam, J.M., (2000) Phys. Rev. B, 62, p. 2743Lucovsky, G., Chen, M.F., (1970) Solid State Commun., 8, pp. 1397-140
Shkolnayar Biblioteka glya Kazakhskikh Shkd (School Library for Kazakh Schools)
No full textHere is a well-worn book. Its well-creased cover paper is so thick that it feels like cloth. The front cover features a lovely illustration of Quartet under the title and the branch-bending bear over it. The pamphlet offers seven well-chosen Krylov fables: Spectacles; The Wood-Breaking Bear; The Elephant and the Pug; Quartet; The Sightseer in the Museum; The Wolf and the Cat; and The Fox (and his frozen tail and the wolf). This pamphlet has more than its share of stains, scribbles, and tears, and is thus a testimony to being well used for almost sixty years! There is a separate vocabulary for each fable at the end. It was fun for me to figure out which fables were being presented: The Sightseer in the Museum had no illustration and so was difficult. I had to match size of fable and quoted material within the fable. Enjoyable sleuthing! One last entry on the title-page is Kazaxskoe Godusdarstevennoe Uyeblo-Pedagogiyeskoe Izdatelbstvo.Language note: RussianI.A. Krylo
On eigenvalue and canonical form assignments
No full textAbstractWe first present a constructive matrix procedure to assign an arbitrary nonderogatory matrix by state feedback. Specifically, given a controllable pair (M,cT), the procedure finds a vector f and a transforming matrix L such that the closed loop matrix M − cTfT is similar to a preassigned arbitrary nonderogatory matrix such as the Jordan, companion, Schwarz, or triangular. The method is direct in the sense that it does not require knowledge of eigenvalues and eigenvectors of M, or solution of any matrix equation, or even computation of the characteristic polynomial. We then propose an algorithm to assign an arbitrary normalized Hessenberg matrix. Given a controllable pair (M,cT) and a normalized upper Hessenberg matrix B, the algorithm computes an upper triangular matrix L = (lij) with |lij| ⩽ 1 and a vector f such that L(M − cTf)L−1 = B. The algorithm seems to be computationally more effective than the former, and in particular can be used to assign most of the important canonical forms above and a given set of eigenvalues as well
An algorithm for computing powers of a Hessenberg matrix and its applications
No full textAbstractA simple algorithm for computing the first n powers of an n×n Hessenberg matrix with unit codiagonal or for evaluating a polynomial of degree ⩽n in such a matrix is proposed in this paper. Several applications of the algorithm are mentioned, including the solution of Lyapunov matrix equations associated with stability problems
PARALLEL AND LARGE SCALE MATRIX COMPUTATIONS IN CONTROL: SOME IDEAS****Permanent Address: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115
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