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Watch fans spent a week falling in love with colorful Royal Oak wristwatches that didn’t exist—then the real thing arrived。 Now, fantasy is becoming a manufacturing opportunity
Klimošová, Piguet, and Rozhoň conjectured that any graph with minimum degree $k/2$ and sufficiently many vertices of degree $k$ should contain all trees with $k$ edges. We prove an asymptotic version of this conjecture for dense host graphs. We obtain interesting corollaries: the first is an asymptotic version of the Erdős--Sós conjecture for dense host graphs, which works without any bounded-degree restriction on the guest trees. Secondly, by leveraging recent results by Pokrovsky, we can translate our results to sparse host graphs in the case of bounded-degree guest trees.
It is shown how spin one vector matter fields can be coupled to a Yang-Mills theory. Such matter fields are defined as belonging to a representation $R$ of this Yang-Mills gauge algebra $\mathfrak{g}$. It is also required that these fields together with the original gauge fields be the gauge fields of an embedding total gauge algebra $\mathfrak{g}_{\rm tot}$. The existence of a physically consistent Yang-Mills action for the total algebra is finally required. These conditions are rather restrictive, as shown in some examples: non-trivial solutions may or may not exist depending on the choice of the original algebra $\mathfrak{g}$ and of the representation $R$. Some examples are shown, the case of the initial algebra $\mathfrak{g}$ = $\mathfrak{u}(1)\oplus\mathfrak{su}(2)$ being treated in more detail.
In the de Broglie-Bohm quantum theory, particles describe trajectories determined by the flux associated with their wave function. These trajectories are studied here for relativistic spin-one-half particles.Based in explicit numerical calculations for the case of a massless particle in dimension three space-time, it is shown that if the wave function is an eigenfunction of the total angular momentum, the trajectories begin as circles of slowly increasing radius until a transition time at which they tend to follow straight lines. Arrival times at some detector, as well as their probability distribution are calculated, too. The chosen energy and momentum parameters are of the orders of magnitude met in graphene's physics.
Komlos [Komlos: Tiling Turan Theorems, Combinatorica, 2000] determined the asymptotically optimal minimum-degree condition for covering a given proportion of vertices of a host graph by vertex-disjoint copies of a fixed graph H, thus essentially extending the Hajnal-Szemeredi theorem which deals with the case when H is a clique. We give a proof of a graphon version of Komlos's theorem. To prove this graphon version, and also to deduce from it the original statement about finite graphs, we use the machinery introduced in [Hladky, Hu, Piguet: Tilings in graphons, arXiv:1606.03113]. We further prove a stability version of Komlos's theorem.
It's not entirely clear how the exploit works。 Microsoft says it's investigating
Astronomers using NASA’s James Webb Space Telescope have created the clearest map yet of the universe’s “cosmic web” — the enormous hidden structure that connects galaxies across space。 By analyzing more than 164,000 galaxies through the massive COSMOS-Web survey, researchers were able to trace this vast network back to when the universe was just a
Scientists at UC Santa Barbara have created a remarkable new material that works like a “rechargeable solar battery,” storing sunlight inside tiny molecules and releasing it later as heat — even long after the sun goes down。 Inspired by reversible changes found in DNA and photochromic sunglasses, the system captures solar energy without relying on
NASA’s Roman Space Telescope could expose a vast hidden population of neutron stars lurking unseen across the Milky Way。 By detecting subtle shifts in starlight caused by gravity, the mission may identify and even weigh isolated neutron stars that are otherwise impossible to see。 Scientists hope the discoveries will reveal how these extreme objects
NASA’s Curiosity rover had an unexpectedly stubborn Mars souvenir after drilling into a rock nicknamed “Atacama” — the entire chunk ripped loose from the ground and stayed stuck to the rover’s drill。 Engineers watched as Curiosity shook, vibrated, tilted, and spun the drill over several days in an effort to free the rock, while cameras captured the
A mysterious comet from beyond our solar system is giving astronomers a rare glimpse into alien worlds — and it may have formed in a place far colder and stranger than anything around our Sun。 The interstellar visitor, called 3I/ATLAS, contains an astonishingly high amount of “heavy water,” far exceeding anything seen in our own solar system
Polo GTI takes plenty of inspiration from the original Golf GTI of 1976
The little pauses, “ums,” and moments when you struggle to find the right word may reveal far more about your brain than anyone realized。 Researchers discovered that everyday speech patterns are closely tied to executive function — the mental system that powers memory, planning, focus, and flexible thinking。 By using AI to analyze natural conversat
Astronomers using the James Webb Space Telescope have spotted something that shouldn’t exist—at least not so early in the universe。 A massive galaxy, formed less than 2 billion years after the Big Bang, appears to have no rotation at all, a trait usually seen only in much older, evolved galaxies。 This challenges current theories that young galaxies
Scientists in Germany have pulled off a staggering computing feat by fully simulating a 50-qubit quantum computer for the first time ever using Europe’s new exascale supercomputer, JUPITER。 The breakthrough shatters the previous 48-qubit record and highlights just how powerful next-generation supercomputers have become
Publishers would have to offer "independent" play patch or refunds after server shutdowns