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Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…

Contour integration is a crucial technique in many numeric methods of interest in physics ranging from differentiation to evaluating functions of matrices. It is often important to determine whether a given contour contains any poles or…

We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for…

We show that a function is real analytic at the origin iff it is arc-analytic, has a subanalytic graph, and its restriction to every monomial curve is analytic. This complements recent results of Kucharz and Kurdyka.

Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…

For a function defined on an arbitrary subset of a Riemann surface, we give conditions which allow the function to be extended conformally. One folkloric consequence is that two common definitions of an analytic arc in ${\mathbb C}$ are…

Let C be real-analytic simple closed curve in the complex plane which is symmetric with respect to the real axis. Let r>0 be such that C+ir misses C-ir. We prove that if a continuous function f extends holomorphically from C+it for each t…

In parameter slices of quadratic rational functions, we identify arcs represented by matings of quadratic polynomials. These arcs are on the boundaries of hyperbolic components.

Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic.…

In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a…

A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…

We show that an arc-analytic subanalytic function on a complex manifold M, which is holomorphic near one point, is a holomorphic function on M. More generally, an arc-analytic subanalytic function on a real analytic CR-manifold M, which is…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…

In this work we study a problem about analytic continuation along parallel algebraic curves.

For any locally analytic curve we show that arc length can be complexified and seen as a conformal parameter. As an application, we show that any such curve defines a unique maximal one and that the notions of analytic Jordan curve…

The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…

There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What…

Under some assumptions, an analytic expression for the transmission spectrum can be obtained, which can form the basis of atmospheric retrievals and allows insight on the degeneracies involved. In this Research Note we present an…

This paper revisits the fundamental mathematics of Taylor series to approximate curves with function representation and arc-length-based parametric representation. Parametric representation is shown to preserve its form in coordinate…