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Multilayer diffusion problems have found significant importance that they arise in many medical, environmental, and industrial applications of heat and mass transfer. In this article, we study the solvability of a one-dimensional nonhomogeneous multilayer diffusion problem. A new generalized Laplace-type integral transform is used, namely, the M ρ , m -transform. First, we reduce the nonhomogeneous multilayer diffusion problem into a sequence of one-layer diffusion problems including time-varying given functions, followed by solving a general nonhomogeneous one-layer diffusion problem via the M ρ , m -transform. Hence, by means of general interface conditions, a renewal equations’ system is determined. Finally, the M ρ , m -transform and its analytic inverse are used to obtain an explicit solution to the renewal equations’ system. Our results are of general attractiveness and comprise a number of previous works as special cases.

Background:The COVID-19 is known as the foremost threat to humankind since the Second World War, and the most important global health catastrophe of the century. Aim: the aim of this study was assessment of knowledge of nursing students regarding COVID-19. Design: Cross-sectional descriptive study A descriptive study design was used. Sample: A stratified simple random sample of 334 nursing students. Setting: Sohag faculty of nursing. Tools: An electronic questionnaire was used it included two parts, Part I: Demographic data of the nursing students; this part is composed of 5 questions covering: name, gender, residence and academic level/year. (Q1-Q5). Part II: Assessment of nursing students' knowledge regarding COVID-19(Q6-Q17): it included information about concept of COVID-19, modes of transmission, clinical symptoms, risk groups, vaccine and treatment. Results: 91.6% of them reported that COVID-19 can be transmitted through close contact, eating wild and drinking. 69.2% of them were unable to differentiate between COVID-19 and common cold signs and symptoms. Total satisfactory knowledge of nursing students regarding COVID-19 was 64%. Conclusion: More than one-third of nursing students had unsatisfactory knowledge about COVID-19. Recommendation: posters about difference between clinical symptoms of COVID-19 and common cold should be placed at placed at university.