Using the compensating and equivalent variations to define the Slutsky Equation under a discrete price change

In our experience, all textbook presentations of the Slutsky Equation under a discrete price change use a compensation scheme based on the compensating variation. Our students have sensed this convention is arbitrary in that they have asked, why consider this compensation scheme, and not one based on the equivalent variation? The present paper outlines how one might address this matter analytically, and then discusses how our findings provide a new insight into the Giffen Paradox.Compensating Variation

Optimal guidance law development for an advanced launch system

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems

Anion Distribution, Structural Distortion, and Symmetry-Driven Optical Band Gap Bowing in Mixed Halide Cs2SnX6 Vacancy Ordered Double Perovskites.

Mixed anion compounds in the Fm3̅m vacancy ordered perovskite structure were synthesized and characterized experimentally and computationally with a focus on compounds where A = Cs+. Pure anion Cs2SnX6 compounds were formed with X = Cl, Br, and I using a room temperature solution phase method. Mixed anion compounds were formed as solid solutions of Cs2SnCl6 and Cs2SnBr6 and a second series from Cs2SnBr6 and Cs2SnI6. Single phase structures formed across the entirety of both composition series with no evidence of long-range anion ordering observed by diffraction. A distortion of the cubic A2BX6 structure was identified in which the spacing of the BX6 octahedra changes to accommodate the A site cation without reduction of overall symmetry. Optical band gap values varied with anion composition between 4.89 eV in Cs2SnCl6 to 1.35 eV in Cs2SnI6 but proved highly nonlinear with changes in composition. In mixed halide compounds, it was found that lower energy optical transitions appeared that were not present in the pure halide compounds, and this was attributed to lowering of the local symmetry within the tin halide octahedra. The electronic structure was characterized by photoemission spectroscopy, and Raman spectroscopy revealed vibrational modes in the mixed halide compounds that could be assigned to particular mixed halide octahedra. This analysis was used to determine the distribution of octahedra types in mixed anion compounds, which was found to be consistent with a near-random distribution of halide anions throughout the structure, although some deviations from random halide distribution were noted in mixed iodide-bromide compounds, where the larger iodide anions preferentially adopted trans configurations

A Portable Plug-and-Play Imaging System for Physiological Monitoring

Non-contact physiological monitoring has garnered interest in theresearch community. However, studies employ different imagingsystem configuration, including illuminant profile and wavelength,camera type and frame rate, and distance to the skin. In this paper,we propose an easily customizable imaging system for evaluatingphysiological monitoring parameters. The system’s design allowsplug-and-play compatibility with various illumination sources,camera types, lenses, and optical components. Results using oneconfiguration shows the feasibility of spatial blood perfusion analysisusing this imaging system, where areas exhibiting clean bloodpulsatility can be identified at the surface level

An investigation into the management of the deep carious lesion by general dental practitioners in the UK

Objectives: As techniques and dental materials have evolved, the management of deep carious lesions has also changed. This study investigated how UK-based general dental practitioners (GDPs) managed deep carious lesions in permanent, vital teeth and factors that influence their choices. / Methods: This mixed-method study employed an online questionnaire as its primary source of quantitative data collection. The questionnaire enquired about GDPs': a) demographics; b) working environment; and c) whether they had postgraduate training that covered caries management/minimally invasive dentistry (MID). Respondents were presented with a clinical case to elicit qualitative data. Relevant questions were asked in order to examine current practice and explore treatment among the respondents. / Results: In total, 239 responses were received. Overall, 168 (70% [95% CI 64%, 76%]) of the respondents chose a partial caries removal technique, 155 (69.3% [95% CI 60%, 72%]) used an adhesive restorative material and 205 (85.8% [95% CI 81%, 89%]) advised fluoride adjuncts. However, rubber dam (75; 31.4% [95% CI 26%, 38%]) and saliva testing (17; 7.1% [95% CI 4%, 11%]) were not routinely used. A significant relationship between those who had postgraduate training and those who chose partial caries removal as their treatment choice (χ2 = 6.27; p = 0.01) was noted. Respondents working in an NHS-based practice were significantly (χ2 = 34.98; p <0.001) more likely to restore teeth with amalgam. / Conclusions: There is an inconsistent management protocol when presented with a deep carious lesion, but partial caries removal is more widely adopted than previously reported. Rubber dam isolation was not routinely used when choosing to restore a deep carious lesion. Those who have had postgraduate training felt more confident in offering MID, so there is a clear need for further education to ensure its engagement

Z Boson Propagator Correction in Technicolor Theories with ETC Effects Included

We calculate the Z boson propagator correction, as described by the S parameter, in technicolor theories with extended technicolor interactions included. Our method is to solve the Bethe-Salpeter equation for the requisite current-current correlation functions. Our results suggest that the inclusion of extended technicolor interactions has a relatively small effect on S.Comment: 15pages, 8 figure