Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth

We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal nonlinear potential theory. We provide several fine properties of supersolutions and superharmonic functions, and reveal the relation between them. Along the way we prove some results for nonlocal obstacle problems such as the well-posedness and (both interior and boundary) regularity estimates, which are of independent interest.Comment: 42 page

Gradient Riesz potential estimates for a general class of measure data quasilinear systems

We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates for the gradient of solutions are provided in terms of the truncated Riesz potential. This allows us to show a precise transfer of regularity from data to solutions on various scales.Comment: 36 page

Estimation of the Available Rooftop Area for Installing the Rooftop Solar Photovoltaic (PV) System by Analyzing the Building Shadow Using Hillshade Analysis

AbstractFor continuous promotion of the solar PV system in buildings, it is crucial to analyze the rooftop solar PV potential. However, the rooftop solar PV potential in urban areas highly varies depending on the available rooftop area due to the building shadow. In order to estimate the available rooftop area accurately by considering the building shadow, this study proposed an estimation method of the available rooftop area for installing the rooftop solar PV system by analyzing the building shadow using Hillshade Analysis. A case study of Gangnam district in Seoul, South Korea was shown by applying the proposed estimation method

Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations

We investigate the accurate computations for the Greeks using the numerical solutions of the Black-Scholes partial differential equation. In particular, we study the behaviors of the Greeks close to the maturity time and in the neighborhood around the strike price. The Black-Scholes equation is discretized using a nonuniform finite difference method. We propose a new adaptive time-stepping algorithm based on local truncation error. As a test problem for our numerical method, we consider a European cash-or-nothing call option. To show the effect of the adaptive stepping strategy, we calculate option price and its Greeks with various tolerances. Several numerical results confirm that the proposed method is fast, accurate, and practical in computing option price and the Greeks

The Wiener criterion for nonlocal Dirichlet problems

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.Comment: 39 page

THE IMPORTANCE OF LEADERSHIP: AN INVESTIGATION OF EFFECTS OF TRANSFORMATIONAL LEADERSHIP ON MIDDLE SCHOOL STUDENTS INTRINSIC MOTIVATION AND EXPECTANCY-VALUE IN PHYSICAL EDUCATION

The leadership practices exhibited by physical education teachers have been found to have a significant impact on promoting students learning. The main purpose of this study was to explore: (a) differences on middle school students\u27 perception regarding expectancy-value and intrinsic motivation according to their grade, gender, and ethnicity, (b) the relationship between physical education teachers\u27 transformational leadership and middle school students\u27 expectancy-value and intrinsic motivation. To conduct this study, three questionnaires were employed: transformational teaching questionnaire (Beauchamp et al., 2010), expectancy-value questionnaire (Duncan & Tammen, 1989), and intrinsic motivation index (Eccles & Wigfield, 1995). A total of 295 middle school students participated in this study through a convenience sampling technique, and 262 questionnaires were used for the data analyses. Data collected were analyzed by descriptive, exploratory factor analysis, t-test, ANOVAs, and regression. The study results showed that generally 6th grade students perceived higher expectancy-value and intrinsic value than 8th grade students. Male students had higher expectancy-value and intrinsic value than female students. However, there was no statistically significant difference among ethnic groups. In addition, according to single regression, transformational leadership had a positive impact on students\u27 expectancy-value and intrinsic motivation. Lastly, based on multiple regression, intellectual stimulation was a common factor that affected students\u27 expectancy-value and intrinsic motivation positively. The results of the study support the importance of transformational leadership that affects middle school students\u27 intrinsic motivation and expectancy-value in physical education. Thus, it is recommended that physical education teachers be able to understand and display appropriate leadership, in particular transformational leadership.\u2

Effects of the level of physical activity on physical education state anxiety among college students

The purpose of this project was to examine the effect of physical activity on different kinds of anxiety (e.g., somatic, cognitive, and worry) in physical education class among college students

The Dangers of Responsibilities Assigned to Concussed Athletes: Editor: Thomas H. Sawyer

©, Copyright SHAPE America. A high school freshman suffered post-concussive syndrome after receiving multiple head injuries stemming from assigned actions in the physical education classroom and extracurricular school-sponsored activities