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  • 1
    Electronic Resource
    Electronic Resource
    A relative backward perturbation theorem for the eigenvalue problem (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 625-626 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A-posteriori bound is given for the computed eigenpair ( $$\hat \lambda ,\hat x$$ ), of the eigenvalue problemAx=λx, which is shown to be more realistic than the available one. A simple expression is further presented for calculating the backward error.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396348
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  • 2
    Electronic Resource
    Electronic Resource
    SOME USES OF ECONOMIC ACCOUNTING IN PLANNING ECONOMIC DEVELOPMENT OF THE U.A.R. (1963)
    Oxford, UK : Blackwell Publishing Ltd
    Review of income and wealth 1963 (1963), S. 0 
    Details
    ISSN: 1475-4991
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1475-4991.1965.tb01031.x
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  • 3
    Electronic Resource
    Electronic Resource
    The interval Sylvester equation (1994)
    Springer
    Computing 52 (1994), S. 233-244 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine notwendige und hinreichende bedingung für die Existenz der Lösung der Intervall-Sylvester Gleichung angegeben. Dazu wird eine modifizierte Oettli Ungleichung abgeleitet, um die Lösung zu charakterisieren. Mehrere direkte Methoden für das Lösen der Gleichung werden vorgeschlagen und miteinander verglichen. Diese Methoden basieren auf verschiedenen Techniken wie Simulation, Lineare Programmierung, dem Zusammenhang zwischen einer Intervall-Sylvester Gleichung und einem Intervall-linearen System wie auch der Sensitivitätsanalyse. Weiters wird eine iterative Technik bereitgestellt, für die Konvergenz-Bedingungen verfügbar sind. Als Anwendung wird die Wurzel einer Intervall-Matrix berechnet.
    Notes: Abstract In this paper a necessary and sufficient condition for the existence of a solution for the interval Sylvester equation is given. A modified Oettli's inequality is derived to characterize the solution. Many direct methods for solving the equation are suggested and compared to each other. These methods are based on different techniques such as simulation, linear programming, correspondence between an interval Sylvester equation and an interval linear system as well as sensitivity analysis. An iterative technique for solving the interval Sylvester equation is provided with special conditions to guarantee the convergence. The square root of an interval matrix is calculated as an application to solving interval Sylvester equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02246505
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  • 4
    Electronic Resource
    Electronic Resource
    On the range of eigenvalues of an interval matrix (1992)
    Springer
    Computing 47 (1992), S. 373-377 
    Details
    ISSN: 1436-5057
    Keywords: 15A18 ; 65G10 ; Interval matrix ; eigenvalue ; enclosure ; tolerance analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir beschreiben eine Methode zur Einschliessung der Menge aller reellen Eigenwerte einer Intervallmatrix die zu Eigenvektoren von einer vorgeschriebenen Zeichenstruktur gehören.
    Notes: Abstract We describe a method for enclosing the set of real eigenvalues of an interval matrix pertaining to eigenvectors of a given sign pattern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02320205
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  • 5
    Electronic Resource
    Electronic Resource
    Inverse Problem of the Interval Linear System of Equations (1999)
    Springer
    Computing 63 (1999), S. 185-200 
    Details
    ISSN: 1436-5057
    Keywords: AMS Subject Classifications: ; Key words.Linear systems of equations, interval matrices, inequality constraints, constrained optimization.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract. Given a nonsingular central matrix $A_c$ , a central vector $b_c$ and a prescribed interval solution vector $x^I$ , it is required to find the maximum allowable deviation $\Delta A$ or $\Delta b$ so that the solution of the interval linear system $A^Ix = b^I$ is contained in $x^I$ . Special cases for $\Delta A$ and $\Delta b$ are considered and bounds on the entries of $A^I$ and $b^I$ are obtained either in a closed form, whenever possible, or via solving a specially designed constrained optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006070050058
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  • 6
    Electronic Resource
    Electronic Resource
    Nondiagonable systems under small perturbations (1982)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 33 (1982), S. 282-288 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Ein System heißt nicht-diagonalisierbar, wenn seine Zustandsmatrix nichtlineare Elementarteiler hat In dieser Arbeit werden geschlossene Formeln für die Änderungen der Eigenwerte und der Eigenvektoren eines nicht-diagonalisierbaren Systems angegeben, welche durch kleine Änderungen in den Systemelementen verursacht werden.
    Notes: Abstract By a nondiagonable system, we mean a system whose state matrix is nondiagonable, i.e. having nonlinear elementary divisors. In this paper, closed form formulae are given for the shifts occuring in the eigenvalues and eigenvectors of these types of systems due to small variations in the system elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944977
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  • 7
    Electronic Resource
    Electronic Resource
    The generalized inverse of a perturbed singular matrix (1983)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 34 (1983), S. 291-300 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß wennA singulär ist (A+εA 1)−1 auf eine Laurent-Serie inε erweitert werden kann. Die Koeffizienten der Erweiterung werden in expliziter Form gegeben. Der Fall wo ∥A+εA 1∥ sich identisch inε auflöst wird ebenfalls untersucht und eine verallgemeinerte Umkehrung vonA+εA 1 wird angegeben.
    Notes: Abstract It is shown that, whenA is singular, (A+εA 1)−1 can be expanded into a Laurent's series inε. The coefficients of the expansion are given in an explicit form. The case where ∥A+ɛA 1∥ vanishes identically inε is also studied and a generalized inverse ofA+ɛA 1 is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944850
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  • 8
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    Effect of flaxseed supplementation and exercise training on lipid profile, oxidative stress and inflammation in rats with myocardial ischemia (2012)
    BioMed Central
    Details
    Publication Date: 2012-10-06
    Description: Background: Flaxseed has recently gained attention in the area of cardiovascular disease primarily because of its rich contents of alpha-linolenic acid (ALA), lignans, and fiber. Although the benefits of exercise on any single risk factor are unquestionable, the effect of exercise on overall cardiovascular risk, when combined with other lifestyle modifications such as proper nutrition, can be dramatic.This study was carried out to evaluate the protective role of flaxseed and exercise on cardiac markers, lipids profile and inflammatory markers in isoproterenol (ISO)-induced myocardial ischemia in rats. Methods: The research was conducted on 40 male albino rats, divided into 4 groups (n=10): group I served as control, group II has acute myocardial ischemia induced by isoproterenol, groups III and IV have acute myocardial ischemia induced by isoproterenol pretreated with flaxseed supplementation orally for 6 weeks, additionally group IV practiced muscular exercise through swimming. Results: Alterations of lipid profile, cardiac and inflammatory markers (Il-1beta, PTX 3 and TNF- alpha) were observed in myocardial ischemia group. Flaxseed supplementation combined with exercise training showed significant increase of HDL and PON 1, on the other hand cardiac troponin, Il- 1beta and TNF- alpha levels significantly decreased as compared to myocardial ischemic group. Receiver Operating Characteristics (ROC) analysis of cTnI, PTX 3, Il-1beta and TNF- alpha revealed a satisfactory level of sensitivity and specificity. Conclusion: Regular exercise enhances the improvement in plasma lipoprotein levels and cardiovascular protection that results from flaxseed supplementation by mitigating the pathophysiology of atherosclerosis. Elevation of HDL, the antioxidant PON 1 and the cardioprotective marker PTX 3 emphasizes the protective effects of flaxseed and muscular exercise mutually against the harmful effects of acute myocardial ischemia.
    Electronic ISSN: 1476-511X
    Topics: Biology
    Published by BioMed Central
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  • 9
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    Singular values of an interval matrix (1991)
    Elsevier
    Details
    Publication Date: 1991-06-01
    Print ISSN: 0024-3795
    Electronic ISSN: 1873-1856
    Topics: Mathematics
    Published by Elsevier
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  • 10
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    On the invariance of the sign pattern of matrix eigenvectors under perturbation (1994)
    Elsevier
    Details
    Publication Date: 1994-01-01
    Print ISSN: 0024-3795
    Electronic ISSN: 1873-1856
    Topics: Mathematics
    Published by Elsevier
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