Moreover, this example asserts that −0.5 is one of the solutions because if x = − 0.5, then A ( x ) = [ − 0.5, 0 ). Note that for all y ∈ A ( x ), y > x. Therefore F ( − 0.5, y ) − [ 0, y + 0.5 ] ⊈ − C ∖ { 0 } for all y ∈ [ − 0.5, 0 ). Now, we present an existence theorem for GSVQEP when F is not necessarily monotone.
An interesting classical result [1, 10], which generalizes the example, asserts that the initial value problem { x ′ ( t ) = g ( x ( t ) ), t ≥ 0, x ( 0 ) = x 0, x 0 ∈ R, (1).
One 2005 memorandum, for example, asserts that "enhanced techniques" used on Abu Zubaydah and Mr. Mohammed "yielded critical information".
Ali, for example, asserts that American generals didn't act to stop museum lootings in Baghdad because it would have meant admitting that the "ragheads" had a culture.
Hinduism, for example, asserts that the self is divine, while other traditions claim that God alone exists (Sufism), that God is immediately present to the soul (Christianity and Judaism), and that all things are empty (Mahayana Buddhism).
Sir Peter, for example, asserts that his new symphony "cannot be described literally in terms of any program associated with my Antarctic experience -- it is, rather, an abstract work, using transmuted sound images distantly based on those experiences".
St. Isidore of Sevilla, in his 7th-century Etymologiae ("Etymologies"), for example, asserts that kings rule only on condition of doing right and that their rule reflects a Ciceronic law of nature "common to all people and mankind everywhere by natural instinct".
The suit filed against Advocate Health Care Network of Oak Brook, Ill., for example, asserts that Jannie Watts, one of the plaintiffs, "received numerous threatening and harassing phone calls" seeking payment of $48,008.47 for treatment of her uninsured teenage son, a bystander to a shooting who was hit by multiple gunshots in 1998.
Ortmann (2017), for example, asserts that waste and water pollution are becoming increasingly endemic in Vietnam stemming from the massive increase in population density, industrial activities and urban living.
However, if beauty is entirely subjective that is, if anything that anyone holds to be or experiences as beautiful is beautiful (as James Kirwan, for example, asserts)—then it seems that the word has no meaning, or that we are not communicating anything when we call something beautiful except perhaps an approving personal attitude.
(Markham 1988: 48), for example, asserts that 'purely quantitative techniques do not necessarily mirror the internal thought processes of the subjects.' Similarly, (Storey 1997, p. 214) claims that using qualitative techniques of introspection paves the way for understanding the 'vexed question of what cloze actually measures'.
