Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2009
Volume
Vol. 29
Number
No. 1
Description
Journal Volume
Opuscula Mathematica
Vol. 29 (2009)
Projects
Pages
Articles
Vertices belonging to all or to no minimum locating dominating sets of trees
(2009) Blidia, Mostafa; Lounes, Rahma
A set $D$ of vertices in a graph $G$ is a locating-dominating set if for every two vertices $u$, $v$ of $G \setminus D$ the sets $N(u) \cap D$ and $N(v) \cap D$ are non-empty and different. In this paper, we characterize vertices that are in all or in no minimum locating dominating sets in trees. The characterization guarantees that the $\gamma_L$-excellent tree can be recognized in a polynomial time.
Strong maximum principles for implicit parabolic functional-differential problems together with nonlocal inequalities with functionals
(2009) Byszewski, Ludwik
The aim of the paper is to give strong maximum principles for implicit parabolic functional-differential problems together with nonlocal inequalities with functionals in relatively arbitrary $(n+1)$-dimensional time-space sets more general than the cylindrical domain.
The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation Ut - Uxx = 0
(2009) Golenia, Jolanta; Prykarpatsky, Yarema A.; Wachnicki, Eugeniusz
The generalized Cartan-Monge type approach to the characteristics method is discussed from the geometric point of view. Its application to the classical one-dimensional linear heat equation $u_t-u_{xx}=0$ is presented. It is shown that the corresponding exact solution of the Cauchy problem can be represented in a classical functional-analytic Gauss type form.
Multivariate kernel density estimation with a parametric support
(2009) Jarnicka, Jolanta
We consider kernel density estimation in the multivariate case, focusing on the use of some elements of parametric estimation. We present a two-step method, based on a modification of the EM algorithm and the generalized kernel density estimator, and compare this method with a couple of well known multivariate kernel density estimation methods.
Best approximation in Chebyshev subspaces of L(ln1, ln1)
(2009) Kowynia, Joanna
Chebyshev subspaces of $\mathcal{L}(l_1^n,l_1^n)$ are studied. A construction of a $k$-dimensional Chebyshev (not interpolating) subspace is given.