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Reflexive space. In the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from into its bidual (which is the strong dual of the strong dual of ) is a homeomorphism (or equivalently, a TVS isomorphism ). A normed space is reflexive if and only ...
The palmar grasp reflex (or grasp reflex) is a primitive and involuntary reflex found in infants of humans and most primates. When an object, such as an adult finger, is placed in an infant's palm, the infant's fingers reflexively grasp the object. [1] Placement of the object triggers a spinal reflex, resulting from stimulation of tendons in ...
Australia, officially the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands.
An animation of an RRT starting from iteration 0 to 10000. A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. The tree is constructed incrementally from samples drawn randomly from the search space and is inherently biased to grow ...
1) (similar to trees as graphs) A real tree is a geodesic metric space which contains no subset homeomorphic to a circle. [1] 2) A real tree is a connected metric space which has the four points condition [2] (see figure): For all . 3) A real tree is a connected 0-hyperbolic metric space [3] (see figure). Formally,
Falling cat problem. A falling cat modeled as two independently rotating parts turns around while maintaining zero net angular momentum. The falling cat problem is a problem that consists of explaining the underlying physics behind the observation of the cat righting reflex . Although amusing and trivial to pose, the solution of the problem is ...
Math Images Project. The logo of the Math Images Project. The Math Images Project is a wiki collaboration between Swarthmore College, the Math Forum at Drexel University, and the National Science Digital Library. The project aims to introduce the public to mathematics through beautiful and intriguing images found throughout the fields of math.
A free group of rank k clearly has subgroups of every rank less than k. Less obviously, a (nonabelian!) free group of rank at least 2 has subgroups of all countable ranks. The commutator subgroup of a free group of rank k > 1 has infinite rank; for example for F(a,b), it is freely generated by the commutators [a m, b n] for non-zero m and n.