@journaltitle: MATHEMATICA BOHEMICA
@ISSN: 0682-7959
@year: 1995
@volume: 120
@issue: 2
@remark: 
@EOH
 
@author: Krystyna Zyskowska
@affiliation: Chair of special functions,
Lodz University, Banacha 22, 90-238 Lodz, Poland 
@title: On an extremal problem
@language: English
@pages: 113-124
@classification1: 30C50 
@classification2: 
@keywords: univalent function, coefficient problem 
@abstract: Let $S$ denote the class of functions $f(z) = z + a_2z^2 +
a_3z^3 + \ldots$ univalent and holomorphic in the unit disc
$\varDelta= \{z \: |z| < 1\}$. In the paper we obtain a sharp
estimate of the functional $|a_3 - \alpha a^2_2| + \alpha|a_2|^2$ in the
class $S$ for an arbitrary $\alpha\in\Bbb R$.  
@filename: zyskow
@EOI
 
@author: Gary Chartrand, Frank Harary, Moazzem Hossain, Kelly Schultz
@affiliation: G.~Chartrand, K.~Schultz, Department of
Mathematics and Statistics, Western Michigan University, Kalamazoo,
Michigan 49008-5152; F.~Harary, Department of Computer
Science, New Mexico State University, Las Cruces, New Mexico~88003;
M.~Hossain, Compass Design Automation, M/S 410, 1865 Lundi
Ave., San Jose, California 95131 
@title: Exact $2$-step domination in graphs
@language: English
@pages: 125-134
@classification1: 05C38 
@classification2: 
@keywords: $2$-step domination graph 
@abstract: For a vertex $v$ in a graph $G$, the set $N_2(v)$ consists
of those vertices of $G$ whose distance from $v$ is 2. If a graph $G$
contains a set $S$ of vertices such that the sets $N_2(v)$, $v\in S$,
form a partition of $V(G)$, then $G$ is called a $2$-step domination
graph. We describe $2$-step domination graphs possessing some
prescribed property. In addition, all $2$-step domination paths and
cycles are determined.  
@filename: harary
@EOI
 
@author: Preben Dahl Vestergaard, Bohdan Zelinka
@affiliation: Preben Dahl Vestergaard, Department of
Mathematics and Computer Science, Aalborg University, Frederik Bajers
Vej~7, DK~9220 Aalborg~0, Denmark; Bohdan Zelinka, Department
of Discrete Mathematics and Statistics, Technical University of
Liberec, Halkova~6, 461 17 Liberec, Czech Republic 
@title: Cut-vertices and domination in graphs
@language: English
@pages: 135-143
@classification1: 05035, 05040 
@classification2: 
@keywords: domatic number, total domatic number, cut-vertex, bridge 
@abstract: The paper studies the domatic numbers and the total
domatic numbers of graphs having cut-vertices.  
@filename: zeldahl
@EOI
 
@author: Alexandr Vondra
@affiliation: Department of Mathematics,
Military Academy in Brno, PS 13, 612 00 Brno, Czech Republic 
@title: Geometry of second-order connections and ordinary
differential equations 
@language: English
@pages: 145-167
@classification1: 34A26, 53C05, 70H35 
@classification2: 
@keywords: connection, semispray, differential equation, integral, symmetry 
@abstract: The geometry of second-order systems of ordinary
differential equations represented by $2$-connections on the trivial
bundle $\operatorname{pr_1}\:\Bbb R\times M\to\Bbb R$ is studied.
The formalism used, being completely utilizable within the framework
of more general situations (partial equations), turns out to be of
interest in confrontation with a traditional approach (semisprays),
moreover, it amounts to certain new ideas and results. The paper is
aimed at discussion on the interrelations between all types of
connections having to do with integral sections (geodesics),
integrals and symmetries of the equations studied.  
@filename: vondra
@EOI

@author: Pavel Drabek
@affiliation: Department of Mathematics,
University of West Bohemia, P.O.~Box 314, 306 14 Plzen, Czech
Republic, e-mail:  pdrabek@kma.zcu.cz 
@title: The least eigenvalues of nonhomogeneous degenerated
quasilinear eigenvalue problems 
@language: English
@pages: 169-195
@classification1: 35J20, 35J70, 35B35, 35B45 
@classification2: 
@keywords: weighted Sobolev space, degenerated quasilinear partial
differential equations, weak solutions, eigenvalue problems, Schauder
fixed point theorem, boundedness of the solution 
@abstract: We prove the existence of the least positive eigenvalue
with a corresponding nonnegative eigenfunction of the quasilinear
eigenvalue problem $$\align-\operatorname{div}(a(x,u)|\nablau|^{p-2}\nabla u) = &\lambda b(x,u)|u|^{p-2}u \quad\text{ in }
\Omega,\newline u = &0 \hskip2cm\text{ on } \partial\Omega, \endalign$$
where $\Omega$ is a bounded domain, $p>1$ is a real number and
$a(x,u)$, $b(x,u)$ satisfy appropriate growth conditions. Moreover,
the coefficient $a(x,u)$ contains a degeneration or a singularity. We
work in a suitable weighted Sobolev space and prove the boundedness
of the eigenfunction in $L^\infty(\Omega)$. The main tool is the 
investigation of the associated homogeneous eigenvalue problem and an
application of the Schauder fixed point theorem.  
@filename: drabek
@EOI
 
@author: Horst Alzer
@affiliation: Morsbacher Str. 10, 51545 Waldbrol, Germany 
@title: Two inequalities for series and sums
@language: English
@pages: 197-201
@classification1: 26D15 
@classification2: 
@keywords: inequalities for series and sums, H\"older's inequality 
@abstract: In this paper we refine an inequality for infinite series
due to Astala, Gehring and Hayman, and sharpen and extend a
Holder-type inequality due to Daykin and Eliezer.  
@filename: alzer
@EOI
 
@author: Ferdinand Gliviak, Peter Kys
@affiliation: F.~Gliviak, Faculty of Mathematics and Physics,
KNOM, Comenius University, 842 15 Bratislava, Mlynska dolina,
Slovakia, e-mail:  gliviak@fmph.uniba.sk; P.~Kys,
Faculty of Mathematics and Physics, KPG, Comenius University, 842 15
Bratislava, Mlynska dolina, Slovakia, e-mail: kys@mff.uniba.sk 
@title: Note on the relation between radius and diameter of a graph
@language: English
@pages: 203-207
@classification1: 05C12; 05C20
@classification2: 
@keywords: graph, digraph, strong digraph, radius, diameter
@abstract: The known relation between the standard radius and
diameter holds for graphs, but not for digraphs. We show that no
upper estimation is possible for digraphs. We also give some remarks
on distances, which are either metric or non-metric.
@filename: glivkys
@EOI
 
@author: Ivan Chajda, Petr Emanovsky
@affiliation: Ivan Chajda, katedra algebry a geometrie, Prir.
fak. UP Olomouc, Tomkova 38, 779 00 Olomouc; Petr Emanovsky,
katedra matematiky, Ped. fak. UP Olomouc, Zizkovo nam. 5, 771 40
Olomouc 
@title: Modularity and distributivity of the lattice of
$\Sigma$-closed subsets of an algebraic structure 
@language: English
@pages: 209-217
@classification1: 08A05, 04A05 
@classification2: 
@keywords: algebraic structure, closure system, $\Sigma$-closed subset,
modular lattice, distributive lattice, convex subset 
@abstract: Let $\Cal A =(A,F,R)$ be an algebraic structure of type $\tau$
and $\Sigma$ a set of open formulas of the first order language
$L(\tau)$. The set $C_\Sigma(\Cal A)$ of all subsets of $A$ closed under
$\Sigma$ forms the so called lattice of $\Sigma$-closed subsets of
$\Cal A$. We prove various sufficient conditions under which the lattice
$C_\Sigma(\Cal A)$ is modular or distributive.  
@filename: chaem
@EOI
 
@author: Jiri Vesely
@affiliation: Mathematical Institute of the Charles University,
Sokolovska 83, 186 00 Praha 1, Czech Republic, e-mail:
jvesely@karlin.mff.cuni.cz 
@title: Stolet\'e v\'yro\v c\'\i\ narozen\'\i\ doc. Josefa Holub\'a\v re
@language: Czech
@pages: 219-220
@classification1: 01A70
@classification2: 
@keywords: news and notices
@abstract: 
@filename: zpravy
@EOI


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