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Möbius syndrome does not prevent individuals from experiencing personal and professional success .< ref > Due to the importance of facial expression and smiling in social interaction, the inability to form either can lead to individuals with Möbius being perceived as unfriendly or uninterested in conversations or other social interactions.
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Möbius and syndrome
Möbius syndrome ( also spelled Moebius ) is an extremely rare congenital neurological disorder which is characterized by facial paralysis and the inability to move the eyes from side to side.
Most people with Möbius syndrome are born with complete facial paralysis and cannot close their eyes or form facial expressions.
Most people with Möbius syndrome have normal intelligence, although their lack of facial expression is sometimes incorrectly taken to be due to dullness or unfriendliness.
It is named for Paul Julius Möbius, a neurologist who first described the syndrome in 1888.
Möbius syndrome results from the underdevelopment of the VI and VII cranial nerves.
People with Möbius syndrome are born with facial paralysis and the inability to move their eyes laterally.
It is estimated that there are, on average, 2 to 20 cases of Möbius syndrome per million births.
Also, because a person with Möbius syndrome cannot follow objects by moving their eyes from side to side, they turn their head instead.
Other symptoms that sometimes occur with Möbius syndrome are:
Children with Möbius syndrome may have delayed speech because of paralysis of the lips.
However, with speech therapy, most people with Möbius syndrome can develop understandable speech.
Möbius syndrome has been associated with increased occurrence of the symptoms of autism.
However, some children with Möbius syndrome are mistakenly labeled as mentally retarded or autistic because of their expressionless faces, strabismus, and frequent drooling.
There is no single course of medical treatment or cure for Möbius syndrome.
Also, the surgery cannot be considered a " cure " for Möbius syndrome, because it does not improve the ability to form other facial expressions.
People with Möbius syndrome can compensate for a lack of expression by using body language, posture, and vocal tone to convey emotion.
The causes of Möbius syndrome are poorly understood.
Möbius syndrome is thought to result from a vascular disruption ( temporary loss of bloodflow ) in the brain during prenatal development.
There could be many reasons that a vascular disruption leading to Möbius syndrome might occur.
In the majority of cases of Möbius syndrome in which autosomal dominant inheritance is suspected, sixth and seventh cranial nerve paralysis ( palsy ) occurs without associated limb abnormalities.
The use of the drugs misoprostol or thalidomide by women during pregnancy has been linked to the development of Möbius syndrome in some cases.
Studies show that the use of misoprostal during pregnancy increases the risk of developing Möbius syndrome by a factor of 30.
While this is a dramatic increase in risk, the incidence of Möbius syndrome without misoprostal use is estimated at one in 50000 to 100000 births ( making the incidence of Möbius syndrome with misoprostal use, less than one in 1000 births ).
Möbius and does
In general, a surface is said to be orientable if it does not contain a homeomorphic copy of the Möbius strip ; intuitively, it has two distinct " sides ".
Note that a Möbius transformation does not necessarily map circles to circles and lines to lines: it can mix the two.
The four elements are the identity, a Dehn twist on the two-sided curve which does not bound a Möbius strip, the y-homeomorphism of Lickorish, and the product of the twist and the y-homeomorphism.
Möbius and individuals
The first use of this term is usually attributed to Karl Möbius in 1877, but already in 1825, the French naturalist Adolphe Dureau de la Malle used the term societé about an assemblage of plant individuals of different species.
Möbius and from
Robert Engman's Möbius Strip hangs from the crown of the Barker Engineering Library's reading room located inside the Great Dome
For example, the sphere and torus are orientable, while the real projective plane is not ( because deleting a point or disk from the real projective plane produces the Möbius strip ).
It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above.
If the strip is cut along about a third of the way in from the edge, it creates two strips: One is a thinner Möbius strip — it is the center third of the original strip, comprising 1 / 3 of the width and the same length as the original strip.
Möbius strip belts are no longer manufactured because untwisted modern belts can be made more durable by constructing them from several layers of different materials.
He kept the nickname and later decided to completely change his name from Ralph Möbius to Rio Reiser because he played a leading role in the movie " Johnny West " and needed a catchy artist name.
Concepts of vector spaces emerged from the conception of barycentric coordinates by Möbius in 1827, to the modern definition of vector spaces and linear maps by Peano in 1888.
Möbius aromaticity occurs when a cyclic system of molecular orbitals, formed from p < sub > π </ sub > atomic orbitals and populated in a closed shell by 4n ( n is an integer ) electrons, is given a single half-twist to correspond to a Möbius strip.
This self intersection precludes the cross-cap from being topologically equivalent ( i. e., homeomorphic ) to a Möbius strip.
A model for the Möbius plane that comes from the Euclidean plane is the Riemann sphere.
A locally conformally flat manifold is locally conformal to a Möbius geometry, meaning that there exists an angle preserving local diffeomorphism from the manifold into a Möbius geometry.
Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection ( from the new position of the sphere ) to the plane.
Möbius transformations can be more generally defined in spaces of dimension n > 2 as the bijective conformal orientation-preserving maps from the n-sphere to the n-sphere.
from the general linear group GL ( 2, C ) to the Möbius group, which sends the matrix to the transformation f, is a group homomorphism.
However, IFSs may also be built from non-linear functions, including projective transformations and Möbius transformations.
Universal Teichmüller space is defined to be the space of real analytic quasiconformal mappings of the unit disc D, or equivalently the upper half-plane H, onto itself, with two mappings considered to be equivalent if on the boundary one is obtained from the other by composition with a Möbius transformation.
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