zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A set of stability criteria for delayed cellular neural networks. (English) Zbl 0994.82066
Summary: This brief article presents a set of criteria on the global asymptotic stability of delayed cellular neural networks by constructing suitable Lyapunov functionals, introducing ingeniously real parameters $w_i>0, \alpha_{ij}^*,\beta_{ij}^*,\eta_{ij}^*, \zeta_{ij}^*,\alpha_{ij},\beta_{ij},\eta_{ij},\zeta_{ij}\in R$ with $\alpha_{ij}^*+\beta_{ij}^*=1, \alpha_{ij}+\beta_{ij}=1, \eta_{ij}^*+\zeta_{ij}^*=1,\eta_{ij}+\zeta_{ij}=1$ ($i,j=1,2,\dots,n$) and combining this with the elementary inequality $2ab\le a^2+b^2$. These criteria are of important theoretical and applicable significance in signal processing, especially in speed detection of moving objects, processing of moving images and the design of networks since they possess infinitely adjustable real parameters. This result is also discussed from the point of view of its relationship to earlier results.

82C32Neural nets (statistical mechanics)
78A55Technical applications of optics and electromagnetic theory
94A12Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI