Affine embeddings and intersections of Cantor sets

Let $E, F\subset \R^d$ be two self-similar sets. Under mild conditions, we show that $F$ can be $C^1$-embedded into $E$ if and only if it can be affinely embedded into $E$; furthermore if $F$ can not be affinely embedded into $E$, then the Hausdorff dimension of the intersection $E\cap f(F)$ is strictly less than that of $F$ for any $C^1$-diffeomorphism $f$ on $\R^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of $E$ and $F$ if $F$ can be affinely embedded into $E$. As an application, we show that $\dim_HE\cap f(F)<\min\{\dim_HE, \dim_HF\}$ when $E$ is any Cantor-$p$ set and $F$ any Cantor-$q$ set, where $p,q\geq 2$ are two integers with \log p/\log q\not \in \Q. This is related to a conjecture of Furtenberg about the intersections of Cantor sets.Comment: The paper will appear in J. Math. Pure. App

Fatigue life prediction of RC beams strengthened with externally bonded FRP sheets

Based on the failed criterion of steel reinforcement fracture, an analytical model is presented for predicting the fatigue life of reinforced concrete (RC) beam strengthened with fiber reinforced polymer (FRP) sheets. In this model, the load cycle is divided into some loading blocks evenly and the stress amplitude of the tensile steel reinforcement is thought to be invariable in each loading block. Considering the degradation of material performance, including concrete creep, the stress amplitude of the tensile steel reinforcement is obtained by using the traditional sectional analysis method. Therefore, the fatigue life of the strengthened beam is carried out by using the well-known Palmgren-Miner rule. The reliability of the proposed analytical model is validated through comparisons with previous test results reported by the relative research groups. The compared results show that the proposed models can predict the fatigue life of the strengthened beam with an acceptable degree of accurac

Physical Activity Behavior, Dietary Patterns, and Nutrition Knowledge of Third- and Fourth-Grade Students in Western Massachusetts

Our Extension project assessed physical activity patterns and nutrition behavior and knowledge in elementary school students in a low-income community. Dietary patterns were similar to many large-scale studies, which have shown a trend of lower fat consumption; however, these children were unfamiliar with certain nutrient terms and categories. Most physical activities were performed in PE classes; however, community organizations and family played important roles. This survey provides a basis of children\u27s nutrition knowledge and physical activity behavior. From this project we plan to develop appropriate nutrition and physical activity programs for children of similar age and socioeconomic status

The Reinforcing Effects of Formal Control Enactment in Complex IT Projects

Complex IT projects pose particular challenges for the application of control, because of the dynamism and uncertainty involved. Prior studies suggest self-control can complement formal control within complex projects. However, how managers can enact controlee self-control remains an unsolved question. This paper proposes and investigates how enacted formal control unfolds during the course of an IT project and, in particular, how formal control enactment can promote or hinder controlee self-control. We demonstrate through case studies of a control in two wireless communication product development projects that an enabling control style can induce controlees to act to the benefit of both the controller and the controlee, while an authoritative control style encourages controlees’ self-interested behavior. We also show how controlees influence the enactment of control within complex projects and demonstrate the reinforcing effects of the controller’s enactment and controlee response on project outcomes. For practice, this research identifies preconditions necessary for inducing controlee self-control