Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Semi-active damping using a hybrid control approach

In this article, a hybrid control framework is used to design semi-active controllers for vibration reduction. It is shown that the semi-active skyhook damper, typically used for vibration reduction, can be recast in the framework of an event-driven intermittent controller. By doing this, we can then exploit the well-developed techniques associated with hybrid control theory to design the semi-active control system. Illustrative simulation examples are based on a 2 degree-of-freedom system, often used to model the dynamics of a quarter car body model. The simulation results demonstrate how hybrid control design techniques can improve the overall performance of the semi-active control system

White light induced covalent modification of graphene using phenazine dye

Herein, we report a novel strategy for a covalent modification of graphene nanoplatelets with photoactive dyes. Functionalization of the graphene surface was carried out using white light to photochemically generate phenazine radicals and the reaction progress was followed up spectrophotometrically. Characterization of the modified material was carried out by FTIR, XRD, UV-vis absorption, fluorescence, Raman spectroscopy and SEM imaging. This hybrid material has improved solubility, shows an optical band gap of 1.95 eV and is highly emissive in the visible wavelength region

Tellurite glass as a solid-state mid-infrared laser host material

We present recent results on the material, spectroscopic and laser properties of a range of Tm³⁺, Tm³⁺-Ho³⁺ and Dy³⁺ doped tellurium oxide (TeO₂) based glasses in the 2-4 μm wavelength region.Department of Applied Physic

Tellurite glass as a solid-state mid-infrared laser host material

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Tm³⁺ Tellurite-Modified-Silica Glass Thin Films Fabricated Using Ultrafast Laser Plasma Doping

Thin glass films have been produced by implanting Tm³⁺ doped and Tm³⁺/Er³⁺ codoped tellurite glasses into silica substrates using ultrafast laser plasma doping for the first time. The resulting glass films had thicknesses of up to 2 µm, refractive indices of 1.5 – 1.65 and exhibited photoluminscence in the 1.5 – 2.1 µm wavelength region when excited with 808 nm and 976 nm laser diodes. The OH⁻ content of the silica glass substrate was also found to have an effect on the Tm³⁺: ³F₄ photoluminescence lifetime in the modified thin glass film layer, with the high OH⁻ containing substrate exhibiting a shorter lifetime. Through optimisation of the femtosecond laser ablation parameters, we have produced crack-free thin films of Tm³⁺ doped tellurite-modified silica glass layers with good thickness uniformities of ±10 nm, and the refractive index of the modified layer is up to 13% higher than the bare substrate material

Effect of age, impaction types and operative time on inflammatory tissue reactions following lower third molar surgery

<p>Abstract</p> <p>Background</p> <p>Postoperative mobidity following third molar surgery is affected by a number of factors. The study of these factors is essential for effective planning and limitation of morbidity. The aim of this study was to determine the effect of age, type of impaction and operative time on immediate postoperative tissue reactions following mandibular third molar surgery.</p> <p>Methods</p> <p>Consecutive patients with impacted mandibular third molar teeth were studied. All the third molars were classified according to Winter's classification. Surgical extraction was performed on all the patients by a single surgeon under local anaesthesia. The operation time was determined by the time lapse between incision and completion of suturing. Postoperative pain, swelling and trismus were evaluated.</p> <p>Results</p> <p>There were 120 patients with an age range of 19-42 years. Patients in the age range of 35-42 years recorded a lower pain score (p = 0.5) on day 1. The mouth opening was much better in the lower age group on day 2 and 5 (p = 0.007 and p = 0.01 respectively). Pain, swelling and trismus increased with increasing operative time. Distoangular impaction was significantly associated with higher VAS score on day 1 and 2 (p = 0.01, 0.0, 04). Distoangular and horizontal impaction are associated with a higher degree of swelling and reduced mouth opening on postoperative review days. Vertical impaction was associated with the least degree of facial swelling and best mouth opening.</p> <p>Conclusions</p> <p>Increasing operating time and advancing age are associated with more postoperative morbidity, likewise distoangular and horizontal impaction types.</p

High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. 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