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

Newborn hearing screening program in China: a narrative review of the issues in screening and management

Hearing loss is one of the most common sensory disorders in humans. The purpose of this review is to summarize the history and current status of newborn hearing screening in China and to investigate future developmental trends in newborn hearing screening with the intention of sharing experiences and providing a reference for other populations. In the 1980s, the research on hearing monitoring for high-risk infants led to the gradual development of newborn hearing screening in China. With the continuous improvement of screening technology, the newborn hearing screening program was gradually extended to the whole country and became a government-led multidisciplinary public health program. Genetic screening for deafness has been incorporated into newborn hearing screening in many regions of China to help screen for potential and late-onset deafness in newborns. In the future, it is necessary to further establish and improve whole life-cycle hearing screening and healthcare, conduct screening for congenital cytomegalovirus infection, and create a full-coverage, whole life course hearing screening and intervention system. Screening for deafness in China has been marked by 40 years of achievements, which have been a source of pride for entrepreneurs and comfort for patients and their families. Managing hearing screening data information more efficiently and establishing a quality control index system throughout the whole screening process are of paramount importance. The genetic screening for concurrent newborn hearing and deafness has a great clinical importance for the management of congenital deafness and prevention of ototoxicity. A hearing screening and intervention system across the whole life course should be developed

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