When the nodes or links of communication networks are destroyed,
its effectiveness decreases. Thus, we must design the communication network as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. A graph is considered as a modeling network, many graph theoretic parameters have been ušed to describe the stability of communication networks, including connectivity, integrity, tenacity. Several of these deal with two fundamental questions about the resulting graph. How many vertices can still communicate? How difficult is it to reconnect the graph? Stability numbers of a graph measure its durability respect to break down. The neighbour-integrity of a graph is a measure of graph vulnerability. In the neighbour-integrity, it is considered that any failure vertex effects its neighbour vertices. In this work, we define the accessible sets and accessibility number and we consider the neighbour-integrity of Generalised Petersen graphs and the relation with its accessibility number.
This paper presents development of a day ahead load forecasting (DALF) model for Turkish power system with an artificial neural network (ANN). Effects of special holidays including national and religious days, and hourly random load deviations observed in Turkish power system due to significant arc furnace loads are discussed. Performance of the ANN is investigated in the sense of both DALF performance - in terms of both daily mean absolute percentage error (MAPE) and hourly absolute percentage error (APE) - and hourly secondary reserves required to ensure supply/demand adequacy of the system. The most sensitive cities to DALF in terms of daily city temperature forecasts are ranked in order to reduce the input of the developed ANN and thereby to improve execution of the model. Candidate cities are determined based on both their placement with respect to climatic zones of the country and their contribution to the system load during peak hours. The results show that, although a well-trained ANN could provide very satisfactory daily MAPEs at non-special days, such as ~1%, the hourly absolute percentage errors (APE) could be significant due to large random load disturbances, which necessitate special attention during the day ahead allocation of hourly secondary reserves. By limiting the temperature data set with major cities, the input of ANN reduces significantly while not disturbing the MAPEs. Main contributions of the study are; addressing both benefits of the prioritizing the cities in a power system in the sense of their temperature forecast effects on the DALF performance and assessing the performance of DALF in the sense of necessary amount of secondary reserves in power systems which include significant random load deviations (e.g., large arc furnace loads).
Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions yields a simplified system that accurately agrees with the original system not only qualitatively but also quantitatively. We derive the proper size of the delays for a particular model of circadian rhythms and present numerical results showing the accuracy of this approach.
Achillea asplenifolia Vent. is one of three central European diploid species (together with A. setacea Waldst. et Kit. and A. roseoalba Ehrend.) of the A. millefolium group. Its taxonomic and phytogeographic account from the central European perspective is given mainly on the basis of herbarium and field studies. The synonymy of A. asplenifolia includes A. millefolium var. crustata Rochel and A. scabra Host; both names are typified here. No variation deserving taxonomic recognition was observed. From the taxonomic point of view, A. asplenifolia is a clearly delimited species. It grows in the Czech Republic, Slovakia, Austria, Hungary, Croatia, Serbia, and Romania. From the phytogeographic point of view, it can be classified as a Pannonian geoelement with overlaps to Transylvania and to the marginal parts of the eastern Mediterranean. Within the Czech Republic, its distribution range includes only the warmest and driest part of southern Moravia, with the northernmost site situated near the town of Vyškov. In southern Moravia, A. asplenifolia was confined to extrazonal habitats, mainly to islands of halophilous vegetation such as moist saline meadows (formerly used as pastures) and lowland fens rich in mineral nutrients, but most of the sites were destroyed. Out of six or seven localities preserved up to present, only two host vital populations.
The achromatic number of a graph $G$ is the maximum number of colours in a proper vertex colouring of $G$ such that for any two distinct colours there is an edge of $G$ incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of $K_5$ and $K_n$ for all $n \le 24$.