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That is to say, one gradient evaluation is equivalent to five function evaluations if automatic differentiation is used.
To consider the small scale effects, the nonlocal elasticity theory and strain gradient theory with one gradient parameter are adopted.
One gradient exists during steady-state, due to the combination of the combustion environment next to the free surface and internal cooling of the underlying superalloy substrate.
This work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980's.
The purpose of this study was to evaluate if positron emission tomography (PET)/magnetic resonance imaging (MRI) with just one gradient echo sequence using the body coil is diagnostically sufficient compared with a standard, low-dose non-contrast-enhanced PET/computed tomography (CT) concerning overall diagnostic accuracy, lesion detectability, size and conspicuity evaluation.
In this work it was found that the algorithm of resilient back-propagation that carries out the descent of error (or the difference between the target output and the realized one) gradient adaptively yielded desired results (Wasserman 1993, Wu 1994 and Sivakumar and Berndtsson 2010).
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Based on the elaborated work, in addition to confirmation of having one geothermal gradient in the reservoir, it is found out that the 'affected thermal well bore radius' in wells is about 20 60 cm.
At each iteration, the improved search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost.
The search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost.
Moreover, it was shown that with only one velocity gradient signal measurement, both experimental and theoretical values are obtained for a specified flow rate.
This is a special example but not an unnatural one; a gradient of local properties is among the simplest deterministic ways to break translation-invariance.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com