Abstract: In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest ...

The inverse hyperbolic sine and cosine functions give the "Invalid input" error for values greater than or equal to 10^100. This is because the limit for all trig ...

Evidence strongly indicates that human decision makers discount the future using a hyperbolic function instead of following an exponential, which has been the long-standing assumption. We compare the ...

Artificial intelligence (AI) presents both a large opportunity for employers — and potentially a source of reputational risk — depending on how its adoption is handled. As AI transforms the workplace, ...

American Journal of Mathematics, Vol. 138, No. 3 (June 2016), pp. 821-878 (58 pages) Let f be a modular form of weight k and Nebentypus ψ. By generalizing a construction of Dabrowski and Delbourgo, we ...

With iOS 18.3, Apple made a small but meaningful change to the way the Calculator app works, reintroducing repeating operations. When you tap the equals sign twice, the app will now repeat the last ...

Cupertino-based Apple has reportedly released iOS 18.3 Public Beta 2, offering a glimpse at the upcoming software update. According to a report by Business Today, the latest beta introduces minor ...

Nitin has so far been investing in the stocks directly, but he is planning to take a leap and start investing in derivatives as well. But as a newbie to this, he is facing a dilemma regarding ...

Ever wondered how businesses and investors protect themselves from currency swings? Currency derivatives, such as futures, options, swaps, and forward contracts, offer powerful tools to manage and ...