Consider a directed graph G in which every edge has an associated real-valued distance and a real-valued weight. The weight of an undirected circuit of G is the sum of the weights of the edges, whereas the distance of an undirected circuit is the sum of the distances of the forward edges of the circuit minus the sum of the distances of the backward edges. A trivial circuit is a two-edge circuit...

Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and b 6= 1, α = b − 1. The condition on α implies that Γ is formally self-dual. For b = q we use the adjacency matrix and dual adjacency matrix to obtain an action of the q-tetrahedron algebra ⊠q on the standard module of Γ. We describe four algebra homomorphisms into ⊠q from the quantum affine algebra Uq(ŝl2); using t...

We study variants of the Erd˝ os distance problem and the dot products problem in the setting of the integers modulo q, where q = p is a power of an odd prime.

Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is based on the Wasserstein distance of optimal transportation, which reflects the structure of the distance between random variables. Here, we propose a new i...

Based on a suitable improvement of triangle inequality, we derive new mutual bounds for p-angular distance $$\alpha _p[x,y]=\big \Vert x\Vert ^{p-1}x- y\Vert ^{p-1}y\big $$ , in normed linear space X. We show that our estimates are more accurate than the previously known upper established by Dragomir, Hile and Maligranda. Next, give several characterizations inner product spaces with regard to ...

The purpose of this manuscript is to develop a novel MAIRCA (Multi-Attribute Ideal-Real Comparative Analysis) method solve the MCDM (Multiple Criteria Decision-Making) problems with completely unknown weights in q-rung orthopair fuzzy (q-ROF) setting. Firstly, new concepts q-ROF Lance distance are defined and some related properties discussed paper, from which we establish maximizing deviation ...

Finding the minimum distance between two obstacles is very crucial for robot path planning and localization, especially for the cleaning and industrial robots. Knowledge of minimum distance is needed for a mobile robot to avoid the obstacles and have the efficient trajectory. This problem has been solved in many different ways. In this paper we present an approach to find the minimum distance b...

Q-resolution is a generalization of propositional resolution that provides the theoretical foundation for search-based solvers of quantified Boolean formulas (QBFs). Recently, it has been shown that an extension of Q-resolution, called long-distance resolution, is remarkably powerful both in theory and in practice. However, it was unknown how long-distance resolution is related to QRAT, a proof...

In this paper we determine the minimum distance of orthogonal line-Grassmann codes for q even. The case q odd was solved in [3]. We also show that for q even all minimum weight codewords are equivalent and that symplectic line-Grassmann codes are proper subcodes of codimension 2n of the orthogonal ones.

We consider the problem of finding all approximate occurrences of a given string q, with at most k differences, in a finite database or dictionary of strings. The strings can be e.g. natural language words, such as the vocabulary of some document or set of documents. This has many important application in both offline (indexed) and on-line string matching. More precisely, we have a universe U o...