Ovidiu Bagdasar

On the characterization of periodic generalized Horadam sequences

The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are generated by higher order recurrences for arbitrary initial conditions. The asymptotic behaviour of generalized Horadam sequences generated by roots of unity is also examined, along with upper boundaries for the disc containing periodic orbits. Some applications are suggested, along with a number of future research directions.

Influence Discovery in Semantic Networks: An Initial Approach

Assessing the influence between concepts, which include people, physical objects, as well as theoretical ideas, plays a crucial role in understanding and discovering knowledge. Despite the huge amount of literature on knowledge discovery in semantic networks, there has been little attempt to fully classify and investigate the influence, which also includes causality, of a semantic entity on another one as dynamical entities. In this paper we will introduce an approach to discover and assess influence among nodes in a semantic network, with the aim to provide a tool to identify its type and direction. Even though this is still being developed, the preliminary evaluation shows promising and interesting results.

Elements of Graph Theory

Graphs are mathematical structures used to model and visualize relations between certain objects. One of the first formulations of a graph theory problem was the famous Konigsberg Problem solved by Leonhard Euler. He proposed a model which reduced the problem to a schematic diagram and then concluded that the graph needed to satisfy some general conditions for the problem to be solved affirmatively. His studies highlighted the importance of understanding graphs and their properties, which later lead to the creation of Graph Theory as a distinct mathematical discipline. In this chapter we first introduce graphs through some illustrative examples and then describe the basic elements of graphs, as well some important graph properties. We then present special types of graphs like trees or networks, together with some specific techniques, problems and algorithms.

Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.

Characterizations of generalized exponential trichotomies for linear discrete-time systems.

Abstract The generalized exponential trichotomy (g.e.t) concept is explored for linear time-varying systems. Characterizations and relations with the notion of uniform exponential trichotomy (u.e.t) in the sense of Elaydi-Janglajew are also provided.

On the geometry of certain periodic non-homogeneous Horadam sequences

Abstract Horadam sequences are second-order recurrences depending on a family of four complex parameters: two initial conditions and two recurrence coefficients. The periodicity conditions, as well as the number and geometric structure of self-repeating Horadam sequences of fixed length have been recently investigated. In this paper various geometric properties of non-homogeneous Horadam sequences are explored, including periodicity conditions and the structure of certain periodic orbits.

Local maximum points of explicitly quasiconvex functions

This work concerns generalized convex real-valued functions defined on a nonempty convex subset of a real topological linear space. Its aim is twofold: first, to show that any local maximum point of an explicitly quasiconvex function is a global minimum point whenever it belongs to the intrinsic core of the function’s domain and second, to characterize strictly convex normed spaces by applying this property for a particular class of convex functions.

Traffic assignment: Methods and simulations for an alternative formulation of the fixed demand problem

Abstract Motorists often face the dilemma of choosing the route enabling them to realise the fastest (i.e., shortest) journey time. In this paper we examine discrete and continuous optimisation and equilibrium-type problems for a simplified parallel link traffic model using a variance based approach. Various methodologies used for solving these problems (brute force, dynamic programming, tabu search, steepest descent) are explored and comparison is made with the Beckmann cost function employed in transport modelling.

Unifying local–global type properties in vector optimization

It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min–global min” and “local max–global min” type properties can be extended and unified by a single general local–global extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local–global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.

On some results concerning generalized arithmetic triangles

Abstract In this paper we present theoretical and computational results regarding generalized arithmetic m-triangles. The numerical values recover well-known number sequences, indexed in the OEIS including binomial coefficients and their extensions. Some combinatorial interpretations, generating functions and also asymptotic formulae for these triangles are provided.