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Register a new userOn some of properties of Lie groups and Fuzzy Lie groups
دراسة بعض خصائص زمر لي و زمر لي الضبابي
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هدفنا في هذا البحث دراسة بعض خصائص زمر لي و زمر لي الضبابية في حالات متفرقة، حيث قمنا بتحديد بعض الخصائص لزمر لي التي استطعنا التوصّل إليها و البرهان عمليا من خلال الفضاءات التبولوجية المبنية على زمر لي و التي تتصف بصفات محددة كالفضاءات صفرية-البعد و الفضاءات المترابطة. ثمّ تطرقنا لزمرة لي الضبابية و استطعنا البرهان على بعض النتائج التي تمّ التوصّل إليها في هذا المجال.
Our aim of this paper is to study some properties of Lie groups and fuzzy Lie groups in many statements. So we can determine some properties of Lie groups and we prove on its by the Topological spaces constructing on the Lie groups as the Zero- dimensional space and connected space. In fuzzy Lie groups, we can also get some results and we prove on its in this paper.
References used
ANTONY, P. L 2012 Solvable and Nilpotent Fuzzy Lie ~ Ideal Over Fuzzy Field, St. Thomas College, India, Vol. 6, No. 17, PP. 843-855
ALGHOUSSEIN, A and YACOUB, S2010On Lie groups and p- tow norm algebras, Tishreen University journal, vol. 32, No. 3, PP. 124-131
BAKER,A 2002-Matrix group: An introduction to Lie group theory. Springer – verlag, London, 330P
DI CONCILIO, A 2007 Group action on zero- dimensional spaces, University of Salerno, PP. 2051-2055
DI KRANJAN, D 2011-Introduction to Topological Groups. Udine, 104P
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The aim of this paper is to use some properties of Lie groups and
fuzzy Lie groups in many statements to prove on some open
problems, so we can prove on the lemma(1) and (2).
A Lie algebra g over a field F is a vector space together with a bilinear
map [ , ] satisfying [x ,x ] = 0 in addition to Jacobi identity . A Lie subalgebra
B of a Lie algebra g is said to be a Cartan subalgebra if it is a nilpotent and
equals its
normalizer, and it is proved that semi simple Lie algebra g
decomposes into weight spaces for B.
In this scientific paper we present the conception of distinguished
element 0 h in finite dimensional semi simple Lie algebra over a field F has
characteristic 0 and we will prove that the previous decomposition g into
weight spaces for B is the same to decomposition g as a direct sum of h0 ad eigen
spaces. This leads us to construct algorithm to test simple Lie algebras.
We programmed the previous algorithm to test simple linear Lie algebras
over a numeral field by Mathematica 5.0 program where applied this algorithm
on semi simple linear Lie algebra SL(3, ) to prove that it is simple.
The objective of this studying is the important answer on the following open question : Let G and G' be two fuzzy groups and L(G), L(G') be lattices for them, respectively,
We have shown that this statement don’t true in the case general, and we sup
pose some certain conditions on the purposed groups to be the statement holds. Moreover, some important theorems are proved
In this scientific paper, we describe an algorithm to test if the weighted
Dynkin diagram of type -Cn corresponds to one of the nilpotent orbits of sp2n,
then we defined the necessary and sufficient condition on this representative
that makes the
diagram even. We applied this algorithm on one of the weighted
Dynkin diagrams of type –C3 to prove that it is true
The aim of this study was to determine some physical, chemical and microbiological density (fungi – bacteria) of a Pine forest soil in the coastal region (Al-Ballotiah forest, Banias) where Quercus calliprinus is the main dominant plant.
Three soi
l profiles were taken and their morphological characteristics were determined, the thickness of accumulated organic matter and GPS data were also recorded.
For physical and chemical analysis, samples from each profile horizon were taken and air- dried, whereas for the microbial diversity analysis, samples were taken twice in autumn and spring; and transported and stored at 4C.
The results showed that the studied soil belongs to Mollisols, Entisols with A-AC-C1-C2 profile types. Our results also showed that the soil depth was (153-150 cm) and rich in calcium carbonate.
Soil pH is alkali, where the pH ranged between (7.91-9.13) that increased bacterial activity and density in organic litter and mineral soil, which was related with the organic matter ratio. This ratio decreased significantly with soil depth that affected the microorganisms density which behave in the same manner. However, an increasing of microorganisms density was detected in spring especially in first horizon.
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