This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermore, providing the necessary condition for α-feebly normality property to become hereditary. Also, using a new topological model for graphs are the edges represented as points which enables us to express in a topological language about combinatorial concepts. Moreover, showing that an α-connected orderable spaces are exactly α-topologized graphs. Finally, realizing the relationship between the α-topology on the vertex set and the once on the whole space by α-feebly regularity property.
SOME ALPHA-TOPOLOGICAL CONCEPTS USING GRAPH THEORY
α-feebly Hausdorff
α-feebly regular
α-feebly normal
α-connected orderable spaces
α-topologized graphs.
Publication Date
Fri Mar 01 2019
Journal Name
Applied Acoustics
Theoretical model of absorption coefficient of an inhomogeneous MPP absorber with multi-cavity depths
Micro-perforated panel (MPP) absorber has been known as an alternative absorber to classical porous material given its facile installation
long durability
environmental friendliness and attractive appearance. Extensive studies of MPP absorber proposing the improvement of its absorption frequency bandwidth have been published. This study presents a MPP absorber introduced with inhomogeneous perforations and with multi-cavity depths. The MPP is divided into two sub-area
where each area has different hole diameter
perforation ratio and a separated backed cavity depth. The acoustic impedance is modelled using electrical equivalent circuit and the absorption coefficient is calculated under normal-incidence of sound. It is found that the inhomogeneous MPP can have good bandwidth of absorption by designing the sub-MPP of smaller perforation ratio with large hole diameter and the one having the larger perforation ratio with smaller hole diameter. The absorption bandwidth can be conveniently controlled by adjusting the cavity depth of each sub-MPP. The results from the experimental work show good agreement with the theoretical model.
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