A personal, distributed exposimeter: procedure for design, calibration, validation, and application

This paper describes, for the first time, the procedure for the full design, calibration, uncertainty analysis, and practical application of a personal, distributed exposimeter (PDE) for the detection of personal exposure in the Global System for Mobile Communications (GSM) downlink (DL) band around 900 MHz (GSM 900 DL). The PDE is a sensor that consists of several body-worn antennas. The on-body location of these antennas is investigated using numerical simulations and calibration measurements in an anechoic chamber. The calibration measurements and the simulations result in a design (or on-body setup) of the PDE. This is used for validation measurements and indoor radio frequency (RF) exposure measurements in Ghent, Belgium. The main achievements of this paper are: first, the demonstration, using both measurements and simulations, that a PDE consisting of multiple on-body textile antennas will have a lower measurement uncertainty for personal RF exposure than existing on-body sensors; second, a validation of the PDE, which proves that the device correctly estimates the incident power densities; and third, a demonstration of the usability of the PDE for real exposure assessment measurements. To this aim, the validated PDE is used for indoor measurements in a residential building in Ghent, Belgium, which yield an average incident power density of 0.018 mW/m(2)

A partial differential equation for the strictly quasiconvex envelope

In a series of papers Barron, Goebel, and Jensen studied Partial Differential Equations (PDE)s for quasiconvex (QC) functions \cite{barron2012functions, barron2012quasiconvex,barron2013quasiconvex,barron2013uniqueness}. To overcome the lack of uniqueness for the QC PDE, they introduced a regularization: a PDE for \e-robust QC functions, which is well-posed. Building on this work, we introduce a stronger regularization which is amenable to numerical approximation. We build convergent finite difference approximations, comparing the QC envelope and the two regularization. Solutions of this PDE are strictly convex, and smoother than the robust-QC functions.Comment: 20 pages, 6 figures, 1 tabl

All the lowest order PDE for spectral gaps of Gaussian matrices

Tracy-Widom (TW) equations for one-matrix unitary ensembles (UE) (equivalent to a particular case of Schlesinger equations for isomonodromic deformations) are rewritten in a general form which allows one to derive all the lowest order equations (PDE) for spectral gap probabilities of UE without intermediate higher-order PDE. This is demonstrated on the example of Gaussian ensemble (GUE) for which all the third order PDE for gap probabilities are obtained explicitly. Moreover, there is a {\it second order} PDE for GUE probabilities in the case of more than one spectral endpoint. This approach allows to derive all PDE at once where possible, while in the method based on Hirota bilinear identities and Virasoro constraints starting with different bilinear identities leads to different subsets of the full set of equations.Comment: 22 pages, references corrected, remark adde

Teaching Partial Differential Equations with CAS

Partial Differential Equations (PDE) are one of the topics where Engineering students find more difficulties when facing Math subjects. A basic course in Partial Differential Equations (PDE) in Engineering, usually deals at least, with the following PDE problems: 1. Pfaff Differential Equations 2. Quasi-linear Partial Differential Equations 3. Using Lagrange-Charpit Method for finding a complete integral for a given general first order partial differential equation 4. Heat equation 5. Wave equation 6. Laplace’s equation In this talk we will describe how we introduce CAS in the teaching of PDE. The tasks developed combine the power of a CAS with the flexibility of programming with it. Specifically, we use the CAS DERIVE. The use of programming allows us to use DERIVE as a Pedagogical CAS (PECAS) in the sense that we do not only provide the final result of an exercise but also display all the intermediate steps which lead to find the solution of a problem. This way, the library developed in DERIVE serves as a tutorial showing, step by step, the way to face PDE exercises. In the process of solving PDE exercises, first-order Ordinary Differential Equations (ODE) are needed. The programs developed can be grouped within the following blocks: - First-order ODE: separable equations and equations reducible to them, homogeneous equations and equations reducible to them, exact differential equations and equations reducible to them (integrating factor technique), linear equations, the Bernoulli equation, the Riccati equation, First-order differential equations and nth degree in y’, Generic programs to solve first order differential equations. - First-order PDE: Pfaff Differential Equations, Quasi-linear PDE, Lagrange-Charpit Method for First-order PDE. - Second-order PDE: Heat Equation, Wave Equation, Laplace’s Equation. We will remark the conclusions obtained after using these techniques with our Engineering students.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense

In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative. We give generalized definition and theorem for the symmetry method for PDE with Caputo fractional derivative, according to Bluman's definition and theorem for the symmetry analysis of PDE system. We investigate the symmetry analysis of initial and boundary value problem for fractional diffusion and the third order fractional partial differential equation (FPDE). Also we give some solutions