A nonassociative Groenewold–Moyal (GM) plane is constructed using quaternion-valued function algebras. The symmetrized multiparticle states, the scalar product, the annihilation/creation algebra and the formulation in terms of a Hopf algebra are also developed. Nonassociative quantum algebras in terms of position and momentum operators are given as the simplest examples of a framework whose applications may involve string theory and nonlinear quantum field theory.

One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in a radially symmetric, or angular invariant, manner. This generalization enables the Schrödinger equation solutions to be visualized for Bessel functions and Whittaker functions, and it also enables connections to multi-dimensional physics theories, like string theory.

This study analyzes the geometrical relationship between a classical string and its semiclassical quantum model. From an arbitrary (2+1)-dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical quantum model. In this framework, examples of quantum oscillations and quantum free particles are presented that uniquely determine a classical string and the space-time geometry where its motion takes place.

In the present work a systematic methodology for computing dynamic output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of Lur'e type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an \{LMI\} framework is proposed to design the controller. Asymptotic as well as input-to-state and input-to-output (in a L2 sense) stabilization problems are addressed both in regional (local) and global contexts. The controller structure is composed of a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed to compute the controller considering different optimization criteria. A numerical example illustrates the potentialities of the methodology.

BACKGROUND: Scarce information exists regarding the preventive effect of periodontal treatment in the recurrence of cardiovascular events. Prevention may be achieved by targeting risk factors for recurrent coronary artery disease (CAD) in patients with previous history of cardiovascular events. The aim of this trial is to compare the effect of two periodontal treatment approaches on levels of C-reactive protein, lipids, flow-mediated dilation and serum concentrations of proinflammatory and endothelial markers in stable CAD patients with periodontitis over a period of 12 months. METHODS/DESIGN: This is a randomized, parallel design, examiner blinded, controlled clinical trial. Individuals from both genders, 35 years of age and older, with concomitant diagnosis of CAD and periodontitis will be included. CAD will be defined as the occurrence of at least one of the following events 6 months prior to entering the trial: documented history of myocardial infarction; surgical or percutaneous myocardial revascularization and lesion >50% in at least one coronary artery assessed by angiography; presence of angina and positive noninvasive testing of ischemia. Diagnosis of periodontitis will be defined using the CDC-AAP case definition (>/=2 interproximal sites with clinical attachment loss >/=6 mm and >/=1 interproximal site with probing depth >/=5 mm). Individuals will have to present at least ten teeth present to be included. One hundred individuals will be allocated to test (intensive periodontal treatment comprised by scaling and root planing) or control (community periodontal treatment consisting of one session of supragingival plaque removal only) treatment groups. Full-mouth six sites per tooth periodontal examinations and subgingival biofilm samples will be conducted at baseline, 3, 6 and 12 months after treatment. The primary outcome of this study will be C-reactive protein changes over time. Secondary outcomes include levels of total cholesterol, LDL-C, HDL-C, triglycerides, IL-1beta, IL-6, TNFalpha, fibrinogen, ICAM-1, VCAM-1 and E-selectin. These outcomes will be assessed at all time points over 12 months. Flow-mediated dilation will be assessed at baseline, 1, 3 and 6 months after periodontal therapy. DISCUSSION: This trial will provide new evidence regarding the effect of periodontal treatment on risk markers for recurrence of cardiovascular events in stable coronary artery disease patients. TRIAL REGISTRATION NUMBER: ClinicalTrials.gov Identifier, NCT01609725.