Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Systematic Investigation of Possibilities for New Physics Effects in b --> s Penguin Processes

Although recent experimental results in b-->s penguin process seem to be roughly consistent with the standard model predictions, there may be still large possibilities of new physics hiding in this processes. Therefore, here we investigate systematically the potential new physics effects that may appear in time-dependent CP asymmetries of B --> phi K^0, B--> eta^\prime K^0 and B--> K^0 \pi^0 decay modes, by classifying the cases for the values of the mixing-induced indirect CP asymmetries, S_{phi K^0}, S_{eta^\prime K^0}, S_{K^0 pi^0} which are compared to S_{J/psi K^0}. We also show that several B_s decay modes may help to resolve the ambiguities in such an analysis. Through combining analysis with the time-dependent CP asymmetries of B_s decay modes such as B_s --> phi eta^\prime, B_s--> eta^\prime pi^0 and B_s --> K^0 bar{K}^0, we can determine where the new CP phases precisely come from.Comment: 17 pages, version to be published in Prog.Theor.Phy

Influence of aesthetic design elements on residential satisfaction in apartment Based on Seoul apartment complex

This study aimed to examine the influence of aesthetic design elements on residential satisfaction in urban apartment complexes, focusing on elements that are generally considered less important. A total of 65 apartment complexes in Seoul, a city predominantly characterized by middle-class apartment living, were surveyed to assess residential satisfaction. Using multiple regression analysis, the relationships between the dependent variable (post-occupancy evaluation) and 28 independent variables were analyzed. The results revealed significant correlations between residential satisfaction and various independent variables. Specifically, three out of eight aesthetic design factors, namely the main complex entrance design, exterior mass design, and landscape design, were found to have a significant impact on residential satisfaction, collectively accounting for 17.16% of the total satisfaction variance. This finding suggests that aesthetic design elements play an increasingly important role in metro cities. The practical implications of this study are twofold. Firstly, it provides housing providers with strategic guidelines, emphasizing the significance of incorporating aesthetically pleasing design elements to enhance residential satisfaction. Secondly, the study offers potential customers valuable information regarding the importance of aesthetic design in their decision-making process when choosing residential properties. Overall, this research contributes to a better understanding of the relationship between aesthetic design elements and residential satisfaction in urban apartment complexes, shedding light on the growing importance of aesthetics in the housing market

Non-Classical Response from Quench-Cooled Solid Helium Confined in Porous Gold

We have investigated the non-classical response of solid 4He confined in porous gold set to torsional oscillation. When solid helium is grown rapidly, nearly 7% of the solid helium appears to be decoupled from the oscillation below about 200 mK. Dissipation appears at temperatures where the decoupling shows maximum variation. In contrast, the decoupling is substantially reduced in slowly grown solid helium. The dynamic response of solid helium was also studied by imposing a sudden increase in the amplitude of oscillation. Extended relaxation in the resonant period shift, suggesting the emergence of the pinning of low energy excitations, was observed below the onset temperature of the non-classical response. The motion of a dislocation or a glassy solid is restricted in the entangled narrow pores and is not likely responsible for the period shift and long relaxation

Who Contributes to the Knowledge Sharing Economy?

Information sharing dynamics of social networks rely on a small set of influencers to effectively reach a large audience. Our recent results and observations demonstrate that the shape and identity of this elite, especially those contributing \emph{original} content, is difficult to predict. Information acquisition is often cited as an example of a public good. However, this emerging and powerful theory has yet to provably offer qualitative insights on how specialization of users into active and passive participants occurs. This paper bridges, for the first time, the theory of public goods and the analysis of diffusion in social media. We introduce a non-linear model of \emph{perishable} public goods, leveraging new observations about sharing of media sources. The primary contribution of this work is to show that \emph{shelf time}, which characterizes the rate at which content get renewed, is a critical factor in audience participation. Our model proves a fundamental \emph{dichotomy} in information diffusion: While short-lived content has simple and predictable diffusion, long-lived content has complex specialization. This occurs even when all information seekers are \emph{ex ante} identical and could be a contributing factor to the difficulty of predicting social network participation and evolution.Comment: 15 pages in ACM Conference on Online Social Networks 201