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A gauge function φ of order r on J is said to be a strict gauge function if the inequality in (ii) holds strictly whenever ({t in J backslash{ 0 }}).
It follows from Lemma 4.5, Lemma 4.3 v), and Lemma 2.3 that E is a function of the initial conditions of (T^{(N }) with a strict gauge function (varphi_{N}) of order ({r = 2 N + 1}) on J. Since ξ is a root vector of f, then ({E xi) = 0 in J}).
Let ({T colon D subset X to X}) be an operator in a cone normed space ({ X,|cdot|)}) over a solid vector space ({(Y,preceq)}), and let ({E colon D to mathbb{R}_) be a function of the initial conditions of T with a strict gauge function φ of order ({r ge1}) on an interval J. Suppose that T is an iterated contraction at a point ξ with respect to E and with control function ϕ satisfying (2.7).
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Holcroft's solution was to move the mechanism to a position above the pony truck and ahead of the cylinders and link it to the outside valve rods with extension levers, which had to be accommodated within the strict SECR loading gauge tolerances.
Our "expectational analysis" differs from strict contrarianism in that we gauge the expectations for an event or announcement, then assess the risks to the market should the event or announcement not meet these expectations.
Events in the outer worlds cannot be accurately gauged without paying strict attention to the apparatus of perception.
Using the recommended 30 metre increase (based on self-rated physical function) as a gauge for clinical significance is rather strict, and its usefulnesscan be discussed [ 16, 17].
Time trends in rates can therefore only be gauged in investigations that hold these parameters under strict control over time.
The study, the first to gauge long-term ozone mortality risks, could strengthen the case for stricter regulations of ozone-producing emissions, such as those coming from power plants and vehicles.
The higher level would allow researchers to gauge the prevalence of bovine spongiform encephalopathy (BSE) and determine whether USDA should implement stricter safeguards.
These relatively strict criteria were used to identify a small number of robust measures that are appropriate for gauging levels of wellbeing across populations and for evaluating service level outcomes.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com