Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

The Chang-Łoś-Suszko theorem in a topological setting

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.     

Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

A Language for Teaching Discrete-event Simulation

Courses which teach discrete-event simulation are based on many different simulation languages. The requirements for a language to support teaching simulation are discussed. In particular, it is recommended that such languages separate into distinct modules those aspects of simulation which are taught as separate topics. Implementation of the separation is discussed. The SEESIM language, developed as a teaching aid, is described, and examples of its use are given. Straightforward use of SEESIM can be learned quickly, yet the language provides facilities for a staged introduction to advanced concepts of simulation.     

The study and applications of photochemical-dynamical gravity wave model I

A two-dimensional, nonlinear, compressible, diabatic, nonhydrostatic photochemical-dynamical gravity wave model has been advanced. The model includes diabetic process produced by photochemistry and the effect of gravity wave on atmospheric chemical species. In the horizontal direction, the pseudospectral method is used. The finite difference approximations are used in vertical direction z and time t. The FICE method is used to solve the model. The model results on small amplitude fluctuation are very close to those of linear theory, which demonstrates the correctness of the model.

     

Pediatric Laryngotracheal Stenosis and Airway Reconstruction: A Review of Voice Outcomes, Assessment, and Treatment Issues

Laryngotracheal stenosis is defined as a congenital or acquired narrowing of the airway. Congenital causes may include subglottic membranous or cartilaginous narrowing. Acquired causes may include trauma due to prolonged endotracheal or tracheal intubation or laryngotracheal injury. Although advances have been made over the past 30 years in reconstructive surgeries to improve airway patency in these patients, long-term laryngeal function for voice production is not well defined in this population. This review examines causes, symptoms and signs, and methods for diagnosing laryngotracheal stenosis. Surgical management procedures are briefly summarized. The current literature on voice outcomes is summarized. The predominant voice characteristics in the population are presented, although results are challenged by the heterogeneity of voice presentation and paucity of data from instrumental measures. Considerations for subjective and instrumental assessment, measures of quality of life, instrumental methods, and treatment options specific to the needs of this population are discussed. Research strategies to identify long-term outcomes of surgical and behavioral treatments in this population are posed.     

The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Miscibility of bisphenol-A polycarbonate with poly(methyl methacrylate)

The miscibility of bisphenol-A polycarbonate (PC) with poly(methyl methacrylate) (PMMA) has been reexamined using differential scanning calorimetry (DSC) and optical indications for phase separation on heating, i.e., lower critical solution temperature (LCST) behavior. Various methods have been used to prepare the blends including methylene chloride (CH₂Cl₂) and tetrahydrofuran (THF) solution casting, melt mixing, and precipitation of PC and PMMA simultaneously from THF solution by using the nonsolvents methanol and heptane. It is shown that the resulting phase behavior for PC/PMMA blends is strongly affected by the blend preparation method. However, these blends are miscible over the whole blend composition range (unambiguous single composition-dependent T_g's and LCST behavior) when prepared by precipitation from solution using heptane as the nonsolvent. To the contrary, solution-cast and melt-mixed PC/PMMA blends were all phase separated, which may be attributed to the “solvent” effect and LCST behavior, respectively, not discovered in previous reports. Methanol precipitation does not lead to fully mixed blends, which demonstrates the importance of the choice of nonsolvent when using the precipitation method.