The Wiener index W ( G ) of a simple connected graph G is defined as the sum of distances over all pairs of vertices in a graph. We denote by W [ T n ] the set of all values of the Wiener index for a graph from the class T n of trees on n vertices. The largest interval of consecutive integers (consecutive even integers in case of odd n ) contained in W [ T n ] is denoted by W int [ T n ]. In this paper we prove that both sets are of cardinality 1 ⁄ 6 n 3 + O ( n 5/2 ) in the case of even n , while in the case of odd n we prove that the cardinality of both sets equals 1 ⁄ 12 n 3 + O( n 5/2 ), which essentially solves two conjectures posed in the literature.

Article history: Received 29 June 2017 Received in revised form 4 September 2017 Accepted 5 September 2017 A model was made for prediction of the trajectory of an irregularly shaped body moving through a resistive medium with high velocities, using data for aerodynamic forces obtained from numerical simulations. For a different orientation of the body with respect to the velocity vector of the center of mass, the aerodynamic resistance force is different for two reasons: the exposed surface area is different and the shape is different. In this regard, 216 numerical simulations of airflow around of the body of an irregularly shaped body in different orientations were carried out, for one full rotation (around one axis of rotation) of the body, with angular increments of 15 (0 360), for the following velocities: 0.6, 0.8, 1, 1.2, 1.3, 1.5, 2, 3 and 4 Mach. The outcome of these simulations is the resistance forces and aerodynamic moments as the result of motion of the body in various directions relatively to the body. After the simulations had been performed, the results of the resistance forces and aerodynamic moments were used to integrate the equations of motion with an assumption that the irregularly shaped body had a continuous rotation all the way along the trajectory with relatively high angular velocities. With this assumption, an effective aerodynamic force was calculated which takes into consideration that the aerodynamic force varies due to the rotation of the body. The results show that the trajectory of an irregularly shaped body is curved in space because the side component of the aerodynamic force cannot be ignored because of the irregular shape of the body, which leads to significant lateral movement of the body from the initial direction of flight.

The aim of this study was to research the relation between exposure to maltreatment in childhood and working memory capacity in adulthood. A survey among 376 females in the age between 16 and 67 was administered. Exposure to maltreatment in childhood (sexual, physical and psychological abuse, neglect and witnessing family violence) was assessed retrospectively using the Child Maltreatment Questionnaire (Karlović, Buljan-Flander, & Vranić, 2001), whilst the Working Memory Questionnaire (Vallat-Azouvi, Pradat-Diehl, & Azouvi, 2012) was used to assess working memory capacity (recalling verbal information, numerical information, attention ability and executive functioning). The results suggest a significantly greater prevalence of physical abuse and witnessing family violence in comparison to other forms of maltreatment in childhood. Psychological abuse and witnessing family violence have shown themselves to be statistically significant predictors for deficits in total working memory capacity, verbal recall and attention ability. The results suggest that traumatic experiences during childhood, such as abuse, may trigger particular cognitive changes which may be reflected in adulthood. It is, therefore, exceedingly important to conduct further research in order to contribute to the understanding of the correlation between cognitive difficulties and maltreatment in childhood.