Volume 33, Numbers 2-3, 2007
AN ANALYTIC POINT OF VIEW AT TORIC VARIETIES
Roman J. Dwilewicz
romand@umr.edu
2000 Mathematics Subject Classification: Primary 14M25, 32Q99; Secondary 14L30. Key words: Toric varieties, convex polytopes, polyhedral cones.
SOLVABILITY OF AN INFINITE SYSTEM OF SINGULAR
INTEGRAL EQUATIONS
Mahmoud M. El Borai
m_m_elborai@yahoo.com,
Mohamed I. Abbas
m_i_abbas77@yahoo.com
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15. Key words: Infinite system of singular integral equations, Banach sequence space, Differential equations of fractional orders.
(1) x_{i}(t) = a_{i}(t)+ ∫^{t}_{0} (t − s)^{− α} (s, x_{1}(s), x_{2}(s), …) ds,
where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T].
The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
EXISTENCE OF SOLUTIONS FOR A CLASS OF QUASI-LINEAR
SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS
A. A. M. Hassan,
S. M. Amer
amrsammer@hotmail.com
2000 Mathematics Subject Classification: 45F15, 45G10, 46B38. Key words: Quasi-linear singular integro-differential equations, Schauder's fixed point theorem, Sobolev space.
LINEAR COLLOGATIONS AND DYNAMIC SYSTEM
CORRESPONDING TO OPERATORS IN THE BANACH SPACE
Raed Hatamleh
raedhat@yahoo.com
2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94. Key words: Banach space, Dynamic system, Colligations, Coupling.
ON NILPOTENT SUBSEMIGROUPS IN SOME MATRIX SEMIGROUPS
Olexandr Ganyushkin
ganiyshk@univ.kiev.ua,
Volodymyr Mazorchuk
mazor@math.uu.se
2000 Mathematics Subject Classification: 20M20, 20M10. Key words: Nilpotent semigroup, stochastic matrix, partial order, block, polyhedron.
ON THOM POLYNOMIALS FOR A_{4}(−) VIA SCHUR FUNCTIONS
Özer Öztürk
ozero@metu.edu.tr
2000 Mathematics Subject Classification: 05E05, 14N10, 57R45. Key words: Thom polynomials, singularities, global singularity theory, classes of degeneracy loci, Schur functions, resultants.
INVARIANT FUNCTIONS ON NEIL PARABOLA IN C^{n}
Pawel Zapalowski
Pawel.Zapalowski@im.uj.edu.pl
2000 Mathematics Subject Classification: Primary 32F45. Key words: generalized Neil parabola, Carathéodory pseudodistance, Kobayashi pseudodistance, Carathéodory-Reiffen pseudometric, Kobayashi-Royden pseudometric.
A NOTE ON DIV-CURL LEMMA
Sadek Gala
sadek.gala@gmail.com
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65. Key words: Compactness compensated, Hardy space, Sobolev space.
EXTENDED MAXIMUM PRINCIPLES
M. M. Al-Mahameed
al_mahameed2000@yahoo.com
2000 Mathematics Subject Classification: 35B50, 35L15. Key words: Maximum principles, elliptic equations.
DOES ATKINSON-WILCOX EXPANSION CONVERGES FOR ANY CONVEX DOMAIN?
I. Arnaoudov
jna@tu-sofia.bg,
V. Georgiev
georgiev@dm.unipi.it,
G. Venkov
gvenkov@tu-sofia.bg
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40. Key words: Atkinson-Wilcox expansion theorem, Helmholtz equation, far field pattern, convex domain, second-order recurrence relations.
HERMITIAN MANIFOLDS OF POINTWISE CONSTANT ANTIHOLOMORPHIC SECTIONAL
CURVATURES
Georgi Ganchev
ganchev@math.bas.bg,
Ognian Kassabov
okassabov@vtu.bg
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50. Key words: Hermitian manifolds, antiholomorphic sectional curvatures.