(h8) X is M-det on ({mathbb {R}}.) Under the above settings, if X∼F on ({mathbb {R}}) satisfies one of the conditions (h1) through (h7), then X is M-det on ({mathbb {R}}).
Let T be a self-mapping defined on C and satisfies one of the following: (i) T is a nonspreading mapping; (ii) T is a hybrid mapping; (iii) T is a TY mapping. .
If satisfies one of the following: is continuous, nondecreasing on, for each fixed, there exists a function, and is integrable on such that (3.24).
Consequently, the function w (x, λ) is defined on 0, π 2 ∪ π 2, π by the equality w ( x, λ ) = ω 1 ( x, λ ), x ∈ 0, π 2, ω 2 ( x, λ ), x ∈ π 2, π. is a such solution of Equation 1 on 0, π 2 ∪ π 2, π ; which satisfies one of the boundary conditions and both transmission conditions.
If the kernel function K ( x ) satisfies one of the assumptions L i ( i = 1, 2, 3 ) on ( − ∞, 0 ) and one of R j ( j = 1, 2, …, 6 ) on ( 0, + ∞ ), then ψ is monotonic decreasing on ( 0, c ).
(1) If the kernel function K ( x ) satisfies one of the assumptions L i ( i = 1, 2, 3 ) on ( − ∞, 0 ) and one of R j ( j = 1, 2, …, 6 ) on ( 0, + ∞ ), then ψ is monotonic decreasing on ( 0, c ). (2) If the kernel function K ( x ) satisfies the assumptions L4 on ( − ∞, 0 ) and one of R j ( j = 1, 2, …, 6 ) on ( 0, + ∞ ) and ψ ( μ 0 ) < α 2, then ψ is monotonic decreasing on ( μ 0, c ). .
Assume that is increasing, has nonempty closed values, and satisfies one of the following hypotheses, then has maximal and minimal fixed points on.
First, it satisfies one of the "great forces of human nature": a drive to be altruistic and care for others.
This satisfies one of our patients' primary goals: restoration of fixed dentition as quickly as possible.
the task or delivery order satisfies one of the exceptions in section 2304(c) of this title to the requirement to use competitive procedures.
Occasionally, your help may be solicited to determine whether a transfer student's previous course work satisfies one of the distributional requirements, particularly the SC, SO, or QR requirements.
