The accurate selection of a processing plant site can result in decreasing total mining cost. This problem can be solved by multi-criteria decision-making (MCDM) methods. This research introduces a new approach by integrating fuzzy AHP and gray MCDM methods to solve all decision-making problems. The approach is applied in the case of a copper mine area. The critical criteria are considered adja...

In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

Given an edge-labeled graph, context-free language reachability (CFL-reachability) computes reachable node pairs by deriving new edges and adding them to the graph. The redundancy that limits scalability of CFL-reachability manifests as redundant derivations, i.e., identical can be derived multiple times due many paths between two nodes. We observe most arises from derivations involving transit...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes whose graphs (1-skeletons) contain the TSP polytope graphs as spanning subgraphs. While deciding adjacency of vertices in TSP polytopes is coNP-complete, Arthanari has given a combinatorial (polynomially decidable) characterization of adjacency in Pedigree polytopes. Based on this characterization,...

Pseudo noun incorporation constructions in Sakha and Tamil obey a strict linear adjacency condition, such that not only the NP but its head noun must be adjacent to the verb at PF. I argue that this adjacency condition can be explained if the head of the NP adjoins to the verb to create a unit that is interpreted as a complex predicate at LF. The resulting structure can be linearized at PF if a...

Let D be a division ring and let m,n be integers ≥ 2. Let Mm×n(D) be the space of m × n matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings φ of Mm×n(D) are determined such that both φ and φ−1 preserve adjacency. We show that if a bijective map φ of Mm×n(D) preserves the adjacency then also φ −1 preserves the adjacency. Thus the supposition that φ...

In this paper, we explore what happens when the same techniques are applied to the problem of estimating eigenvalues of the adjacency operator on finite graphs of bounded degree. In Theorem 7, we show how eigenvalues of the adjacency operator on a finite graph Γ may be bounded in terms of the biggest eigenvalues of the adjacency operator on “geodesic balls” in Γ. We find explicit bounds for the...

this article studies sir walter scott’s use of the family-as-nation trope in ivanhoe and anne of geierstein. the importance of this trope in his figuration of nationhood is discerned by carrying out a close reading of the texts and placing them in their historical context, which primarily consists of a comparison with edmund burke and maria edgeworth. consequently, his position is revealed as b...

One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenva...