Location problems have been the focus of considerable attention both in research and practice for many years. Numerous extensions have been described to broaden its appeal and enhance its applicability. This study proposes a spreadsheet approach for three well-known facility location problems, the p-median problem (PMP), capacitated p-median (CPMP), and maximal covering location problem (MCLP)....

We study a conjectural formula for the maximal elements in wavefront set associated with theta representation of covering group over p-adic fields. In particular, it is shown that agrees existing work literature various families groups. also recapitulate results an analogous archimedean case, which motivated setting.

Covering models have found many applications in a wide variety of real-world problems; nevertheless, some assumptions of covering models are not realistic enough. Accordingly, a general approach would not be able to answer the needs of encountering varied aspects of real-world considerations. Assumptions like the unavailability of servers, uncertainty, and evaluating more factors at the same ti...

Let the lattice Λ have covering radius R, so that closed balls of radius R around the lattice points justcover the space. The covering multiplicity CM(Λ) is the maximal number of times the interiors of theseballs overlap. We show that the least possible covering multiplicity for an n-dimensional lattice is n ifn ≤ 8, and conjecture that it exceeds n in all other cases. We determine ...

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

We study the coordinate ring of an $L$-convex polyomino, determine its regularity in terms maximal number rooks that can be placed polyomino. also characterize Gorenstein polyominoes and those which are on punctured spectrum, compute Cohen–Macaulay type any polyomino rectangles covering it. Though main results algebraic nature, all proofs combinatorial.