Findik, Ş.
Outer endomorphisms of free metabelian Lie algebras
(pp. 261−276)
A B S T R A C T S
ON REALIZABILITY OF p-GROUPS AS GALOIS GROUPS
Ivo M. Michailov
ivo_michailov@yahoo.com
Nikola P. Ziapkov
ziapkov2000@yahoo.co.uk
2000 Mathematics Subject Classification:
12F12, 15A66.
Key words:
Inverse problem, embedding problem, Galois group,
p-group, Kummer extension, corestriction, orthogonal
representation, Clifford algebra, spinor, modular group, dihedral
group, quaternion group, Galois cohomology.
In this article we survey and examine the realizability of
p-groups as Galois groups over arbitrary fields. In particular we
consider various cohomological criteria that lead to necessary and
sufficient conditions for the realizability of such a group as a
Galois group, the embedding problem (i.e., realizability over a
given subextension), descriptions of such extensions, automatic
realizations among p-groups, and related topics.
SPECIAL COMPOSITIONS IN AFFINELY CONNECTED SPACES WITHOUT A TORSION
Georgi Zlatanov
zlatanov@uni-plovdiv.bg
2000 Mathematics Subject Classification:
53B05, 53B99.
Key words:
Affinely connected spaces, spaces of compositions, affinor of composition,
tensor of the affine deformation, integrable structure, projective affinors.
Let A_{N} be an affinely connected space without a torsion. With the help of N independent vector fields and their reciprocal covectors is built an affinor which defines a composition X_{n} ×X_{m} (n + m = N). The structure is integrable. New characteristics by the coefficients of the derivative equations are found for special compositions, studied in [A. Norden. Spaces of Cartesian composition. Izv. Vyssh. Uchebn. Zaved.,
Mat. (1963), No 4(35), 117−128], [A. Norden, G. Timofeev. Invariant criteria for special compositions
of multidimensional spaces. Izv. Vyssh. Uchebn. Zaved., Mat. (1972), No 8(123) 81−89]. Two-dimensional manifolds, named as bridges, which cut the both base manifolds of the composition are introduced. Conditions for the affine deformation tensor of two connections where the composition is simultaneously of the kind (g-g) are found.
FORMES DE CONTACT AYANT LE MEME CHAMP DE REEB
Saad Aggoun
saadaggoun@yahoo.fr
2000 Mathematics Subject Classification:
37J55, 53D10, 53D17, 53D35.
Key words:
Contact structures, contact forms, Reeb field.
In this paper, we study contact forms on a 3-manifold having a common Reeb
vector field R. The main result is that when the contact forms induce the
same orientation, they are diffeomorphic.
REMARKS ON BLOW UP TIME FOR SOLUTIONS OF A NONLINEAR DIFFUSION SYSTEM WITH TIME DEPENDENT COEFFICIENTS
M. Marras
mmarras@unica.it
2000 Mathematics Subject Classification:
35K55, 35K60.
Key words:
Parabolic problems, blow-up.
We investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time
dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t^{*}.
OPTIMAL INVESTMENT UNDER STOCHASTIC VOLATILITY AND POWER TYPE
UTILITY FUNCTION
Abbes Benchaabane
abbesbenchaabane@gmail.com
Azzedine Benchettah
abenchetah@hotmail.com
2000 Mathematics Subject Classification:
37F21, 70H20, 37L40, 37C40, 91G80, 93E20.
Key words:
Hamilton-Jacobi-Bellman equation, invariant measure,
Mean-reverting process, Optimal stochastic control, Stochastic volatility.
In this work we will study a problem of optimal investment in financial
markets with stochastic volatility with small parameter. We used the
averaging method of Bogoliubov for limited development for the optimal
strategies when the small parameter of the model tends to zero and the limit
for the optimal strategy and demonstrated the convergence of these optimal
strategies.
ZOLOTAREV'S PROOF OF GAUSS RECIPROCITY AND JACOBI SYMBOLS
Marek Szyjewski
szyjewsk@ux2.math.us.edu.pl
2000 Mathematics Subject Classification:
Primary 11A15.
Key words:
Jacobi symbol, Gauss Reciprocity, permutations.
We extend to the Jacobi symbol Zolotarev's idea that the Legendre symbol is the sign of a permutation, which leads to simple, strightforward proofs of many results, the proof of the Gauss Reciprocity for Jacobi symbols including.
OUTER ENDOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS
Şehmus Findik
sfindik@cu.edu.tr
2000 Mathematics Subject Classification:
17B01, 17B30, 17B40.
Key words:
free metabelian Lie algebras, inner automorphisms, outer endomorphisms.
Let F_{m} be the free metabelian Lie algebra of rank m
over a field K of characteristic 0. We consider the semigroup IE(F_{m}) of the endomorphisms of F_{m} which are identical modulo the commutator ideal of F_{m}. We describe the factor semigroup of IE(F_{m}) modulo the congruence induced by the group of inner automorphisms.
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