Related papers: Mobility spaces and their geodesic paths
We introduce an algebraic system which can be used as a model for spaces with geodesic paths between any two of their points. This new algebraic structure is based on the notion of mobility algebra which has recently been introduced as a…
We begin by introducing an algebraic structure with three constants and one ternary operation to which we call mobi algebra. This structure has been designed to capture the most relevant properties of the unit interval that are needed in…
The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spaces with geodesic paths. In this paper we analyse the…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Membrane computing is a well-established and successful research field which belongs to the more general area of molecular computing. Membrane computing aims at defining parallel and non-deterministic computing models, called membrane…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de…
Two pseudo-Riemannian metrics are called projectively equivalent if their unparametrized geodesics coincide. The degree of mobility of a metric is the dimension of the space of metrics that are projectively equivalent to it. We give a…
We introduce a basic model for human mobility that accounts for the different dynamics arising from individuals embarking on short trips (and returning to their home locations) and individuals relocating to a new home. The differences…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
An orthoset (also called an orthogonality space) is a set $X$ equipped with a symmetric and irreflexive binary relation $\perp$, called the orthogonality relation. In quantum physics, orthosets play a central role. In fact, a Hilbert space…
Human mobility is a fundamental process underpinning socioeconomic life and urban structure. Classic theories, such as egocentric activity spaces and central place theory, provide crucial insights into specific facets of movement, like…
We introduce \textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for $Y$-oriented trivalent spatial graphs and…
From small steps to great leaps, metaphors of spatial mobility abound to describe discovery processes. Here, we ground these ideas in formal terms by systematically studying scientific knowledge mobility patterns. We use low-dimensional…
The configuration space of a mechanical linkage, consisting of rigid bodies moving in space constrained by joints, is defined by algebraic conditions. If these equations do not define a complete intersection, then the dimension of the…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n)…
We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks. The open walk area is defined by closing the walks with a…