In the rapidly-evolving modern civilization, the inspection, collection, and removal of rubbish waste are seen as some of the major causes of dispute because their neglect will lead to leverage unfavourable environmental impacts. A boring method is the conventional approach to physically directing and gathering the garbage, as it necessitates require human labour and assets, which raises expenses further. This study describes an open IoT platform-based trash-checking system that works with an Arduino or Raspberry Pi board. The Arduino is a microcontroller included in the suggested architecture. A Wi-Fi module, an ultrasonic sensor, and a large battery information obtained from the load cell and ultrasonic sensor is achieved with the help of the Arduino microcontroller. Making use of the depth of the debris in the water using an ultrasonic sensor,resolved, and the volume and weight of the waste estimates are also made for the garbage cell's receptacle. The LCD screen is used for showing the information. The displayed information is sent to the web through the Wi-Fi module. An open IoT debate and Thingspeak used to adhere to the garbage framework. In this context, the executive can successfully monitor and manage the waste disposal.
We will have a study on the different proofs of Liouville’s theorem. There are many different ways to prove Liouville’s theorem. Here we study proofs using Cauchy’s integral formula, Cauchy’s estimate and by using Picard’s Little theorem. While comparing these proofs we can conclude that if we use Picard’s Little theorem, we can prove Liouville’s theorem more easily.
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