VOLUME 2, 2011 NUMBER 3
http://repository.enu.kz:8080/handle/data/10626
2020-03-31T01:06:02ZVANISHING OF THE BOCHNER CURVATURE TENSOR OF INDEFINITE ALMOST HERMITIAN MANIFOLDS
http://repository.enu.kz:8080/handle/data/10756
VANISHING OF THE BOCHNER CURVATURE TENSOR OF INDEFINITE ALMOST HERMITIAN MANIFOLDS
Rakesh Kumar; R.K. Nagaich; Jae-Bok Jun
The aim of this paper is to discuss indefinite almost Hermitian manifold
with the vanishing Bochner curvature tensor. Relations between the anti-holomorphic
sectional curvature, the holomorphic sectional curvature and the Bochner curvature
tensor have also been established.
2013-06-26T00:00:00ZORDER-SHARP ESTIMATES FOR HARDY-TYPE OPERATORS ON CONES OF QUASIMONOTONE FUNCTIONS
http://repository.enu.kz:8080/handle/data/10755
ORDER-SHARP ESTIMATES FOR HARDY-TYPE OPERATORS ON CONES OF QUASIMONOTONE FUNCTIONS
M.L. Goldman
The two-sided estimates are obtained for two types of generalized Hardy
operators on cones of functions in weighted Lebesgue spaces with some properties of
monotonicity.
2013-06-26T00:00:00ZON THE NULL-CONTROLLABILITY OF THE HEAT EXCHANGE PROCESS
http://repository.enu.kz:8080/handle/data/10754
ON THE NULL-CONTROLLABILITY OF THE HEAT EXCHANGE PROCESS
Sh. Alimov
A mathematical model of the heat exchange process, where the temperature
inside some domain is controlled by m convectors acting on the boundary, is
considered. The control parameter is a vector-function, whose components are equal
to the magnitude of the output of hot or cold air produced by each convector. The
necessary and sufficient conditions, which initial temperature must satisfy for achieving
the zero value by the projection of the temperature into some m-dimensional subspace,
are studied.
2013-06-26T00:00:00ZON THE DSM VERSION OF NEWTON’S METHOD
http://repository.enu.kz:8080/handle/data/10753
ON THE DSM VERSION OF NEWTON’S METHOD
A.G. Ramm
The DSM (dynamical systems method) version of the Newton’s method
is for solving operator equation F(u) = f in Banach spaces is discussed. If F is a
global homeomorphism of a Banach space X onto X, that is continuously Fr´echet
differentiable, and the DSM version of the Newton’s method is u˙ = −[F0(u)]−1(F(u)−
f), u(0) = u0, then it is proved that u(t) exists for all t 0 and is unique, that there
exists u(1) := limt!1 u(t), and that F(u(1)) = f. These results are obtained for an
arbitrary initial approximation u0. This means that convergence of the DSM version of
the Newton’s method is global. The proof is simple, short, and is based on a new idea.
If F is not a global homeomorphism, then a similar result is obtained for u0 sufficiently
close to y, where F(y) = f and F is a local homeomorphism of a neighborhood of y
onto a neighborhood of f. These neighborhoods are specified.
2013-06-26T00:00:00Z