A new class of generalized close-to-starlike functions defined by the Srivastava-Attiya operator

In this paper, we consider a new class CS*s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function Φ(z, s, a). Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.     

A recursive least-squares algorithm for pairwise comparison matrices

Pairwise comparison matrices are commonly used for setting priorities among competing objects. In a leading decision making method called the analytic hierarchy process the principal right eigenvector components represent the weights of the alternatives. The direct least-squares method extracts the weight vector by first finding a rank-one matrix which minimizes the Euclidean distance from the original ratio matrix. We develop a recursive least-squares algorithm and reveal a striking correspondence between these two approaches for these matrices. The recursion applies for merely positive matrices also. We prove that a convergent iteration leads to matrices by which the Perron-eigenvectors and the Perron approximation of the original matrix may be produced. We show that certain useful properties of the recursion advance the development of reliable measures of perturbations of transitive matrices. Numerical analysis is included for a macroeconomic problem taken from the literature.     

Fitness Landscape Analysis and Metaheuristics Efficiency

Landscape analysis has been identified as a promising way to develop efficient optimization methods. Nevertheless, the links between properties of the landscape and efficiency of methods is not easy to understand. In this article, we propose to give a contribution in this field using a vehicle routing problem as an illustration. Metaheuristics use a neighborhood operator that connects solutions of the search space. Thus, this operator acts on the dynamics of the search and impacts metaheuristics efficiency. Therefore, we characterize two landscapes differenciated by their neighborhood function and then, we analyze the performance of classical metaheuristics using one or the other neighborhood operator. Finally, a discussion provides insights on the relations between results of the landscape analysis and results of methods performance.     

KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector <em>ω</em> <sub>0</sub> is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a Rüssmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that <em>ω</em> <sub>0</sub> has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least <em>d</em> + 1 passing through 0 that is foliated by complex analytic KAM-tori with frequency <em>ω</em> <sub>0</sub>. This is an extension of previous results obtained in [1] to the case of an elliptic fixed point.