Rozumenko, O. V.
On the character of growth of a non-contracting semigroup
(pp. 285-298)
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, Black-Scholes equation, low volatility options, finite difference schemes, non-smooth initial conditions.
In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant scheme of Milev-Tagliani. 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 CR-SUBMANIFOLDS 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 CR-warped product, LP-Sasakian 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 non-existence of contact CR-warped products in the setting of LP-Sasakian manifolds.
UNITS OF F5kD10
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 D10 over any field of characteristic 5 is established in terms of split extensions of cyclic groups.
OSCILLATION CRITERIA OF SECOND-ORDER QUASI-LINEAR NEUTRAL
DELAY DIFFERENCE EQUATIONS
E. Thandapani
S. Pandian
T. Revathi
kalyanrevathi@yahoo.com
2000 Mathematics Subject Classification:
39A10.
Key words:
Oscillation, quasi-linear, neutral type, delay
difference equations.
The oscillatory and nonoscillatory behaviour of solutions of the
second order quasi linear neutral delay difference equation
|
Δ(an | Δ(xn+pnxn-τ)|α-1
Δ(xn+pnxn-τ) + qnf(xn-σ)g(Δxn) = 0 |
|
where n ∈ N(n0), α > 0, τ, σ
are fixed non negative integers, {an}, {pn}, {qn} 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 ZAKHAROV-SHABAT 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, Zakharov-Shabat system, scattering operator.
In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat 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 NON-CONTRACTING SEMIGROUP
O. V. Rozumenko
ovrozumenko@gmail.com
2000 Mathematics Subject Classification:
47A45.
Key words:
Non-contracting semigroup, non-dissipative operator.
An estimation of the growth of a non-contracting semigroup Zt = exp (itA) where A is a non-dissipative operator with a two-dimensional imaginary component is given. Estimation is given in terms of the functional model in de Branges space.
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