Related papers: Trigonometric functions in the $p$-norm

This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…

Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…

A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space…

Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…

Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.

We study the eigenvalues and eigenfunctions of the Laplacian $\Delta_{\mu}=\frac{d}{d\mu}\frac{d}{dx}$ for a Borel probability measure $\mu$ on the interval $[0,1]$ by a technique that follows the treatment of the classical eigenvalue…

In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these…

Let T be a triangulation of a simple polygon. A flip in T is the operation of removing one diagonal of T and adding a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the…

Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two…

Let $x$ and $y$ be two unit vectors in a normed plane $\mathbb{R}^2$. We say that $x$ is Birkhoff orthogonal to $y$ if the line through $x$ in the direction $y$ supports the unit disc. A B-measure (Fankh\"anel 2011) is an angular measure…

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…

A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…

Corresponding to the concept of $p$-angular distance $\alpha_p[x,y]:=\left\lVert\lVert x\rVert^{p-1}x-\lVert y\rVert^{p-1}y\right\rVert$, we first introduce the notion of skew $p$-angular distance $\beta_p[x,y]:=\left\lVert \lVert…

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…

This paper presents a unified metric-based framework for triangle geometric inequalities using barycentric coordinates. By interpreting classical inequalities as squared distances between points(a process termed metricization)we derive and…

One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…

It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…