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Decomposition of the symptom observation matrix and grey forecasting in vibration condition monitoring of machines

Czesław Cempel (2008)

International Journal of Applied Mathematics and Computer Science

With the tools of modern metrology we can measure almost all variables in the phenomenon field of a working machine, and many of the measured quantities can be symptoms of machine conditions. On this basis, we can form a symptom observation matrix (SOM) intended for condition monitoring and wear trend (fault) identification. On the other hand, we know that contemporary complex machines may have many modes of failure, called faults. The paper presents a method of the extraction of the information...

Delay-dependent stability of high-order neutral systems

Yanbin Zhao, Guang-Da Hu (2021)

Kybernetika

In this note, we are concerned with delay-dependent stability of high-order delay systems of neutral type. A bound of unstable eigenvalues of the systems is derived by the spectral radius of a nonnegative matrix. The nonnegative matrix is related to the coefficient matrices. A stability criterion is presented which is a necessary and sufficient condition for the delay-dependent stability of the systems. Based on the criterion, a numerical algorithm is provided which avoids the computation of the...

Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem

Tin-Yau Tam, William C. Hill (2016)

Special Matrices

A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.

Diffeomorphisms of Rn with oscillatory jacobians.

Waldyr M. Oliva, Nelson M. Kuhl, Luiz T. Magalhâes (1993)

Publicacions Matemàtiques

The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of Rn with oscillatory jacobian at every point and such that NM(f(x) - f(y)) ≤ NM(x - y) for all elements x,y ∈ Rn, where NM(x) - 1 denotes the maximum number of sign changes in the components zi of z ∈ Rn, where all zi are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation...

D-optimal and highly D-efficient designs with non-negatively correlated observations

Krystyna Katulska, Łukasz Smaga (2016)

Kybernetika

In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient....

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