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At least 937 records · Page 52

Minimal Time Problem with Impulsive Controls

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Splenic Pregnancy: A New Minimally Invasive Approach to Treatment

The spleen is a rare site of abdominal ectopic pregnancy. In a review of the literature, we found 16 published cases of primary splenic pregnancies. Of the cases identified, all received surgical intervention, with one case successfully treated with laparoscopic methotrexate injection, and the rest underwent splenectomy. We would like to present a case of primary splenic pregnancy in a 35-year-old woman successfully treated with percutaneous image-guided injection of methotrexate and KCl.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗

Optimized Viewing Techniques to Minimize Radiation Damage From X-ray Imaging Systems

X-ray inspection of ball grid arrays (BGAs) is typically performed at one or more viewing angles to examine adhesion sites for errors such as voids, joint cracking, or head-in-pillow. During this inspection process, the cir cuit board assembly is subject to ionizing radiation exposure, which can cause trapped charge within oxide layers of semiconductor devices. Some x-ray machines allow for programmable inspection routines, which could be used to optimize radiation exposure to semiconductor components. Using Monte Carlo methods, x-ray inspection of a BGA was simulated to determine a range of acceptable viewing angles. Dose rates to circuit board components were estimated at each inspection angle to determine the view resulting in optimized radiation exposure. Results showed that for each BGA, the maximum unobstructed viewing times without exceeding a 5 Gy dose limit to a single part ranged from 82 to 94 minutes. Using a radiation cost function method, optimized viewing across all components was found. Here, it was observed that for a consistent dose limit applied to silicon-based components, performing inspection with BGAs facing the x-ray source was optimal. A third method was applied, assigning individual dose limits based on empirical data from the NASA Goddard Space Flight Center radiation database. This method showed that optimized viewing maximizes the distance between the radiation source and highly sensitive components. It was also observed that cumulative effects from viewing two BGAs will influence viewing angles, causing the optimal view of one BGA to exist nearly 180° from the other.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

On the Ultrasolvability of Some Classes of Minimal Nonsplit p-Extensions with Cyclic Kernel for p > 2

For any nonsplit p > 2-extension of finite groups with a cyclic kernel and a quotient group with two generators all the accompanying extensions of which split, there exists a realization of the quotient group as a Galois group of number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions).

97 MATHEMATICS AND COMPUTING↗

A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace

In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.

36 MATERIALS SCIENCE↗

Strategies for Minimizing Occupational Radiation Exposure in Cardiac Imaging

Purpose of Review: Radiation safety has been at the center of interest of both researchers and healthcare institutions. This review will summarize and shed light on the various techniques adapted to reduce staff exposure to ionizing radiation (IR) in the field of cardiac imaging. Recent Findings: In the last years, with the advance of awareness and the development of new technologies, there have been several tools and techniques adapted. The breakthrough of several technologies to lower radiation dose and shorten the duration of diagnostic tests associated with IR, the use of protection devices by staff members, and mostly the awareness of exposure to IR are the hallmark of these advances. Using all these measures has led to a significant decrease in staff exposure to IR. Summary: Reducing staff exposure to meet the “As Low As Reasonably Achievable” principle is feasible. This review introduces the most important strategies applied in cardiac imaging.

61 RADIATION PROTECTION AND DOSIMETRY↗

Compressible fluids with Maxwell-type equations, the minimal coupling with electromagnetic field and the Stefan–Boltzmann law

In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac’s constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge condition were obtained. The path integral formalism was used to obtain the partition function for the corresponding higher-derivative Hamiltonian and the Faddeev–Popov ansatz was used to construct an effective Lagrangian. Through the partition function, a Stefan–Boltzmann type law was obtained. - Highlights: • Higher-derivative Lagrangian for a charged fluid. • Electromagnetic coupling and Dirac’s constraint analysis. • Partition function through path integral formalism. • Stefan–Boltzmann-kind law through the partition function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Inflationary universe in the presence of a minimal measurable length

In this paper, we will study the effect of having a minimum measurable length on inflationary cosmology. We will analyze the inflationary cosmology in the Jacobson approach. In this approach, gravity is viewed as an emergent thermodynamical phenomena. We will demonstrate that the existence of a minimum measurable length will modify the Friedmann equations in the Jacobson approach. We will use this modified Friedmann equation to analyze the effect of minimum measurable length scale on inflationary cosmology. This analysis will be performed using the Hamiltonian-Jacobi approach. We compare our results to recent data, and find that our model may agree with the recent data. - Highlights: • We study the inflationary cosmology in the Jacobson thermodynamic approach. • We analyze the short distance correction to inflation from a minimum measurable length. • This analysis is done using the Hamiltonian-Jacobi approach. • This model of inflationary cosmology is consistent with the observational data.

79 ASTRONOMY AND ASTROPHYSICS↗