On the momentum-dependence of K−K^{-}-nuclear potentials

The momentum dependent $K^{-}$-nucleus optical potentials are obtained based on the relativistic mean-field theory. By considering the quarks coordinates of $K^-$ meson, we introduced a momentum-dependent "form factor" to modify the coupling vertexes. The parameters in the form factors are determined by fitting the experimental $K^{-}$-nucleus scattering data. It is found that the real part of the optical potentials decrease with increasing $K^-$ momenta, however the imaginary potentials increase at first with increasing momenta up to $P_k=450\sim 550$ MeV and then decrease. By comparing the calculated $K^-$ mean free paths with those from $K^-n$/$K^-p$ scattering data, we suggested that the real potential depth is $V_0\sim 80$ MeV, and the imaginary potential parameter is $W_0\sim 65$ MeV.Comment: 9 pages, 4 figure

The properties of kaonic nuclei in relativistic mean-field theory

The static properties of some possible light and moderate kaonic nuclei, from C to Ti, are studied in the relativistic mean-field theory. The 1s and 1p state binding energies of $K^-$ are in the range of $73\sim 96$ MeV and $22\sim 63$ MeV, respectively. The binding energies of 1p states increase monotonically with the nucleon number A. The upper limit of the widths are about $42\pm 14$ MeV for the 1s states, and about $71\pm 10$ MeV for the 1p states. The lower limit of the widths are about $12\pm 4$ MeV for the 1s states, and $21\pm 3$ MeV for the 1p states. If $V_{0}\leq 30$ MeV, the discrete $K^-$ bound states should be identified in experiment. The shrinkage effect is found in the possible kaonic nuclei. The interior nuclear density increases obviously, the densest center density is about $2.1\rho_{0}$.Comment: 9 pages, 2 tables and 1 figure, widths are considered, changes a lo

Toward Sustainable Construction: Optimizing Carbon Emission Reduction in the Building Supply Chain through Game-Theoretic Strategies, Government Subsidies, and Cost-Sharing Contract

The carbon emission reduction (CER) in the construction industry can aid in achieving the international community's carbon neutrality target. However, the low motivation of construction enterprises to reduce carbon emissions and the unsatisfactory effect of CER are still unresolved issues. This study aims to address these issues by constructing a building supply chain (BSC) consisting of a developer and a contractor using government subsidies and cost-sharing contracts. The optimal government subsidy and feedback equilibrium strategies of the BSC are examined using a combination of differential game theory and numerical simulations. The findings demonstrate that (1) Cost-sharing contracts may enhance developer and contractor profits and building CER, goodwill, and demand without relying on government subsidies. (2) When subsidized by the government, each equilibrium strategy meets or exceeds the performance of the centralized model, with the cost-sharing contract having a negligible effect on the enhancement of each equilibrium strategy. (3) Both the game structure and the positioning of construction enterprises in the BSC are connected to the number of government subsidies. The city of Shenzhen, one of China's first low-carbon pilot cities, provides a realistic environment for the simulation analysis, with the Block K residential building in Nanshan District serving as a case study. Furthermore, this work contributes to the body of knowledge by proposing a novel CER model for the BSC using differential game theory. The research provides new insights into the role of government subsidies in shaping profit distribution, game structure, and enterprise positioning. Findings demonstrate the value of cost-sharing contracts in improving CER, goodwill, demand, and profits when implemented collaboratively. This advances the theoretical understanding of incentives and strategies for promoting CER in construction. Practical applications: This research highlights the importance of collaborative efforts between the government and the BSC to promote sustainable construction and CER. The study found that government subsidies can be an effective tool to encourage developers and contractors to adopt CER practices. However, relying solely on subsidies is insufficient - collaboration through mechanisms like cost-sharing contracts can further enhance sustainability outcomes when enterprises work together. To facilitate low-carbon construction, the government could provide subsidies for developers' promotional and marketing activities as well as funding for contractors' research and development of sustainable materials and technologies. Financial incentives like tax breaks and preferential lending for potential homebuyers can also accelerate consumer demand. Ultimately, creating a supportive environment where enterprises proactively pursue CER creates a win-win situation - the BSC becomes more sustainable while firms improve their branding and profitability. The insights from this research highlight the need for a multi-pronged approach. Governments play a key role through policy and financial support. Realizing the full potential of sustainable construction also requires active participation from developers, contractors, and consumers. By outlining optimal strategies and incentives, this study provides valuable guidance to construction industry stakeholders seeking to implement CER collaboratively