Rozumenko, O. V.
On the character of growth of a noncontracting semigroup
(pp. 285298)
A B S T R A C T S
NEW COEFFICIENT CONDITIONS FOR FUNCTIONS STARLIKE WITH RESPECT TO SYMMETRIC POINTS
R. Aghalary
raghalary@yahoo.com
A. Ebadian
a.ebadian@mail.urmia.ac.ir
2000 Mathematics Subject Classification:
Primary 30C45, secondary 30C80.
Key words:
starlike functions with symmetric points, hypergeometric functions, close to convex function, odd functions.
We consider some familiar subclasses of functions starlike with respect to symmetric points and obtain sufficient conditions for these classes in terms of their Taylor coefficient. This leads to obtain several new examples of these subclasses.
LOW VOLATILITY OPTIONS AND NUMERICAL DIFFUSION OF FINITE DIFFERENCE SCHEMES
Mariyan Milev
mariyan.milev@unive.it
Aldo Tagliani
tagliani@unitn.it
2000 Mathematics Subject Classification:
65M06, 65M12.
Key words:
Numerical diffusion, spurious oscillations, BlackScholes equation, low volatility options, finite difference schemes, nonsmooth initial conditions.
In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the BlackScholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard nonoscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the CrankNicolson variant scheme of MilevTagliani. We present a short survey of these two schemes, investigate the origin of the respective artificial numerical diffusion and demonstrate how it could be diminished.
WARPED PRODUCT CRSUBMANIFOLDS IN LORENTZIAN PARA SASAKIAN MANIFOLDS
Siraj Uddin
siraj.ch@gmail.com
2000 Mathematics Subject Classification:
53C15, 53C40, 53C42.
Key words:
Warped product, doubly warped product, contact CRwarped product, LPSasakian manifold.
Many research articles have recently appeared exploring existence or non existence of warped product submanifolds in known spaces (cf. [2, 5, 8]). The objective of the present paper is to study the existence or nonexistence of contact CRwarped products in the setting of LPSasakian manifolds.
UNITS OF F_{5k}D_{10}
Joe Gildea
gildea.joe@itsligo.ie
2000 Mathematics Subject Classification:
20C05, 16U60, 16S84, 15A33.
Key words:
Unit group, group ring, group algebra, dihedral, cyclic.
The Structure of the Unit Group of the Group Algebra of the group D_{10} over any field of characteristic 5 is established in terms of split extensions of cyclic groups.
OSCILLATION CRITERIA OF SECONDORDER QUASILINEAR NEUTRAL
DELAY DIFFERENCE EQUATIONS
E. Thandapani
S. Pandian
T. Revathi
kalyanrevathi@yahoo.com
2000 Mathematics Subject Classification:
39A10.
Key words:
Oscillation, quasilinear, neutral type, delay
difference equations.
The oscillatory and nonoscillatory behaviour of solutions of the
second order quasi linear neutral delay difference equation
Δ(a_{n}  Δ(x_{n}+p_{n}x_{nτ})^{α1}
Δ(x_{n}+p_{n}x_{nτ}) + q_{n}f(x_{nσ})g(Δx_{n}) = 0 

where n ∈ N(n_{0}), α > 0, τ, σ
are fixed non negative integers, {a_{n}}, {p_{n}}, {q_{n}} are real
sequences and f and g real valued continuous functions are
studied. Our results generalize and improve some known results of
neutral delay difference equations.
WAVE OPERATORS FOR DEFOCUSING MATRIX ZAKHAROVSHABAT SYSTEMS
WITH POTENTIALS NONVANISHING AT INFINITY
Francesco Demontis
fdemontis@unica.it
Cornelis van der Mee
cornelis@krein.unica.it
2000 Mathematics Subject Classification:
Primary: 34L25;
secondary: 47A40, 81Q10.
Key words:
Wave operator, ZakharovShabat system, scattering operator.
In this article we prove that the wave operators describing the direct scattering of the defocusing matrix ZakharovShabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.
ON THE CHARACTER OF GROWTH OF A NONCONTRACTING SEMIGROUP
O. V. Rozumenko
ovrozumenko@gmail.com
2000 Mathematics Subject Classification:
47A45.
Key words:
Noncontracting semigroup, nondissipative operator.
An estimation of the growth of a noncontracting semigroup Z_{t} = exp (itA) where A is a nondissipative operator with a twodimensional imaginary component is given. Estimation is given in terms of the functional model in de Branges space.
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