Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2009
Volume
Vol. 29
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 29 (2009)
Projects
Pages
Articles
On the global offensive alliance number of a tree
(2009) Bouzefrane, Mohamed; Chellali, Mustapha
For a graph $G=(V,E)$, a set $S \subseteq V$ is a dominating set if every vertex in $V - S$ has at least a neighbor in $S$. A dominating set $S$ is a global offensive alliance if for every vertex $v$ in $V - S$, at least half of the vertices in its closed neighborhood are in $S$. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set of $G$ and the global offensive alliance number $\gamma_o(G)$ is the minimum cardinality of a global offensive alliance of $G$. We first show that every tree of order at least three with $l$ leaves and $s$ support vertices satisfies $\gamma_o(T) \geq (n-l+s+1)/3$ and we characterize extremal trees attaining this lower bound. Then we give a constructive characterization of trees with equal domination and global offensive alliance numbers.
Smoothed estimator of the periodic hazard function
(2009) Dudek, Anna
A smoothed estimator of the periodic hazard function is considered and its asymptotic probability distribution and bootstrap simultaneous confidence intervals are derived. Moreover, consistency of the bootstrap method is proved and some applications of the developed theory are presented. The bootstrap method is based on the phase-consistent resampling scheme developed in Dudek and Leśkow [A. Dudek, J. Leśkow, Bootstrap algorithm in periodic multiplicative intensity model, to appear].
Sensitivity analysis in piecewise linear fractional programming problem with non-degenerate optimal solution
(2009) Kheirfam, Behrouz
In this paper, we study how changes in the coefficients of objective function and the right-hand-side vector of constraints of the piecewise linear fractional programming problems affect the non-degenerate optimal solution. We consider separate cases when changes occur in different parts of the problem and derive bounds for each perturbation, while the optimal solution is invariant. We explain that this analysis is a generalization of the sensitivity analysis for $LP$, $LFP$ and $PLP$. Finally, the results are described by some numerical examples.
Approximation methods for a class of discrete Wiener-Hopf equations
(2009) Nowak, Michał Andrzej
In this paper, we consider approximation methods for operator equations of the form $Au + Bu = f$, where $A$ is a discrete Wiener-Hopf operator on $l_{p}$ $1 \leq p \lt \infty$ which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation $B$ and $f$ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.
Monotone iterative technique for fractional differential equations with periodic boundary conditions
(2009) Ramirez, J. D.; Vatsala, A. S.
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.