Sentence examples for for the proof and from inspiring English sources

For the proof and details, see Chapter 7 in [16].

Hit up the video above for the proof (and the pudding).

For those still unfamiliar with the concept Bitcoin is a peer-to-peer network that allows for the proof and transfer of ownership without the need of a trusted third party, the Goldman Sachs report explains.

Then, we have the following result (see, e.g., [1, 15] for the proof and more precise results): The time t c is a conjugate time along xif and only if the mapping (exp _{x_{0}}(t_{c},cdot)) is not an immersion at p 0, i.e., the differential of the mapping (exp _{x_{0}}(t_{c},cdot)) is not injective.

For simplifying the proof and convenience, γ is taken as an integer and satisfies condition (5) throughout the proof.

For the proofs and more details as regards ANR-spaces and multivalued maps, we recommend [7, 8].

The first major step was the adoption of desktop publishing software for producing the proofs and final copy of volume 33 in 1994.

A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian functions standardization.

Special thanks are also due to Prof. Miklas for the proof reading and discussion of the manuscript.

For the convergence proof and the settings of β and μ, the interested reader is referred to [29].

The appearance of new bands is used for the direct proof, and changes of i.r.r