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

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

Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois

For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds

Neutron-rich rare isotope production from projectile fission of heavy beams in the energy range of 20 MeV/nucleon

We investigate the possibilities of producing neutron-rich nuclides in projectile fission of heavy beams in the energy range of 20 MeV/nucleon expected from low-energy facilities. We report our efforts to theoretically describe the reaction mechanism of projectile fission following a multinucleon transfer collision at this energy range. Our calculations are mainly based on a two-step approach: the dynamical stage of the collision is described with either the phenomenological Deep-Inelastic Transfer model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The deexcitation/fission of the hot heavy projectile fragments is performed with the Statistical Mul- tifragmentation Model (SMM). We compared our model calculations with our previous experimental projectile-fission data of 238U (20 MeV/nucleon)+208Pb and 197Au (20 MeV/nucleon)+197Au and found an overall reasonable agreement. Our study suggests that projectile fission following periph- eral heavy-ion collisions at this energy range offers an effective route to access very neutron-rich rare isotopes toward and beyond the astrophysical r-process path

Community Group-Based Models of Medication Delivery: Applicability to Cardiovascular Diseases.

The rising global burden of chronic non-communicable diseases (NCDs) has put a strain on healthcare systems globally, especially in low- and middle-income countries, which have seen disproportionate mortality rates due to non-communicable diseases. These deaths are in part due to challenges with medication adherence, which are compounded by lack of access to medication and weak community support systems. This paper aims to propose a potential solution using models of service delivery in HIV/AIDS, given the many similarities between NCD and HIV/AIDS. Models that have been particularly effective in HIV/AIDS are the community-based peer-support medication delivery groups: medication adherence clubs and community antiretroviral therapy (ART) groups. The positive outcomes from these models, including improved medication adherence and patient satisfaction, provide evidence for their potential success when applied to non-communicable diseases, particularly hypertension and cardiovascular disease