In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential repres...

Imaginary Interfaces are screen-less ultra-mobile interfaces. Previously we showed that even though they offer no visual feedback they allow users to interact spatially, e.g., by pointing at a location on their non-dominant hand. The primary goal of this paper is to provide a deeper understanding of palm-based imaginary interfaces, i.e., why they work. We perform our exploration using an intera...

Understanding the Spectral Induced Polarization (SIP) response to saturation is required to improve application of this geophysical technique in the vadose zone. SIP measurements (0.11000 Hz) were conducted on three unconsolidated sediments during evaporative drying. Sample grain size distribution was determined from laser particle size diffraction measurements. The dependence of the real and i...

The objective of this study is to find the temperature distribution of a slab as it moves through the pusher-type preheat furnaces. First, the imaginary planes method (IPM) as a new and applicable method for calculation of radiation heat transfer in industrial furnaces is studied, and the two-dimensional form of this method is used to calculate heat flux and temperature distribution in the furn...

This note provides the connection between the paper “Absolute stability analysis for negative-imaginary systems” and classical results in absolute stability. Strictly negative-imaginary systems satisfy the Aizerman conjecture.