There are several sections. The goal is to link complex analysis and imbeddings of graphs so that graph imbeddings can be performed systematically using identification spaces based on group actions in the complex plane. We give a short primer of basic calculus and then explain some of the finer aspects that obfuscate a complete solution to the Riemann Hypothesis. This is not central to our main...

in this paper, a novel matched filter based on a new kernel function with cauchy distribution is introduced to improve the accuracy ofthe automatic retinal vessel detection compared with other available matched filter‑based methods, most notably, the methods builton gaussian distribution function. several experiments are conducted to pick the best values of the parameters for the new designedfi...

We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: ut = J ∗u−u , where J is a symmetric continuous probability density. Depending on the tail of J , we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a su...

Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two disciplines has so far been neglected, a situation this paper is meant to remedy. As the role of the Cauchy completion is relevant for both effective approa...

In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions Gλ which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these functions in analogy with Schur functions. In particular we will describe: • a Pieri and dual-Pieri formula for ribbon functions, • a ribbon Murnagham-Nakayama formula, • ribbon Cauchy and dual Cauchy identities, • and...

In this paper, the inverse Cauchy problem for Laplace equation defined in an arbitrary plane domain is investigated by using the collocation Trefftz method (CTM) with a better postconditioner. We first introduce a multiple-scale Rk in the T-complete functions as a set of bases to expand the trial solution. Then, the better values of Rk are sought by using the concept of an equilibrated matrix, ...

In this paper, the inverse Cauchy problem for Laplace equation defined in an arbitrary plane domain is investigated by using the collocation Trefftz method (CTM) with a better postconditioner. We first introduce a multiple-scale Rk in the T-complete functions as a set of bases to expand the trial solution. Then, the better values of Rk are sought by using the concept of an equilibrated matrix, ...

We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps. Analytically, these situations can be described through a system of ordinary differential equations coupled with a scalar conservation law in several space dimensions. This paper provides a complete well posedne...