For a linear ordinary differential equation of variable coefficients in which the highest order derivative $d^{n}y/dx^n$ is multiplied by a small parameter $\epsilon ...

Kyoto, Japan -- Black holes embody the ultimate abyss. They are the most powerful sources of gravity in the universe, capable of dramatically distorting space and time around them. When disturbed, ...

Black holes embody the ultimate abyss. They are the most powerful sources of gravity in the universe, capable of dramatically distorting space and time around them. When disturbed, they begin to "ring ...

It’s surprising how much complexity and beauty emerge from these equations,” said Taiga Miyachi, referring to the winding patterns his team discovered in the vibrations of black holes. Astronomers are ...

Scientists have uncovered a breakthrough in our understanding of black holes by using a powerful mathematical tool known as the exact Wentzel-Kramers-Brillouin (WKB) method. The study, published in ...

Black holes are some of the most intriguing objects in the Universe. Their gravitational pull is so strong that not even light can escape from their surfaces. Astronomers can only observe light ...

Figure 1: The merger of two black holes can set off vibrations in the resulting black hole. RIKEN researchers have analyzed these vibrations using a versatile ...