Assessment of the temporomandibular joint condition using two-dimensional ultrasound scanning and doppler ultrasonography methods in patients with chronic inflammatory periodontal diseases

Introduction. Currently, dentists are increasingly detecting changes in the temporomandibular joint in patients with chronic inflammatory periodontal disease.Aim of the study. To carry out a comprehensive dynamic assessment of the temporomandibular joint (TMJ) condition and the registration of regional blood flow using two-dimensional ultrasound scanning to improve the efficiency of diagnostics of inflammatory periodontal diseases.Materials and methods. The study included 2 groups of patients: group 1 (control) consisted of 20 volunteers aged 20–25; Group 2 consisted of 52 people aged 25–45 years with moderate chronic periodontitis. For TMJ ultrasound and Doppler ultrasound, a portable ultrasound scanner LogicScan  128 with an HL-10  linear ultrasound transducer  with an operating frequency of 5     to 12 MHz was used.Results and discussion. During ultrasound examination of the temporomandibular joint and measuring the size of the joint space in patients with moderate chronic periodontitis in a state of relative physiological rest, the following  values were obtained:   in the anterior region – 2.3 ± 0.5 mm; in the upper section – 1.6 ± 0.6 mm; in the posterior section – 1.8 ± 0.3 mm. We also measured the area of the temporomandibular joint disc in various positions. According to ultrasound data, an increase in the size of the joint space from 12.2 to 16.1% and an increase in the area of the articular disc by 17.1 to 36.7% were found in patients with chronic periodontitis. When assessing the trajectory of the articular track, motion delay and joint wedging are determined. In addition, in the color Doppler mapping (CDM) mode, the speed and index indicators of Doppler ultrasonography of the external carotid and temporal arteries were calculated.Conclusions. Modern diagnostic methods of ultrasound and Doppler mapping, assessing the hemodynamics and functional state of the TMJ, allow early diagnosis of changes in order to prevent the development of TMJ disorders in patients with chronic inflammatory periodontal diseases

State constraints in the linear regulator problem: Case study

In this paper, we consider the problem of minimum-norm control of the double integrator with bilateral inequality constraints for the output. We approximate the constraints by piecewise linear functions and prove that the Langrange multipliers associated with the state constraints of the approximating problem are discrete measures, concentrated in at most two points in every interval of discretization. This allows us to reduce the problem to a convex finite-dimensional optimization problem. An algorithm based on this reduction is proposed and its convergence is examined. Numerical examples illustrate our approach. We also discuss regularity properties of the optimal control for a higher-dimensional state-constrained linear regulator problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45244/1/10957_2005_Article_BF02192567.pd

Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods

This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips

Search for additional neutral gauge bosons

We have searched for a heavy neutral gauge boson, Z′, using the decay channel Z′ → ee. The data were collected with the DØ detector at the Fermilab Tevatron during the 1992-1993 pp̄ collider run at √s = 1.8 TeV from an integrated luminosity of 15 ± 1 pb-1. Limits are set on the cross section times branching ratio for the process pp̄ → Z′ → ee as a function of the Z′ mass. We exclude the existence of a Z′ of mass less than 490 GeV/c2, assuming a Z′ with the same coupling strengths to quarks and leptons as the standard model Z boson