On the ternary complex analysis and its applications

Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are given, and in particuler one type of holomorphic function gives rise to a new form of stationary magnetic field. The movement of a monopole type object in this field is then studied and shown to be integrable. The monopole scattering in the ternary field is finally studied.Comment: LaTeX 28 page

Differential psychophysiological interactions of insular subdivisions during varied oropharyngeal swallowing tasks

Abstract The insula is a highly integrated cortical region both anatomically and functionally. It has been shown to have cognitive, social–emotional, gustatory, and sensorimotor functions. Insular involvement in both normal and abnormal swallowing behavior is well established, yet its functional connectivity is unclear. Studies of context‐dependent connectivity, or the connectivity during different task conditions, have the potential to reveal information about synaptic function of the insula. The goal of this study was to examine the functional connectivity of specific insular regions (ventral anterior, dorsal anterior, and posterior) with distant cortical regions during four swallowing conditions (water, sour, e‐stim, and visual biofeedback) using generalized psychophysiological interactions (gPPI). In 19 healthy adults, we found that the visual biofeedback condition was associated with the most and strongest increases in functional connectivity. The posterior insula/rolandic operculum regions had the largest clusters of increases in functional connectivity, but the ventral anterior insula was functionally connected to a more diverse array of cortical regions. Also, laterality assessments showed left lateralized increases in swallowing functional connectivity. Our results are aligned with reports about the insula's interconnectivity and extensive involvement in multisensory and cognitive tasks

Observation of resonant interactions among surface gravity waves

We experimentally study resonant interactions of oblique surface gravity waves in a large basin. Our results strongly extend previous experimental results performed mainly for perpendicular or collinear wave trains. We generate two oblique waves crossing at an acute angle, while we control their frequency ratio, steepnesses and directions. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory with no fitting parameter. Off-resonance experiments are also reported and the relevant theoretical analysis is conducted and validated.Comment: 11 pages, 7 figure