Your English writing platform
Discover LudwigExact(1)
Theorem 3.3 Let C be a nonempty closed and convex subset of a complete strictly convex hyperbolic space X.
Similar(59)
It requires the respective Member's Office to complete a strictly confidential antemortem data form for each missing person, following the ICRC principles.
The so-called Volcker Rule, which is supposed to stop banks from engaging in proprietary trading but allow them to hedge or engage in market-making activities, should be completed and strictly enforced.
The election officials, who all belonged to parties opposed to Mr. López Obrador, rejected calls for a complete recount and strictly interpreted the law to limit the number of ballot boxes reopened.
Let D1, D2, … be complete descriptions in strictly descriptive terms of how these worlds are.
In 1961, Kuczma [13] gave a complete description of strictly monotonic and continuous functions having roots.
We now apply the condition (i) and Proposition 2.1, the system J i ( S 1, Q ) is strictly complete, and the sets α i and α ¯ i by (3.1) are well defined such that.
The system of matrices {J i }, i = 1, 2,..., N, is said to be strictly complete if for every x ∈ R n {0} there is i ∈ {1, 2,..., N} such that x T J i x < 0. It is easy to see that the system {J i } is strictly complete if and only if ⋃ i = 1 N α i = R n { 0 }, where α i = { x ∈ R n : x T J i x < 0 }, i = 1, 2, …, N. Proposition 2.1.
Definition 2.2 The system of matrices { J i }, i = 1, 2, …, N, is said to be strictly complete if for every x ∈ R n ∖ { 0 } there is i ∈ { 1, 2, …, N } such that x T J i x < 0. It is easy to see that the system { J i } is strictly complete if and only if ⋃ i = 1 N α i = R n ∖ { 0 }, where α i = { x ∈ R n : x T J i x < 0 }, i = 1, 2, …, N. Proposition 2.1 ([38]).
For the equation (Δ+c) u=uα, whereΔis the Beltrami Laplace operator on a complete Riemannian manifoldE, strictly positive solutions inEwere studied in connection with a geometrical problem: Which two functions represent scalar curvatures of two Riemannian metrics related by a conformal mapping (see [1] and references there)?
We now apply condition (i) and Proposition 2.1, the system J i is strictly complete, and the sets α i and α ¯ i by (3.1) are well defined such that ⋃ i = 1 N α i = R n ∖ { 0 }, ⋃ i = 1 N α ¯ i = R n ∖ { 0 }, α ¯ i ∩ α ¯ j = ∅, i ≠ j.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com