The 3D graph approach for breakdown voltage calculation in BaTiO3 ceramics

After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

Universal Scientific Database

Science is about connections. A very suitable application of mathematical graph theory can be accomplished for tracking all the human scientific knowledge.

Graph Theory for Temporal Structure

This chapter introduces mathematical graph theory and develops graph-theory concepts that are useful for temporal networks. By generating chord progressions from networks, the potential musical and temporal meaning of graph-theory concepts, especially cycles, is emphasized. A number of concepts related to trees are introduced to show hierarchical aspects of temporal structure, and to allow for a comparison of Fred Lerdahl and Ray Jackendoff’s prolongational trees to temporal structures. This suggests an enrichment of MOPs through spanning trees, and is channelled into a discussion of graph-theoretic algebras, cycle and edge-cut algebras, as they apply to temporal structures.

MODELLING OF TWO STAGES DNA SPLICING LANGUAGES ON DE BRUIJN GRAPH

Finding the sequence of the genome from its compositions as well as a mathematical graph is the most interesting topic in a field of DNA molecular. Since lack of technology is the big obstacle that biologists are facing to read a long sequence of the genome from beginning up to the end, therefore finding the compositions of the genome having very long sequence and also its description via de Bruijn graph is challenging or even impossible. In this paper, Yusof-Goode (Y-G) approach is used to generate the DNA splicing languages based on cutting sites of initial strings (one or two cutting sites) and crossing and contexts factors of restriction enzymes. The two short sequences of DNA (8bp) and two restriction enzymes are considered to create a connection between mathematics and DNA molecular. This relation will be presented as de Bruijn graph so that every edge of the de Bruijn graph gives a k-mer composition of DNA molecule and also each path of the de Bruijn graph gives a DNA sequence and vice-versa. Besides, the persistency and permanency of two stages DNA splicing languages can be predicted using this model.