IN MEMORIAM  Andrey Nikolov Todorov
A B S T R A C T S
DIRAC TYPE CONDITION AND HAMILTONIAN GRAPHS
Kewen Zhao
kwzqzu@yahoo.cn
2010 Mathematics Subject Classification:
05C38, 05C45.
Key words:
Dirac type condition, sufficient condition, Hamiltonian graph.
In 1952, Dirac introduced the degree type condition and proved that if G is a connected graph of order n ≥ 3 such that its minimum degree satisfies δ(G) ≥ n/2, then G is Hamiltonian.
In this paper we investigate a further condition and prove that if G is a connected graph of order n ≥ 3 such that δ(G) > (n2)/2, then G is Hamiltonian or G belongs to four classes of wellstructured exceptional graphs.
ON THE GENERALIZED KATO SPECTRUM
Mohammed Benharrat
Benharrat2006@yahoo.fr,
mohammed.benharrat@gmail.com,
Bekkai Messirdi
messirdi.bekkai@univoran.dz
2010 Mathematics Subject Classification:
47A10.
Key words:
Semiregular operators, Kato type operators, generalized Kato spectrum, essential spectrum.
We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [S. Goldberg. Unbounded Linear Operators. McGrawHill, NewYork,
1966] by σ_{ec}(T) = {λ ∈ C ; R(λIT) is not closed} is at most countable and we also give some relationship between this spectrum and the SVEP theory.
DOUBLE COMPLEXES AND VANISHING OF NOVIKOV COHOMOLOGY
Thomas Hüttemann
t.huettemann@qub.ac.uk
2010 Mathematics Subject Classification:
Primary 18G35; Secondary 55U15.
Key words:
mapping torus, truncated product, double complex, finite domination, Novikov cohomology.
We consider nonstandard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasiisomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.
POLYNOMIAL AUTOMORPHISMS OVER FINITE FIELDS: MIMICKING TAME MAPS BY THE DERKSEN GROUP
Stefan Maubach
s.maubach@jacobsuniversity.de
Roel Willems
roelwill@gmail.com
2010 Mathematics Subject Classification:
14L99, 14R10, 20B27.
Key words:
Polynomial automorphisms, permutation groups, tame
automorphism group.
If F is a polynomial automorphism over a finite field F_{q} in dimension n, then it induces a permutation π_{qr}(F) of (F_{qr})^{n} for every r ∈ N^{*}. We say that F can be `mimicked' by elements of a certain group of automorphisms G if there are g_{r} ∈ G such that π_{qr}(g_{r}) = π_{qr}(F).
Derksen's theorem in characteristic zero states that the tame automorphisms in dimension n ≥ 3 are generated by the affine maps and the one map (x_{1}+x_{2}^{2}, x_{2}, …, x_{n}). We show that Derksen's theorem is not true in characteristic p in general. However, we prove a modified, weaker version of Derksen's theorem over finite fields: we introduce the Derksen group DA_{n}(F_{q}), n ≥ 3, which is generated by the affine maps and one wellchosen nonlinear map, and show that DA_{n}(F_{q}) mimicks any element of TA_{n}(F_{q}). Also, we do give an infinite set E of nonaffine maps which, together with the affine maps, generate the tame automorphisms in dimension 3 and up. We conjecture that such a set E cannot be finite.
We consider the subgroups GLIN_{n}(k) and GTAM_{n}(k).
We prove that for k a finite field, these groups are equal if and only if
k ≠ F_{2}. The latter result provides a tool to show that a map is not linearizable.
EQUICONVERGENCE AND EQUISUMMABILITY OF JACOBI SERIES
Georgi Boychev
GBoychev@hotmail.com
2010 Mathematics Subject Classification:
33C45, 40G05.
Key words:
Jacobi polynomials, Jacobi series, asymptotic formula, convergence, summabiliy, equisummabiliy, equiconvergence.
In this paper we give some results concerning the equiconvergence and equisummability of series in Jacobi polynomials.
GROWTH OF SOME VARIETIES OF LEIBNIZPOISSON ALGEBRAS
S. M. Ratseev
RatseevSM@rambler.ru
2010 Mathematics Subject Classification:
17A32, 17B63.
Key words:
Poisson algebra, LeibnizPoisson algebra, variety of algebras, growth of variety.
Let V be a variety of LeibnizPoisson algebras over an
arbitrary field whose ideal of identities contains the identities
{{x_{1},y_{1}},{x_{2},y_{2}},¼,{x_{m},y_{m}}} = 0, {x_{1},y_{1}}·{x_{2},y_{2}}· ¼ ·{x_{m},y_{m}} = 0 

for some m. It is shown that the exponent of V exists and is an integer.
WEIGHTED COMPOSITION FOLLOWED BY DIFFERENTIATION BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS
Elke Wolf
lichte@math.unipaderborn.de
2010 Mathematics Subject Classification:
47B33, 47B38.
Key words:
weighted composition operators followed by differentiation, weighted Banach spaces of holomorphic functions.
Let f be an analytic selfmap of the open unit disk D in the complex plane and y be an analytic map on D. Such maps induce a weighted composition operator followed by differentiation DC_{f, y} acting between weighted Banach spaces of holomorphic functions. We characterize boundedness and compactness of such operators in terms of the involved weights as well as the functions f and y.
ON STRONGLY REGULAR GRAPHS WITH m_{2} = qm_{3} AND m_{3} = qm_{2}
Mirko Lepovic
lepovic@kg.ac.rs
2010 Mathematics Subject Classification:
05C50.
Key words:
Strongly regular graph, conference graph, integral graph.
We say that a regular graph G of order n and degree r ≥ 1
(which is not the complete graph) is strongly regular if there exist
nonnegative integers τ and θ such that
S_{i}∩S_{j} = τ for any two adjacent vertices i and j, and
S_{i}∩S_{j} = θ for any two distinct nonadjacent vertices i and j,
where S_{k} denotes the neighborhood of the vertex k. Let
λ_{1} = r, λ_{2} and λ_{3} be the distinct eigenvalues of a connected strongly regular graph. Let m_{1} = 1, m_{2} and m_{3} denote the multiplicity of r, λ_{2} and λ_{3}, respectively. We here describe the parameters n, r,
τ and θ for strongly regular graphs with m_{2} = qm_{3}
and m_{3} = qm_{2} for q = 2, 3, 4.
(2,3)GENERATION OF THE GROUPS PSL_{6}(q)
K. Tabakov
ktabakov@fmi.unisofia.bg,
K. Tchakerian
kerope@fmi.unisofia.bg,
2010 Mathematics Subject Classification:
20F05, 20D06.
Key words:
(2,3)generated group.
We prove that the group PSL_{6}(q) is (2,3)generated for any q. In fact, we provide explicit generators x and y of orders 2 and 3, respectively, for the group SL_{6}(q).
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