Information om | Engelska ordet ISOMETRICALLY

Exempel på hur man kan använda ISOMETRICALLY i en mening

• If the underlying field is the real numbers, the two are isometrically isomorphic; if the underlying field is the complex numbers, the two are isometrically anti-isomorphic.
• It cannot exist as a solid object in ordinary three-dimensional Euclidean space, although its surface can be embedded isometrically (bent but not stretched) in five-dimensional Euclidean space.
• So importantly, for a Banach space to be reflexive, it is not enough for it to be isometrically isomorphic to its bidual; it is the canonical evaluation map in particular that has to be a homeomorphism.
• If the sphere is isometrically embedded in Euclidean space, the sphere's intersection with a plane is a circle, which can be interpreted extrinsically to the sphere as a Euclidean circle: a locus of points in the plane at a constant Euclidean distance (the extrinsic radius) from a point in the plane (the extrinsic center).
• In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent space.
• A slight crouch is adopted in order to be in a more effective striking posture whilst also isometrically preloading the muscles; this allows the stroke to be played more dynamically.
• The runners take up position in the blocks on the "ready" command, adopt a more efficient starting posture which isometrically preloads their muscles on the "set" command, and stride forwards from the blocks upon hearing the starter's pistol.
• In 1971, Jeff Cheeger and Detlef Gromoll proved that if a geodesically complete and connected Riemannian manifold of nonnegative Ricci curvature contains any geodesic line, then it must split isometrically as the product of a complete Riemannian manifold with.
• Setup: When performing a deadlift, a lifter sets in a position that eccentrically loads the gluteus maximus, gluteus minimus, biceps femoris, semitendinosus and semimembranosus while the muscles of the lumbar contract isometrically in an effort to stabilize the spine.
• When the sprinters adopt the 'set' position in the blocks they are able to adopt a more efficient starting posture and isometrically preload their muscles.
• The sprinters follow three initial instructions: 'on your marks', instructing them to take up position in the starting blocks; 'set', instructing them to adopt a more efficient starting posture, which also isometrically preloads their muscles.
• The erector spinae muscles of the lower back work isometrically to keep the spine in an extended position while the hamstrings and gluteus maximus work isotonically to perform hip extension.
• An IPJ involves a crouched position being assumed for a longer period of time in the interests of maximising the ability to isometrically preload the muscles.
• Thus a closed Riemannian 2-manifold of non-positive curvature can never be embedded isometrically in ; however, as Adriano Garsia showed using the Beltrami equation for quasiconformal mappings, this is always possible for some conformally equivalent metric.
• The claws are sexually dimorphic, with males' claws showing positive allometry, while females' claws grow isometrically; a male's claws thus become proportionally larger as the crab grows, becoming much larger than those of females.
• He proved the Rådström embedding theorem, which implies that the collection of all nonempty compact convex subsets of a normed real vector-space (endowed with the Hausdorff distance) can be isometrically embedded as a convex cone in a normed real vector-space.
• Caprace and Sageev proved that if G is a finitely generated group acting isometrically properly discontinuously and cocompactly on a geodetically complete CAT(0) cubical complex X, then either X splits as a direct product of two unbounded convex subcomplexes, or G contains a rank-1 element.

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