BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula

In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in which the terminal values and the generators are allowed to be general functions of Brownian paths. In this way we have established a new type of nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of regularities for this new PDE was obtained

Interfacial Bond Adhesion Enhancement Mechanism Analysis of Self Stressing Alkali Activated Slag Concrete-Filled Round Steel Tube

To investigate the interfacial adhesion behaviour and its enhancement mechanism of self-stressing alkali activated slag concrete-filled round steel tube, push-out samples, expansion performance test specimens, and SEM, XRD micro-test specimens were made with different dosage of calcium sulphoaluminate and calcium oxide expansive agent. The results show that the maximum interfacial adhesion stress is at 70-80 mm from the free end of the samples, and increases with the increase of the expansive agent dosage. The expansive agent such as calcium sulphoaluminate and calcium oxide can effectively reduce the drying shrinkage performance of the core concrete, and then improve the interaction between steel tube and core concrete. Micro-test analysis results show that the main expansive source providing expansive power in the AASC system is Ca(OH)

Aging, the urban-rural gap and disability trends: 19 years of experience in China - 1987 to 2006

As the age of a population increases, so too does the rate of disability. In addition, disability is likely to be more common in rural compared with urban areas. The present study aimed to examine the influence of rapid population changes in terms of age and rural/urban residence on the prevalence of disability. Data from the 1987 and 2006 China Sampling Surveys on Disability were used to estimate the impacts of rapid ageing and the widening urban-rural gap on the prevalence of disability. Stratum specific rates of disability were estimated by 5-year age-group and type of residence. The decomposition of rates method was used to calculate the rate difference for each stratum between the two surveys. The crude disability rate increased from 4.89% in 1987 to 6.39% in 2006, a 1.5% increase over the 19 year period. However, after the compositional effects from the overall rates of changing age-structure in 1987 and 2006 were eliminated by standardization, the disability rate in 1987 was 6.13%, which is higher than that in 2006 (5.91%). While in 1987 the excess due to rural residence compared with urban was ,1.0%, this difference increased to .1.5% by 2006, suggesting a widening disparity by type of residence. When rates were decomposed, the bulk of the disability could be attributed to ageing, and very little to rural residence. However, a wider gap in prevalence between rural and urban areas could be observed in some age groups by 2006. The increasing number of elderly disabled persons in China and the widening discrepancy of disability prevalence between urban and rural areas may indicate that the most important priorities for disability prevention in China are to reinforce health promotion in older adults and improve health services in rural communities

A novel polymer platform for endoscopic tattooing with high efficacy and safety

Endoscopic tattooing plays a pivotal role in modern endoscopic localization of gastrointestinal lesions, facilitating further surgical intervention and aiding in the postoperative identification and repositioning of lesions. However, traditional endoscopic tattoo dyes often suffer from drawbacks such as side effects, short tattoo duration, and high overall costs. In this study, we developed polyvinylpyrrolidone (PVP)-modified polypyrrole (PPy) nanoparticles by oxidizing pyrrole in a PVP aqueous solution to create a PPy/PVP nanoparticle solution. This innovation aims to enhance endoscopic tattooing efficiency and mitigate the limitations associated with current tattooing methods. Both in vitro and in vivo evaluations confirmed the biosafety of PPy/PVP nanoparticles. Endoscopic tattooing experiments conducted in a pig model demonstrated the dye’s stability within the digestive tract. Similarly, subcutaneous tissue tattooing experiments performed in a mouse model revealed the sustained stability of the PPy/PVP tattoo dye for at least 180 days. With its robust stability, safety, and longevity, PPy/PVP nanoparticles hold promise as novel tattoo dyes for marking intestinal lesion sites. This advancement has the potential to enhance the accuracy of lesion localization and long-term tracking