2,761 research outputs found
Perturbation analysis of a matrix differential equation
Two complex matrix pairs and are contragrediently
equivalent if there are nonsingular and such that
. M.I. Garc\'{\i}a-Planas and V.V. Sergeichuk
(1999) constructed a miniversal deformation of a canonical pair for
contragredient equivalence; that is, a simple normal form to which all matrix
pairs close to can be reduced by
contragredient equivalence transformations that smoothly depend on the entries
of and . Each perturbation of defines the first order induced perturbation
of the matrix , which is the first order
summand in the product . We find all
canonical matrix pairs , for which the first order induced perturbations
are nonzero for all nonzero perturbations in
the normal form of Garc\'{\i}a-Planas and Sergeichuk. This problem arises in
the theory of matrix differential equations , whose product of two
matrices: ; using the substitution , one can reduce by
similarity transformations and by contragredient equivalence
transformations
Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils
V. I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a simple
normal form for a family of complex n-by-n matrices that smoothly depend on
parameters with respect to similarity transformations that smoothly depend on
the same parameters. We construct analogous normal forms for a family of real
matrices and a family of matrix pencils that smoothly depend on parameters,
simplifying their normal forms by D. M. Galin [Uspehi Mat. Nauk 27 (1) (1972)
241-242] and by A. Edelman, E. Elmroth, B. Kagstrom [Siam J. Matrix Anal. Appl.
18 (3) (1997) 653-692].Comment: 20 page
Detection and discrimination between ochratoxin producer and non-producer strains of Penicillium nordicum on a ham-based medium using an electronic nose
The aim of this work was to evaluate the potential use of qualitative volatile
patterns produced by Penicillium nordicum to discriminate between ochratoxin A
(OTA) producers and non-producer strains on a ham-based medium. Experiments were
carried out on a 3% ham medium at two water activities (aw ; 0.995, 0.95)
inoculated with P. nordicum spores and incubated at 25°C for up to 14days.
Growing colonies were sampled after 1, 2, 3, 7 and 14days, placed in 30-ml
vials, sealed and the head space analysed using a hybrid sensor electronic nose
device. The effect of environmental conditions on growth and OTA production was
evaluated based on the qualitative response. However, after 7days, it was
possible to discriminate between strains grown at 0.995 aw, and after 14days,
the OTA producer and non-producer strain and the controls could be discriminated
at both aw levels. This study suggests that volatile patterns produced by P.
nordicum strains may differ and be used to predict the presence of toxigenic
contaminants in ham. This approach could be utilised in ham production as part
of a quality assurance system for preventing OTA contaminatio
Rigid systems of second-order linear differential equations
We say that a system of differential equations
d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex
matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by
substitutions x(t)=Sy(t), u(t)=Udy(t)/dt+Vy(t)+Pv(t) with nonsingular S and P
to each system obtained from it by a small enough perturbation of its matrices
A,B,C. We prove that there exists a rigid system if and only if
m<n(1+square_root{5})/2, and describe all rigid systems.Comment: 22 page
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