Nigerian Mathematical Society

Happy Pi day 3.14

New Image from the James Webb Space Telescope

Cosmic cliffs & a sea of stars. The James Webb Space Telescope reveals baby stars in the Carina Nebula, where ultraviolet radiation and stellar winds shape colossal walls of dust and gas.

This landscape of “mountains” and “valleys” speckled with glittering stars is actually the edge of a nearby, young, star-forming region called NGC 3324 in the Carina Nebula. Captured in infrared light by NASA’s new James Webb Space Telescope, this image reveals for the first time previously invisible areas of star birth.

Called the Cosmic Cliffs, Webb’s seemingly three-dimensional picture looks like craggy mountains on a moonlit evening. In reality, it is the edge of the giant, gaseous cavity within NGC 3324, and the tallest “peaks” in this image are about 7 light-years high. The cavernous area has been carved from the nebula by the intense ultraviolet radiation and stellar winds from extremely massive, hot, young stars located in the center of the bubble, above the area shown in this image.

Credit: NASA/ESA/CSA

New Image from the James Webb Space Telescope

Captured in exquisite detail, the James Webb Space Telescope peered through the thick dust of Stephan’s Quintet, a galaxy cluster showing huge shockwaves and tidal tails.

Stephan’s Quintet, a visual grouping of five galaxies, is best known for being prominently featured in the holiday classic film, “It’s a Wonderful Life.” Today, NASA’s James Webb Space Telescope reveals Stephan’s Quintet in a new light. This enormous mosaic is Webb’s largest image to date, covering about one-fifth of the Moon’s diameter. It contains over 150 million pixels and is constructed from almost 1,000 separate image files. The information from Webb provides new insights into how galactic interactions may have driven galaxy evolution in the early universe.

With its powerful, infrared vision and extremely high spatial resolution, Webb shows never-before-seen details in this galaxy group. Sparkling clusters of millions of young stars and starburst regions of fresh star birth grace the image. Sweeping tails of gas, dust and stars are being pulled from several of the galaxies due to gravitational interactions. Most dramatically, Webb captures huge shock waves as one of the galaxies, NGC 7318B, smashes through the cluster.

Credit: NASA/ESA/CSA

How can we compute (for the first time) all the non trivial zeros of the Riemann zeta function and show they lie only on one line (where the real part is Re(z) = 1/2)?

For this we derived an integral, showed that it is equal to the Dirichlet eta function and used it to proof, that the non trivial zeros can only be delivered if the (complex) harmonic numbers fulfill a specific criteria.

For a detailed look and a complete derivation of the equations, we refer you to:

https://www.academia.edu/38300048/Distribution_of_primes_the_computation_of_the_non_trivial_zeros_of_the_Riemann_zeta_function_root_identities_replication_identity_zero_free_zone_and_Weil_conjecture

Everyone can now compute the non trivial zeros of the Riemann zeta function. Have fun!

I probably have to work out some minor details in the coming weeks and also look how the new results are connected to the 'expansion of the prime number theorem'.

Assuming we have party A with three members and party B with also three members, they are to cross a river but the boot can only take two people at a time including the boot driver. In how many ways can all those passengers cross without any party out number another because if that happen the party with more member will kill the one with less number, remember that any body can be the driver.

Prof Bashir Ali of Math department Bayero university Kano was just Elected President of Nigerian Mathematical Society

Morning to all our fellow mathematians

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