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This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.

In this work, we study the existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative Caputo fractional differential equation by first inverting it as an integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem to prove our new results. At the end we give an example to illustrate our obtained results.

We prove the existence and uniqueness of mild solutions for initial value problems of nonlinear hybrid first order Caputo fractional integro-differential equations. The main tool employed here is the Krasnoselskii and Banach fixed point theorems. An example is also given to illustrate the main results. In addition, the case of the Higher order Caputo fractional integro-differential equations is studied.

La prescription médicale, souvent réduite à l’ordonnance, est un acte médical d’une importance capitale. Elle doit répondre à un impératif technique certes, mais aussi à un cadre juridique. La prescription est une source d’obligations, toute erreur dans sa formulation ou manquement aux règles de droit, peut être évoqué pour poursuivre le prescripteur, autant devant les juridictions civile, disciplinaire que pénale. Les aspects médicolégaux relatifs au sujet, concernent le prescripteur, les aspects de la prescription et ses limites, et les retombées économiques.

Gas detection is vital for safety in important industrial and private sectors. Its major significance lies in its proactive risk mitigation, safeguarding lives and resources. In this paper, the focus is on the development of a gas sensor based on quartz crystal microbalance coated with a sensitive layer of zinc oxide (ZnO)--graphene nanocomposite for the detection of volatile organic compounds at room temperature. The incorporation of graphene or reduced graphene oxide is preferred in such applications due to their excellent electrical conductivity, chemical stability, and high surface area. These nanocomposites were synthesized using a chemical method via spray pyrolysis. Various techniques were employed to analyze the coated QCM electrode: contact angle measurements to assess surface wettability, Fourier transform infrared and energy-dispersive X-ray spectroscopy to investigate the composition of the coated electrode, and scanning electron and atomic force microscopies were used to study its surface morphology. These analyses provided valuable insights into the nanocomposite's interaction with the environment, composition, structure, and topography of the sensor's sensitive layer. To evaluate the sensor's sensitivity, the frequency shift (_f) of the coated QCM electrode is monitored when exposed to different gas concentrations of ethanol, toluene, chloroform, humidity, and formamide, ranging from 47 to 142 ppm. The frequency shift indicated the detected gas concentration. The results demonstrate good repeatability and reversibility, which are crucial indicators of a sensor's reliability. This reliability is essential for applications in environmental monitoring or industrial safety, where accurate gas detection is critical. [ABSTRACT FROM AUTHOR]

Silicon alloys have the highest specific capacity when used as anode material for lithium-ion batteries; however, the drastic volume change inherent in their use causes formidable challenges toward achieving stable cycling performance. Large quantities of binders and conductive additives are typically necessary to maintain good cell performance. In this report, only 2% (by weight) functional conductive polymer binder without any conductive additives was successfully used with a micron-size silicon monoxide (SiO) anode material, demonstrating stable and high gravimetric capacity (>1000 mAh/g) for ∼500 cycles and more than 90% capacity retention. Prelithiation of this anode using stabilized lithium metal powder (SLMP) improves the first cycle Coulombic efficiency of a SiO/NMC full cell from ∼48% to ∼90%. The combination enables good capacity retention of more than 80% after 100 cycles at C/3 in a lithium-ion full cell.