Sentence examples for by graphs of functions from inspiring English sources

According to Theorem 6, the interior of the set { ( t, x ) ∈ R 2 : 0 ≤ t ≤ T, v 0, min ( t ) ≤ x ≤ v c ∗, max ( t ) } is fully covered by graphs of functions from ℛ. Finally, we deduce from Theorems 7-9 thet the set { t k − 1 v : v ∈ R ∗ } is compact in C [ 0, T ].

The next theorem shows that the set V = { ( t, x ) ∈ R 2 : t ∈ ( 0, T ], x ≥ v 0, min ( t ) }. is covered by graphs of the functions from ℛ. Theorem 6 Let ( H 1 0 )-( H 3 0 ) hold.

Remark 1 Corollary 1 says that the set U = { ( t, x ) ∈ R 2 : t ∈ [ 0, T ], x ≥ u 0, min ( t ) } is covered by the graphs of functions from S, that is, U = { ( t, u ( t ) ) : t ∈ [ 0, T ], u ∈ S }.

A few elementary concepts in graph theory are required for the discussion of the Fig. 5 graphs (not to be confused with graphs of functions).

The assumption of proportional hazards was investigated by graphs of the log minus log survivor function against log t over grouped values of the covariates.

If the interior of the set { ( t, x ) ∈ R 2 : 0 ≤ t ≤ T, v c, min ( t ) ≤ x ≤ v c, max ( t ) } is nonempty, we show that this interior is fully covered by ordered graphs of other functions belonging to R c for each c ≥ 0 ; see Theorem 6.

Figure 1 Graph of functions    for.

One can quickly convince oneself of this by graphing such functions.

Usually, they were to interpret the graph of derived function as the graph of function.

Tables of the functions may be used to sketch the graphs of the functions.

Figure 2 Graphs of hazard functions.