Partial data inverse problems for Maxwell equations via Carleman estimates

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim–Uhlmann and Kenig–Sjöstrand–Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.     

SOME COMBINATORIAL GEOMETRY FOR CONVEX QUADRILATERALS

Any nine points in the plane, no three collinear, contain the vertices of two nonintersecting convex quadrilaterals. Extensions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Big data analytics: an aid to detection of non-technical losses in power utilities

Computational Management Science - The great amount of data collected by the Advanced Metering Infrastructure can help electric utilities to detect energy theft, a phenomenon that globally costs...     

Lie completion of pseudo-groups

By far the most important class of pseudo-groups, both for theory and in essentially all applications, are the Lie pseudo-groups. In this paper we propose a definition of the Lie completion of a regular pseudo-group, and establish some of its basic properties. In particular, a pseudo-group and its Lie completion have exactly the same differential invariants and invariant differential forms. Thus, for practical purposes, one can exclusively work within the category of Lie pseudo-groups.     

Differential Equations in Engineering Courses

This paper formed part of a research project carried out by the author into the mathematical education of engineers.¹ In this part of the work an attempt was made to assess the relative importance of various aspects of ordinary differential equations in the teaching of engineering students and to find out which types of equations were used in the various engineering disciplines. A questionnaire was circulated and the replies were collated to give the results.     

Strong Ground‐ and Excited‐State Charge Transfer in C3‐Symmetric Truxene‐Derived Phenothiazine‐Tetracyanobutadine and Expanded Conjugates

The C₃‐symmetric star‐shaped phenothiazene‐substituted truxene 1 was reacted with the electron acceptors tetracyanoethylene (TCNE) and 7,7,8,8‐tetracyanoquinodimethane (TCNQ). The cycloaddition–retroelectrocyclization reaction yields the conjugates 2 and 3 . A combination of spectral, electrochemical, and photophysical investigations of 2 and 3 reveals that the functionalization of the triple bond has a pronounced effect on their ground and excited‐state interactions. Specifically, the existence of strong ground‐state interactions between phenothiazine and the electron‐accepting groups results in charge‐transfer states, while subsequent ultrafast charge separation yields electron transfer products. This is unprecedented not only in phenothiazine chemistry but also in tetracyanobutadiene‐ and dicyanoquinodimethane‐derived donor–acceptor conjugates. Additionally, by manipulating spectroelectrochemical data, a spectrum of the charge‐separated species is construed for the first time, and shown to be highly useful in interpreting the rather complex transient spectra.