The economic production quantity (EPQ) model for delayed deteriorating items considering two-phase production periods, exponential demand rate and linearly increasing function of time holding cost is proposed to solve a production problem similar to the one caused by the Covid-19 pandemic. Without shortages, the necessary and sufficient conditions for optimality of this model are characterized through a theorem and lemmas while a solution methodology based on differential calculus is adopted. This paper determines the best replenishment cycle length corresponding to the optimal total variable cost and production quantity of imperfect production industry. To illustrate this model, a numerical experiment is conducted. The results demonstrate that a higher carrying charge decreases the production quantity and a longer demanding period decreases the total variable cost of an industry with a distracted production period. Finally, managerial insights are discussed using sensitivity analysis and future research directions are exposed.
The global impact of COVID-19 has led to the development of numerous mathematical models to understand and control the pandemic. However, these models have not fully captured how the disease's dynamics are influenced by both within-host and between-host factors. To address this, a new mathematical model is proposed that links these dynamics and incorporates immune response. The model is compartmentalized with a fractional derivative in the sense of Caputo-Fabrizio, and its properties are studied to show a unique solution. Parameter estimation is carried out by fitting real-life data, and sensitivity analysis is conducted using various methods. The model is then numerically implemented to demonstrate how the dynamics within infected hosts drive human-to-human transmission, and various intervention strategies are compared based on the percentage of averted deaths. The simulations suggest that a combination of medication to boost the immune system, prevent infected cells from producing the virus, and adherence to COVID-19 protocols is necessary to control the spread of the virus since no single intervention strategy is sufficient.
The linear regression is critical for data modelling, especially for scientists. Nevertheless, with the plenty of high-dimensional data, there are data with more explanatory variables than the number of observations. In such circumstances, traditional approaches fail. This paper proposes a modified sparse regression model that solves the problem of heterogeneity using seaweed big data as a use case. The modified heterogeneity models for ridge, LASSO and Elastic net were used to model the data. Robust estimations M Bi-Square, M Hampel, M Huber, MM and S were used. Based on the results, the hybrid model of sparse regression for before, after, and modified heterogeneity robust regression with the 45 high ranking variables and a 2-sigma limit can be used efficiently and effectively to reduce the outliers. The obtained results confirm that the hybrid model of the modified sparse LASSO with the M Bi-Square estimator for the 45 high ranking parameters performed better compared with other existing methods.
Despite many dedicated efforts, the fabrication of high-quality ZnO-incorporated Zinc@Silicon (Zn@Si) core-shell quantum dots (ZnSiQDs) with customized properties remains challenging. In this study, we report a new record for the brightness enhancement of ZnSiQDs prepared via a unified top-down and bottom-up strategy. The top-down approach was used to produce ZnSiQDs with uniform sizes and shapes, followed by the bottom-up method for their re-growth. The influence of various NH4OH contents (15 to 25 µL) on the morphology and optical characteristics of ZnSiQDs was investigated. The ZnSiQDs were obtained from the electrochemically etched porous Si (PSi) with Zn inclusion (ZnPSi), followed by the electropolishing and sonication in acetone. EFTEM micrographs of the samples prepared without and with NH4OH revealed the existence of spherical ZnSiQDs with a mean diameter of 1.22 to 7.4 nm, respectively. The emission spectra of the ZnSiQDs (excited by 365 nm) exhibited bright blue, green, orange-yellow, and red luminescence, indicating the uniform morphology related to the strong quantum confinement ZnSiQDs. In addition, the absorption and emission of the ZnSiQDs prepared with NH4OH were enhanced by 198.8% and 132.6%, respectively. The bandgap of the ZnSiQDs conditioned without and with NH4OH was approximately 3.6 and 2.3 eV, respectively.