Search results for "universal"
showing 10 items of 678 documents
How Universal Is the Relationship between Remotely Sensed Vegetation Indices and Crop Leaf Area Index? A Global Assessment
2016
This study aims to assess the relationship between Leaf Area Index (LAI) and remotely sensed Vegetation Indices (VIs) for major crops, based on a globally explicit dataset of in situ LAI measurements over a significant set of locations. We used a total of 1394 LAI measurements from 29 sites spanning 4 continents and covering 15 crop types with corresponding Landsat satellite images. Best-fit functions for the LAI-VI relationships were generated and assessed in terms of crop type, vegetation index, level of radiometric/atmospheric processing, method of LAI measurement, as well as the time difference between LAI measurements and satellite overpass. These global LAI-VI relationships were evalu…
Group graded algebras and almost polynomial growth
2011
Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FCp, the group algebra of a cyclic group of order p, where p is a prime number and p||G|; (2) UT2G(F), the algebra of 2×2 upper triangular matrices over F endowed with an elementary G-grading; (3) E, the infinite dimensional Grassmann algebra with trivial G-grading; (4) in case 2||G|, EZ2, the Grassmann algebra with canonical Z2-grading.
Varieties with at most cubic growth
2019
Abstract Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c n ( V ) , n = 1 , 2 , … , and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x ( y z ) ≡ 0 such that c n ( V ) C n α , with 1 ≤ α 3 , for some constant C. We prove that if 1 ≤ α 2 then c n ( V ) ≤ C 1 n , and if 2 ≤ α 3 , then c n ( V ) ≤ C 2 n 2 , for some constants C 1 , C 2 .
The enveloping algebra of the Lie superalgebra osp(1,2)
1990
International audience
Quasi-Projective Varieties
2000
We have developed the theory of affine and projective varieties separately. We now introduce the concept of a quasi-projective variety, a term that encompasses both cases. More than just a convenience, the notion of a quasi-projective variety will eventually allow us to think of an algebraic variety as an intrinsically defined geometric object, free from any particular embedding in affine or projective space.
The History of Algebra in Mathematics Education
2006
In this chapter, we analyse key issues in algebra history from which some lessons can be extracted for the future of the teaching and learning of algebra. A comparative analysis of two types of pre-Vietan languages (before 16th century), and of the corresponding methods to solve problems, leads to conjecture the presence of didactic obstacles of an epistemological origin in the transition from arithmetic to algebraic thinking. This illustrates the value of historic and critical analysis for basic research design in mathematics education. Analysing the interrelationship between different evolution stages of the sign system of symbolic algebra and vernacular language supports the inference th…
An Overview on Algebraic Structures
2016
This chapter recaps and formalizes concepts used in the previous sections of this book. Furthermore, this chapter reorganizes and describes in depth the topics mentioned at the end of Chap. 1, i.e. a formal characterization of the abstract algebraic structures and their hierarchy. This chapter is thus a revisited summary of concepts previously introduced and used and provides the mathematical basis for the following chapters.
On the group of the automorphisms of some algebraic systems
1968
Within a framework of general algebra we firstly formulate a proposition on the group of the automorphisms of some irreducible algebrae (id est algebrae without proper non trivial subalgebrae). This proposition includes as particular cases the uniqueness of the automorphisms of the rational field and the Burnside theorem on the commutant of an irreducible set of operators of a finite dimensional vector space over an algebraically closed field. Afterwards we apply the general proposition to modules with irreducible sets of semilinear operators and we obtain a theorem which generalises from several points of view the Burnside theorem. Finally we derive as an application a proposition which sp…
On P-compatible hybrid identities and hyperidentities
1994
P-compatible identities are built up from terms with a special structure. We investigate a variety defined by a set ofP-compatible hybrid identities and answer the question whether a variety defined by a set ofP-compatible hyperidentities can be solid.
Banach elements and spectrum in Banach quasi *-algebras
2006
A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).