Several algorithms, including the Floyd-Warshall algorithm, have been developed to calculate the shortest path between every pair of vertices in a graph (network) with cycles. This study proposes an exact algorithm, the Cascade Rectangle (CR) algorithm, for calculating the shortest paths between every pair of vertices in cycled graphs. The algorithm is developed by designing and implementing certain improvements to the available exact algorithms. In particular, the proposed algorithm has an improved computational complexity, although its worst computational complexity is O(n3). Moreover, the CR algorithm is easier to implement, which is an advantage for teaching and learning purposes. In addition to this, we introduce a new concept, the transposition matrix, which has important applications in sensitivity analysis and re-optimization of the shortest path networks. An example illustrates the CR algorithm and the new concept of transposition matrix.
The author proposes this paper to present a solution for natural distribution of prime numbers along numbers line, the author discovers the new pattern and proposes two formulas and the new method to generate prime numbers accurately, the two formulas work as series of processes without any presumption. The paper enhances efforts in the field of theory of numbers, Author transforms the method that is proposed by him into programming language code written in C++ and the code is so easy to implement, execute and develop.
In this research we set a functional equation of Jensen type which comes from the so called Jensen m-convex inequality. We formulate and prove properties of its solutions and give a characterization of them under certain conditions as well. To close the article we have added a section on stability of this type of functional equation, which initially contains some results based on the work from Z. Kominek and nally a result supported on ideas from S. Jung.
Nowadays people are becoming increasingly dependent on wireless networks. Taking precautions and acting in advance to avoid problems of wireless networks have already shown great importance. In analyzing problems of wireless telecommunication systems, current methods mainly rely on structured data, like alarm data. Compared with structured data, log data are more abundant and recently implemented to detect problems of wireless telecommunication systems. In order to predict future problems, it becomes essential to predict future log data based on current log data. In the paper, we propose a novel method to predict log data of the wireless telecommunication system based on a sequence-to-sequence model. We use current logs as input, and generate future log with our model. In addition we discuss the effects of different parameters of our model through some experimental results.