Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables

The author studies the 2D isentropic Euler equations with the ideal gas law. He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry. These solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time 1 3-H¨older bound. Moreover, these point shocks are of self-similar type and share the same profile, which is a solution to the 2D self-similar Burgers equation. The proof of the solutions, following the 3D construction of Buckmaster, Shkoller and Vicol (in 2023), is based on the stable 2D self-similar Burgers profile and the modulation method.     

Recent studies on advance spectroscopic techniques for the identification of microorganisms: A review

The continuous development of resistance to antibiotic drugs by microorganisms causes high mortality and morbidity. Pathogens with distinct features and biochemical abilities make them destructive to human health. Therefore, early identification of the pathogen is of substantial importance for quick ailments and healthcare outcomes. Several phenotype methods are used for the identification and resistance determination but most of the conventional procedures are time-consuming, costly, and give qualitative results. Recently, great focus has been made on the utilization of advanced techniques for microbial identification. This review is focused on the research studies performed in the last five years for the identification of microorganisms particularly, bacteria using advanced spectroscopic techniques including mass spectrometry (MS), infrared (IR) spectroscopy, Raman spectroscopy (RS), and nuclear magnetic resonance (NMR) spectroscopy. Among all the techniques, MS techniques, particularly MALDI-TOF/MS have been widely utilized for microbial identification. A total of 44 bacteria i.e., 6 Staphylococcus spp., 3 Enterococcus spp., 6 Bacillus spp., 4 Streptococcus spp., 6 Salmonella spp., and one from each genus including Escherichia, Acinetobacter, Pseudomonas, Proteus, Clostridioides, Candida, Brucella, Burkholderia, Francisella, Yersinia, Moraxella, Vibrio, Shigella, Serratia, Citrobacter, and Haemophilus (spp.) were discussed in the review for their identification using the above-mentioned techniques. Among all the identified microorganisms, 21% of studies have been conducted for the identification of E. coli, 14% for S. aureus followed by 37% for other microorganisms.