This paper proposes and solves a new problem called spatial matching (SPM). Let P and O be two sets of objects in an arbitrary metric space, where object distances are defined according to a norm satisfying the triangle inequality. Each object in O represents a customer, and each object in P indicates a service provider, which has a capacity corresponding to the maximum number of customers that...

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automa...

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving wha...

The (negative) Torricelli triangle T1(ABC) of a nondegenerate (positively oriented) triangle ABC is defined to be the triangle A1B1C1, where ABC1, BCA1, and CAB1 are the equilateral triangles drawn outwardly on the sides of ABC. It is known that not every triangle is the Torricelli triangle of some initial triangle, and triangles that are not Torricelli triangles are characterized in [28]. In t...

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...