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Oxygen tweaking may be key to accelerator optimization

Particle accelerators are pricey, but their cost comes with good reason: These one-of-a-kind, state-of-the-art machines are intricately designed and constructed to help us solve mysteries about what makes up our universe. ...

New study reveals oceanic seabirds chase tropical cyclones

A new study published today in Current Biology, "Oceanic Seabirds Chase Tropical Cyclones," reveals that the rare Desertas Petrels (Pterodroma deserta), a wide-ranging seabird in the North Atlantic, exhibit unique foraging ...

Moon 'swirls' could be magnetized by unseen magmas

Lunar swirls are light-colored, sinuous features on the moon's surface, bright enough to be visible from a backyard telescope. Some people think they look like the brushstrokes in an abstract painting. But these are not mere ...

Researchers thwart resistant bacteria's strategy

Antibiotic resistant bacteria are experts in evolving new strategies to avoid being killed by antibiotics. One such bacterium is Pseudomonas aeruginosa, which is naturally found in soil and water, but also hospitals, nursing ...

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In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball or bagel. On the other hand, there are surfaces which cannot be embedded in three-dimensional Euclidean space without introducing singularities or intersecting itself — these are the unorientable surfaces.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide coordinates on it — except at the International Date Line and the poles, where longitude is undefined. This example illustrates that not all surfaces admits a single coordinate patch. In general, multiple coordinate patches are needed to cover a surface.

Surfaces find application in physics, engineering, computer graphics, and many other disciplines, primarily when they represent the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

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