Use of Microsoft Object Linking and Embedding ( OLE ) objects limits the interoperability, because these objects are not widely supported in programs for viewing or editing files ( e. g. embedding of other files inside the file, such as tables or charts from a spreadsheet application in a text document or presentation file ).

* Torkel Franzen ( 2005 ), Godel's theorem: An Incomplete Guide to its Use and Abuse, A. K.

Two long papers published in 1840 — one on attractions and Clairaut's theorem, and the other on the variation of gravity at the surface of the earth — also demand notice, as do his mathematical memoirs on the critical values of sums of periodic series ( 1847 ) and on the numerical calculation of a class of definite integrals and infinite series ( 1850 ) and his discussion of a differential equation relating to the breaking of railway bridges ( 1849 ), research related to his evidence given to the Royal Commission on the Use of Iron in Railway structures after the Dee bridge disaster of 1847.

Use the binomial theorem to expand ( a + b )< sup > n + m − 1 </ sup > ( with commutativity assumed ):

# Use the factor theorem to conclude that is a factor of.

Use of these roads by the public results in substantial benefits to the localities the roads serve.

Use nuclear propulsions to keep our long-range military aircraft in the air for the majority of their useful life.

Use this section to plan now to make the most of your vacation in photogenic America.

Use well-wedged clay, free of air bubbles and pliable enough to bend without cracking.

Use white or buff clay, rolled to 3/16'' '' thickness.

Use mold to cut four side pieces.

Use water on finger to smooth seams and edges.

Use one coat of Firzite and one coat of marine paint.

Use deductable insurance wherever feasible.

Use the air hose for this job.

Use of the characteristics of the platform components for an indication of true heading.

`` Use of such weapons has been outlawed by the general opinion of civilized mankind.

Use one 6-ounce chicken breast for each guest.

Use dramatization -- for example, in discussing the Lord's Supper or church symbolism.

Use audio-visual aids.

Use a textbook with assigned readings each week.

Use all the lotion you want, and for goodness' sake, stay in out of the sun for a couple of days ''.

Use of Video Arraignment system allows the courts to conduct the requisite arraignment process without the need to transport the person who has been formally accused ( offender ) to the courtroom by using an audio-visual link between the location where the offender is being held and the courtroom.

Use of the video arraignment process addresses the problems associated with having to transport offenders.

Some Transparency, No Accountability: The Use of Oil Revenues in Angola and Its Impact on Human Rights.

Use of the name " Ashes " was suggested by the Australian team when rugby league matches between the two countries commenced in 1908.

:( 2 ) Use work slides or some other form of carrier so that when a workman completes his operation, he drops the part always in the same place — which place must always be the most convenient place to his hand — and if possible have gravity carry the part to the next workman for his operation.

:( 3 ) Use sliding assembling lines by which the parts to be assembled are delivered at convenient distances.

Use of the term to describe writers, for example, is certainly valid, but less common, and mostly restricted to contexts like criticism.

Use of the word " artiste " can also be a pejorative term.

In particular, as follows from the Whitney embedding theorem, any m-dimensional Riemannian manifold admits an isometric C < sup > 1 </ sup >- embedding into an arbitrarily small neighborhood in 2m-dimensional Euclidean space.

The interest here is in how large n must be, in terms of the dimension m of M. The Whitney embedding theorem states that n = 2m is enough.

* Whitney embedding theorem

In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney:

* The strong Whitney embedding theorem states that any smooth m-dimensional manifold ( required also to be Hausdorff and second-countable ) can be smoothly embedded in Euclidean 2m-space, if m > 0.

* The weak Whitney embedding theorem states that any continuous function from an n-dimensional manifold to an m-dimensional manifold may be approximated by a smooth embedding provided m > 2n.

Since is simply-connected, one can assume this path bounds a disc, and provided one can further assume ( by the weak Whitney embedding theorem ) that the disc is embedded in such that it intersects the image of only in its boundary.

The occasion of the proof by Hassler Whitney of the embedding theorem for smooth manifolds is said ( rather surprisingly ) to have been the first complete exposition of the manifold concept precisely because it brought together and unified the differing concepts of manifolds at the time: no longer was there any confusion as to whether abstract manifolds, intrinsically defined via charts, were any more or less general than manifold extrinsically defined as submanifolds of Euclidean space.

This result is an isotopy version of the weak Whitney embedding theorem.

This result is an isotopy version of the strong Whitney embedding theorem.

# REDIRECT Whitney embedding theorem

For example, the Whitney embedding theorem tells us that every smooth manifold can be embedded as a smooth submanifold of R < sup > n </ sup >, whereas it is " rare " for a complex manifold to have a holomorphic embedding into C < sup > n </ sup >.

By the Whitney embedding theorem any second-countable smooth n-manifold can be smoothly embedded in R < sup > 2n </ sup >.

The precise reason for the difference at dimension 5 is because the Whitney embedding theorem, the key technical trick which underlies surgery theory, requires 2 + 1 dimensions.

All compact topological manifolds can be embedded into for some n, by the Whitney embedding theorem.

* Whitney embedding theorem

Another simple procedure for triangulating differentiable manifolds was given by Hassler Whitney in 1957, based on his embedding theorem.

A Whitney triangulation or clean triangulation of a surface is an embedding of a graph onto the surface in such a way that the faces of the embedding are exactly the cliques of the graph ( Hartsfeld and Gerhard Ringel 1981 ; Larrión et al.

# REDIRECT Whitney embedding theorem