We consider an infinite series, due to Ramanujan, which converges to a simple expression involving the natural logarithm. We show that Ramanujan’s series represents a completely monotone function, and explore some of its consequences, including a non-trivial family of inequalities satisfied by the natural logarithm, some formulas for the Euler–Mascheroni constant, and a recurrence satisfied by the Bernoulli numbers. We also provide a one-parameter generalization of Ramanujan’s series, which includes as a special case another related infinite series evaluation due to Ramanujan.
Category: futurism – Page 84
Researchers create a 2D array of molecular switches with 12 controllable states per molecule, showing promise for next-generation ultra-high-density memory systems.
New research hints that plate tectonics began earlier than 4 billion years ago — not long after Earth had formed.
It’s critical for leaders to know when to make a difficult decision before it leads to an unavoidable setback.
Paraconsistent Logic
Posted in futurism
Unlike the Concorde
Posted in futurism, transportation
Boom Supersonic has taken another step towards its ambitious goal of reintroducing commercial supersonic air travel by the end of this decade. The Colorado-based company released key updates on Tuesday regarding its flagship Overture aircraft and the Symphony engine that will power the supersonic commercial jet. This comes a month after Boom Supersonic officially inaugurated its state-of-the-art factory located at the Piedmont Triad International Airport in Greensboro, North Carolina. The American company chose the Farnborough International Airshow in the UK to reveal Overture’s cutting-edge flight deck, which is built around technology developed by partner Honeywell.
“As we stand here at Farnborough in 2024, it’s now been two decades since either Boeing or Airbus has launched an all-new airliner programme,” said Chief Executive Blake Scholl. “We’re in danger of going a generation without new airliners. We’ve stopped progressing and, in many ways, we’ve gone backwards. It’s never been more clear that passengers and airlines are not well-served by the duopoly we have today.”
According to the information revealed by Boom, Overture’s state-of-the-art flight deck runs on Honeywell’s Anthem avionics suite. Electric vertical takeoff and landing (eVTOL) aircraft manufacturers Lilium and Vertical Aerospace have also gone with the same futuristic system. Boom claims Overture would be the commercial jet to feature dual-force feedback sidesticks, which will give a tactile feel to the pilots of how the aircraft is flying. “Overture’s fly-by-wire system sends artificial feel to the stick, giving the pilot a tactile stick and rudder experience,” Scholl added.
A ULA (United Launch Alliance) Atlas V rocket rolled to Launch Complex 41 on the afternoon of Saturday, July 27.
Is a gamma-ray laser possible?
Posted in futurism
Federal funding will allow Rochester scientists and their European collaborators to study the feasibility of producing coherent gamma rays.