Original title:
Banachovy algebry
Translated title:
Banach Algebras
Authors:
Machovičová, Tatiana ; Nechvátal, Luděk (referee) ; Franců, Jan (advisor) Document type: Master’s theses
Year:
2021
Language:
slo Publisher:
Vysoké učení technické v Brně. Fakulta strojního inženýrství Abstract:
[slo][eng]
Banachovou algebrou nazývame Banachov priestor obohatený o operáciu násobenia. Jedná sa o matematickú štruktúru, ktorá sa uplatňuje pri neperiodickej homogenizácii kompozitných materiálov. Teória klasickej homogenizácie študuje materiály za predpokladu periodicity štruktúry. Pri skutočných materiáloch však samotný predpoklad periodicity nestačí a je nahradený tzv. abstraktnou hypotézou, ktorá sa opiera o koncept zložený hlavne zo spektra Banachovej algebry a Sigma konvergencie. Táto teória bola predstavená v roku 2004.
By Banach algebra we mean Banach space enriched with a multiplication operation. It is a mathematical structure that is used in the non-periodic homogenization of composite materials. The theory of classical homogenization studies materials assuming the periodicity of the structure. For real materials, the assumption of a periodicity is not enough and is replaced by the so-called an abstract hypothesis based on a concept composed mainly of the spectrum of Banach algebra and Sigma convergence. This theory was introduced in 2004.
Keywords:
Banach algebra; homogenization; homogenization algebra; homogenization structure; Sigma convergence; two-scale convergence
Institution: Brno University of Technology
(web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library. Original record: http://hdl.handle.net/11012/200080