In this decade there will an unprecedented growth of generated data, computations, instructions, and operations. This growth may not compromise clean air, clean water and a sustainable energy and material usage, but rather facilitate these prerequisites for flora and fauna. There are many indications (expected trends and estimates) showing that the Internet Sector will be able to provide solutions to other Sectors such as Buildings, Transportation and Industry which will help reduce the total global consumption of energy and materials. For instance, products are replaced by virtual services e.g. by using e-readers instead of paperbacks, and transportation is avoided by online shopping or Internet meetings. This is more resource and energy efficient than before and entire sectors, like transport, industry, and agriculture can be optimized. Internet may foster new sustainable lifestyles which can lower the affluence despite certain rebound effects. The underlying idea is that e.g. human-related global greenhouse gas (GHG) supply can be significantly halted if existing and developing ICT Solutions are used in other sectors (and in the Internet infrastructure itself) to cause a handprint. Such solutions include products-sold-as-services, smart Grid and smart metering. Compared to earlier approaches, the 2020 transformative effects on smart work, land use and smart circularity are included in the discussion, as well as consequential LCA modelling. Internet’s handprint will be 4-7 times its footprint in 2030. The handprint is highly dependent e.g. on how large share of the buildings can adopt smart metering and the product to service rate. Internet will in itself use intelligent ICT solutions as well as neuromorphic, reversible and superconducting computing as well as nanophotonics to mitigate its own material and energy use. However, more importantly the intelligent ICT solutions should be used in the rest of the society to reach efficiency goals. Power saving is a highly efficient strategy for cost reduction in the Internet Sector itself and beyond.

Nowadays, scholars are very interested to determine the solution of different Diophantine equations because these equations have numerous applications in the field of coordinate geometry, cryptography, trigonometry and applied algebra. These equations help us for finding the integer solution of famous Pythagoras theorem and Pell’s equation. Finding the solution of Diophantine equations have many challenges for scholars due to absence of generalize methods. In the present paper, author studied the exponential Diophantine equation \((2^{2m+1}-1)+(13)^n=z^2\), where \(m,n\) are whole numbers, for its solution in whole numbers. Results show that the exponential Diophantine equation \((2^{2m+1}-1)+(13)^n=z^2\), where \(m\), \(n\) are whole numbers, has no solution in whole number.

We theoretically present the physical realization of one dimensional (1D) atom localization by superposition of three standing wave fields in a four-level tripod atomic configuration. The most interesting result that we observe is the variation of the bandwidth of the localization peaks with the intensity of the space independent Rabi frequency. A sharp single and double localized peaks are observed at different direction of the wave numbers. The bandwidth of a localized peak is reduced as the intensity of the space independent Rabi frequency goes on increasing, which corresponds to the reduction in the uncertainty. These results will hopefully contribute to the development of current high tech-applications.