Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces

In this paper, we prove the existence of a renormalized solution for the quasilinear Riccati-type equation with low integrability-measure data in Lorentz spaces. The result is established in both regular and singular cases. Our proof is based on the gradient estimates for a solution to a class of quasilinear elliptic equations.     

Robust FIPP p-cycles against dual link failures

We propose a new generic flow formulation for Failure-Independent Path-Protecting (FIPP) p-cycles subject to multiple failures. While our new model resembles the decomposition model formulation proposed by Orlowski and Pioro (Networks, 2011) in the case of classical shared path protection, its originality lies in its adaptation to FIPP p-cycles. When adapted to that last pre-configured pre-cross connected protection scheme, the bandwidth sharing constraints must be handled in a different way in order to take care of the sharing along the FIPP p-cycles. It follows that, instead of a polynomial-time solvable pricing problem as in the model of Orlowski and Pioro (Networks, 2011), we end up with a much more complex pricing problem, which has an exponential number of constraints due to some subtour elimination constraints. Consequently, in order to efficiently solve the pricing problem, we consider: (i) a hierarchical decomposition of the original pricing problem; (ii) heuristics in order to go around the large number of constraints in the pricing problem. Performance evaluation is made in the case of FIPP p-cycles subject to dual failures. For small to medium size networks, the proposed model remains fairly scalable for increasing percentages of dual failures, and requires much less bandwidth than p-cycle protection schemes (ratio varies from 2 to 4). For larger networks, heuristics are required in order to keep computing times reasonable. In the particular case of single link failures, it compares very favorably (5 to 10 % of bandwidth saving) to the previously proposed column generation ILP model of Rocha, Jaumard and Stidsen (Telecommun. Syst., 2012).     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Morley’s trisector Theorem for isosceles tetrahedron

We extend Morley’s trisector theorem in the plane to an isosceles tetrahedron in three-dimensional space. We will show that the Morley tetrahedron of an isosceles tetrahedron is also isosceles tetrahedron. Furthermore, by the formula for distance in barycentric coordinate, we introduce and prove a general theorem on an isosceles tetrahedron.

     

Atomic spectroscopy with surface wave plasmas

The use of microwave induced plasmas, particularly of surface wave plasmas, as detectors in atomic emission spectrometry for elemental analysis is reviewed. Surface wave plasmas have been produced at low HF power and used as gas chromatographic detectors. The analytical performances for the detection of non-metals with a Fourier transform spectrometer and a two-channel filter unit are reported. The excitation behavior of non-metals in helium-based mixed gas-plasmas has also be studied. In particular, the effect of power and of nitrogen concentration on the bromine emission has been systematically investigated. A nine-fold improvement of the detection limits for bromine can be obtained in a high power (900 W) helium-nitrogen (0.1–0.2%) plasma.     

Modified broadside-coupled microstrip lines suitable for MIC andMMIC applications and a new class of broadside-coupled band-pass filters

Modified broadside-coupled microstrip lines, suitable for microwave and millimeter-wave integrated and monolithic integrated circuit (MIC and MMIC) applications requiring wide bandwidths and tight couplings, are presented. Their analysis, based on the quasi-static spectral domain technique, is described. Using these broadside structures, a new class of broadside-coupled band-pass filters has been developed at X-band (8-12 GHz) with about 1-dB insertion loss. Fair agreement between the measured and calculated results has been observed even though a major approximation is used     

An improved pulse-basis conjugate gradient FFT method for the thinconducting plate problem

A conjugate-gradient fast Fourier transform (CG-FFT) formulation for the scattering by a thin, perfectly conducting plate is presented. Pulse basis functions and a Dirac δ function are used for expansion and testing purposes, respectively. Particular attention is paid to the generation of the terms in the impedance matrix of the resulting matrix equation. Except for the self-coupling terms, all the other terms are computed by explicit integrations. Comparison with two previously reported pulse-basis CG-FFT formulations shows that the present method is more stable when the error tolerance of the solution is reduced. When sufficient cell discretizations are used, smooth distributions can be obtained which resemble those obtained via rooftop-CG-FFT formulation. The numerical results are further validated by comparing the far-field radar cross section with an analytical technique for a circular plate     

Measurement of the electric field pattern of a Fabry-Perot resonator used in quasi-optical gyrotrons

The field pattern of the resonator used in a quasi-optical gyrotron operating in the millimetre wave range is measured. Two resonators are studied: one composed of a spherical mirror and an ellipsoidal grating and the other symmetric using two mirrors with annular slots. The measurements indicate that the electric field distribution is gaussian, in spite of the complex geometry of the resonator, and thus provide an experimental basis for the assumption often used to compute the efficiency of quasi-optical gyrotrons.