Applied sciences

Bulletin of the Polish Academy of Sciences: Technical Sciences

Content

Bulletin of the Polish Academy of Sciences: Technical Sciences | 2016 | 64 | No 4 (Special Section on Civil Engineering – Ongoing Technical Research. Part I) |

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Abstract

AbstractThe paper presents the problem of estimating in-situ compressive strength of concrete in a comprehensive way, taking into account the possibility of direct tests of cored specimens and indirect methods of non-destructive tests: rebound hammer tests and ultrasonic pulse velocity measurements. The paper approaches the discussed problem in an original, scientifically documented and exhaustive way, in particular in terms of application.
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Authors and Affiliations

L. Brunarski
M. Dohojda

Abstract

AbstractThe classical Cayley-Hamilton theorem is extended to Drazin inverse matrices and to standard inverse matrices. It is shown that knowing the characteristic polynomial of the singular matrix or nonsingular matrix, it is possible to write the analog Cayley-Hamilton equations for Drazin inverse matrix and for standard inverse matrices.
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Abstract

AbstractThis paper describes how to calculate the number of algebraic operations necessary to implement block matrix inversion that occurs, among others, in mathematical models of modern positioning systems of mass storage devices. The inversion method of block matrices is presented as well. The presented form of general formulas describing the calculation complexity of inverted form of block matrix were prepared for three different cases of division into internal blocks. The obtained results are compared with a standard Gaussian method and the “inv” method used in Matlab. The proposed method for matrix inversion is much more effective in comparison in standard Matlab matrix inversion “inv” function (almost two times faster) and is much less numerically complex than standard Gauss method.
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Authors and Affiliations

T. Trawiński
A. Kochan
P. Kielan
D. Kurzyk

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