An orthogonality space is a set equipped with symmetric, irreflexive relation called orthogonality. Every has an associated complete ortholattice, the logic of space. To every poset, we associate consisting proper quotients (that means, nonsingleton closed intervals), certain relation. We prove that finite bounded poset lattice if and only its orthomodular lattice. chain Boolean algebra.

We will prove that the path minimizes the number of closed walks of length l among the connected graphs for all l. Indeed, we will prove that the number of closed walks of length l and many other properties such as the spectral radius, Estada index increase or decrease along a certain poset of trees. This poset is a leveled poset with path as the smallest element and star as the greatest element.

Suppose P is a partially ordered set that is locally finite, has a least element, and admits a rank function. We call P a weighted-relation poset if all the covering relations of P are assigned a positive integer weight. We develop a theory of covering maps for weighted-relation posets, and in particular show that any weighted-relation poset P has a universal cover P̃ → P , unique up to isomorph...

As a result of the widespread industrial use of polychlorinated hydrocarbons, they have accumulated in nearly all types of environmental compartments, especially in aquatic systems. Particularly, chloroaromatics are among the most undesirable industrial effluents because of their persistence and toxicity. To predict chlorobenzene (CB) toxicities, we make use of a novel scheme that looks beyond ...