2003, Vol 4, No 1
http://hdl.handle.net/123456789/3463
2020-11-28T10:40:34ZInverse problems for the kinetic equation of plasma physics and a uniqueness theorem
http://hdl.handle.net/123456789/3468
Inverse problems for the kinetic equation of plasma physics and a uniqueness theorem
Neshchadim, Mikhail V.
In this paper we consider the kinetic equation of plasma physics. A uniqueness theorem for an inverse problem for this equation is proved.
2003-01-01T00:00:00ZObject oriented finite element calculations using maple
http://hdl.handle.net/123456789/3467
Object oriented finite element calculations using maple
Chibisov, Dmytro; Ganzha, Victor G.; Zenger, Christoph
Modern Computer Algebra Systems (CAS), such as Maple or Mathematica, with their symbolic facilities and visualization possibilities are powerful tools to design data structures and algorithms used in numerical simulation, with significantly lower costs compared to straightforward implementation in ''real'' programming languages, such as, for example, C or Java. The present paper shows how the CAS Maple can be used to design finite element software using linear and hierarchical bases. As a computational example the two-dimensional Poisson-equation with Dirichlet boundary conditions is presented.
2003-01-01T00:00:00ZGraphics Constructor 2.0
http://hdl.handle.net/123456789/3466
Graphics Constructor 2.0
Bulgak, Ayşe; Eminov, Diliaver
An experimental version of computer-aided methods of teaching mathematical analysis has been elaborated in the Research Centre of Applied Mathematics of the Selk University. The main part of this version is a textbook "Analysis"[1]. It is supported by the computer dialogue program Graphics Constructor [4] and its extended version Graphics Constructor 2.0.
2003-01-01T00:00:00ZOn location of the matrix spectrum inside an elipse
http://hdl.handle.net/123456789/3465
On location of the matrix spectrum inside an elipse
Bulgak, Ayşe; Demidenko, Gennadii; Matveeva, Inessa
In the present article we consider the problem on location of the spectrum of an arbitrary matrix $A$ inside the ellipse
calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b.
calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b.
One of the authors (see~[9]) established a connection of the problem with solvability of the matrix equation
H−left(frac12a2+frac12b2ight)A∗HA−left(frac14a2−frac14b2ight)(HA2+(A∗)2H)=C.
H−left(frac12a2+frac12b2ight)A∗HA−left(frac14a2−frac14b2ight)(HA2+(A∗)2H)=C.
In this article we construct a Hermitian positive definite solution $H$ to the equation in the form of a power series. We prove that the norm $|H|$ characterizes an immersion depth of eigenvalues of the matrix $A$ in the inside of the ellipse ${cal E}$. On the base of these results we propose an algorithm to determine whether the spectrum of the matrix $A$ belongs to the inside of the ellipse ${cal E}$.
The research was financially supported by the Scientific and Technical Research Council of Turkey (TUBITAK) in the framework of the NATO-PC Fellowships Programme.
2003-01-01T00:00:00Z