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In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We apply these results to partial differential calculus. On étudie une itération de Rd dans Rd définie par un difféomorphisme polynomial borné. On montre que les courbes semi invariantes tendent asymptotiquement vers des courbes paramétrées par des fonctions de Weierstrass. Cela justifie les calculs d'échelle d'autosimilarité et de dimension fractale comme le pratiquent des praticiens à partir d'intuitions pertinentes sur des itérations chaotiques. On applique ces résultats au calcul différentiel.
A new quantum device can generate precisely controlled bursts of sound-like particles, or phonons, by forcing electrons through an ultra-thin crystal at extremely low temperatures。 The surprising behavior pushes beyond the limits predicted by current theories, suggesting scientists need to rethink how energy moves through advanced materials。 In the
Researchers found that twisting layered sheets of hexagonal boron nitride can dramatically change the light produced by quantum emitters embedded within the material。 The technique offers an unexpected new level of control over components that could power future quantum computers, communications systems, and sensors
Hubble has captured a spectacular view of LH 95, where about 2,500 young stars are still on their journey to becoming full-fledged stars。 Scientists discovered these growing stars can keep pulling in gas and dust for millions of years, extending an important stage of stellar development。 The region also contains multiple generations of stars living
A strange "chirping" signal from a distant supernova has revealed the birth of a magnetar, confirming that these incredibly magnetic neutron stars can power the universe's brightest stellar explosions。 The discovery also marks the first time Einstein's general relativity has been used to explain the mechanics of a supernova
Physicists have developed a new optical centrifuge that can precisely spin molecules inside a superfluid for the first time。 The advance could help unravel some of the biggest mysteries of quantum liquids and reveal how superfluidity breaks down at the atomic scale
Celebrating the United States' 250th anniversary, NASA released a stunning Hubble portrait of Messier 3, an ancient globular cluster with more than 500,000 stars。 The remarkable cluster is helping scientists unravel the Milky Way's past thanks to its rare stars and possible origins in a long ago cosmic merger
Two newly confirmed "super-puff" planets are so diffuse that they are less dense than cotton candy, despite being about the size of Jupiter。 Their rare orbital relationship and enormous, lightweight atmospheres could provide valuable clues about how some of the strangest planets in the galaxy come to exist
A rare meteorite has revealed evidence of a massive lost world that once orbited the young Sun before being destroyed in a catastrophic collision。 The discovery suggests some early planets formed from dramatically different materials than Earth and Mars, rewriting part of the solar system’s origin story
An unusual gravitational wave signal has renewed hopes that primordial black holes, long considered purely theoretical, may finally be within reach of discovery。 If confirmed, they could solve one of astronomy's greatest mysteries by explaining the nature of dark matter
Scientists have uncovered new evidence that fireworks can pollute both the air and water in ways that extend beyond the visible smoke。 The findings show that leftover debris, fine particles, and airborne chemicals may affect ecosystems and increase people's exposure to air pollution during major celebrations
Move affects ~20% of the gaming division, which will refocus on its biggest franchises
What if consciousness isn’t limited to brains like ours。 Philosophers Eric Schwitzgebel and Jeremy Pober argue that consciousness could arise in many different forms of life, even in beings built from radically different materials than those found on Earth。 Drawing on the vastness of the universe and the likely existence of countless alien civiliza
The discovery underscores the increased effort being poured into Mac infostealers
A new AI-powered framework could transform how astronomers measure the expansion of the Universe。 By analyzing images of Type Ia supernovae and modeling their environments in unprecedented detail, researchers can estimate cosmic distances with near-spectroscopic accuracy。 The technique is designed for the flood of data expected from the upcoming Ve