Sentence examples for an embedding exists from inspiring English sources
We show that such an embedding exists for every uniformly Eberlein compact space.
In particular such an embedding exists for the C∗-algebra of a second countable amenable locally compact maximally almost periodic group.
We show that the quantum analogue of this embedding exists.
Foulis and Randall show that no such embedding exists for which B is orthocoherent.
We construct Neumann Wigner type potentials for the massive relativistic Schrödinger operator in one and three dimensions for which an embedded eigenvalue exists.
Then P has at least one fixed point in B. Proof By Theorem 3.3, there exists an embedding j : S → G. Let B be a nonempty, closed, bounded and convex subset of S. Since j is isometry, it follows that j ( B ) is also a closed and bounded subset of G.
By the Sobolev embedding inequality, one can see that there exists an embedding constant C 0 > 0 such that ∥ u m + s 2 ∥ 2 N N − 2 2 ≤ C 0 2 ∥ ∇ u m + s 2 ∥ 2 2. (12).
The technical significance of the restriction α > d is that these are the indices such that there exists an embedding H α ( D ) into a H α 1 ( D ) with d / 2 < α 1 < α, which is of Hilbert Schmidt typec due to Maurin's theorem and H α 1 ( D ) is embedded into C ( D ¯ ) due to the Sobolev embedding theorem.
If 0 < m < N − 2 N + 2, one can show that there exists an embedding constant C 00 > 0 such that ∥ u ∥ s + 1 m + s ≤ | Ω | 1 − ( s + 1 ) ( N + 2 ) N ( m + s ) ∥ u ∥ N ( m + s ) N − 2 m + s ≤ C 00 2 | Ω | 1 − ( s + 1 ) ( N + 2 ) N ( m + s ) ∥ ∇ u m + s 2 ∥ 2 2. by multiplying both sides of (1) by u s ( s > N ( 1 − m ) 2 − 1 ) and integrating the result over Ω, and the Sobolev embedding inequality.
To establish this, we have to show that, if 𝒞(N1) is interval-realizable with respect to π, then there exists an embedding τ1 of ℱ(N1) such that π is a non-interleaving order w.r.t.
Moreover, the mth-order derivative of (y_0 x)) with respect to the embedding parameter exists at (p=0) for all positive integral values of m.
