This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.
In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.
We report the self-assembly of an extensive inter-ligand hydrogen-bonding network of octylphosphonates on the surface of cesium lead bromide nanocrystals (CsPbBr3 NCs). The post-synthetic addition of octylphosphonic acid to oleic acid/oleylamine-capped CsPbBr3 NCs promoted the attachment of octylphosphonate to the NC surface, while the remaining oleylammonium ligands maintained the high dispersability of the NCs in non-polar solvent. Through powerful 2D solid-state 31P-1H NMR, we demonstrated that an ethyl acetate/acetonitrile purification regime was crucial for initiating the self-assembly of extensive octylphosphonate chains. Octylphosphonate ligands were found to preferentially bind in a monodentate mode through P-O-, leaving polar P[double bond, length as m-dash]O and P-OH groups free to form inter-ligand hydrogen bonds. The octylphosphonate ligand network strongly passivated the nanocrystal surface, yielding a fully-purified CsPbBr3 NC ink with PLQY of 62%, over 3 times higher than untreated NCs. We translated this to LED devices, achieving maximum external quantum efficiency and luminance of 7.74% and 1022 cd m-2 with OPA treatment, as opposed to 3.59% and 229 cd m-2 for untreated CsPbBr3 NCs. This represents one of the highest efficiency LEDs obtained for all-inorganic CsPbBr3 NCs, accomplished through simple, effective passivation and purification processes. The robust binding of octylphosphonates to the perovskite lattice, and specifically their ability to interlink through hydrogen bonding, offers a promising passivation approach which could potentially be beneficial across a breadth of halide perovskite optoelectronic applications.
In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field.