Corollary 2 Let ( X, d ) be complete metric space and ( X, d, G ) obey condition (6).
Note that the symplectic matrices (1.7) associated with matrix Sturm-Liouville equation (1.1) for two arbitrary values λ = a and λ = b, a ≠ b obey condition (2.21) only for the case when R i does not depend on λ.
Transmission of doxastic justification presumably obeys conditions that parallel those delineated in Sect. 2 for transmission of propositional justification.
Obeying condition in equation (7) implies that begin{aligned} &alpha'_{1} gealpha_{1}, &alpha'_{M} lealpha_{M}.
Let and be increasing or decreasing sequences obeying condition then by condition, is a monotonic and order-bounded sequence, so Hence, condition holds.
Let ({x_{n}}) and ({y_{n}}) be two increasing or decreasing sequences obeying condition (H3), then, by condition (H1), ({f t, x_{n}, y_{n}, z_{n})+Mx_{n}}) is a monotonic and order-bounded sequence.
We assume that G j contains an additional edge e0 located upwards from the root as shown in Figure 2. Given a set V ∈ P, a vertex v of tree G j is called good (with respect to V) if at least one of its children obeys condition (4) or the first condition in (4) if v is the super-root.
The mapping given by,, where is an eigenfunction to the least eigenvalue of (1.1), (2.2), transforms obeying boundary conditions (2.2) to obeying Dirichlet boundary conditions of the form (2.14).
A federal judge in Manhattan ordered New York City yesterday to allow a group of protesters to sleep on the sidewalk across from Gracie Mansion, provided that they obey certain conditions.
They were both released on lifelong licence in 2001 with new identities, requiring them to obey strict conditions such as not contacting each other or returning to the city where James was killed.
