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This is simply the empirical sample mean of a certain transformation of the materialized and the arcsinh-transformed counts, respectively.
Their method is based on Unitary-ESPRIT, which involves a certain transformation of the data to real valued matrices.
Now, in order for each element to fulfill itself through its relations to its others, Rosenzweig asserts, each must undergo a certain transformation.
For needs of optimization, a certain transformation pattern of the load time history was assumed, which allowed to considerably accelerate the fatigue analysis process.
Your eye "knows" that to focus on a more distant object, it has to perform a certain transformation on the lens in order to bring that object into focus.
With a certain transformation, the differential equation of motion is changed into an integral equation related to the dynamic loads, and the problem of load identification turns into solving a Volterra integral equation of the first kind.
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"There's a view that certain transformation of news into entertainment has been a great kind of downfall of civic society, but that kind of blames the news as opposed to the lack of interest in news when it's not entertaining," said Amir Kamenica on the Freakonomics Podcast episode " Why Do We Really Follow the News?".
There are other approaches to the problem of spatially correlated noise: one is based on the assumption that the correlation structure of the noise field is invariant under a rotation or a translation of the array, while another is based on a certain linear transformation of the sensor output vectors [8 13].
Moreover, and based on a certain Whipple transformation, two new closed formulas for summing certain terminating hypergeometric functions of the unit argument are deduced.
In the first application, four new formulas for definite integrals involving three products of Jacobi polynomials of certain parameters are given, while in the second, and based on a certain Whipple transformation, two new reduction formulas for certain hypergeometric functions of the type (_{4}F_{3}(1)) are deduced.
Visual thinking includes thinking with external visual representations (e.g., diagrams, symbol arrays, kinematic computer images) and thinking with internal visual imagery; often the two are used in combination, as when we are required to visually imagine a certain spatial transformation of an object represented by a diagram on paper or on screen.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com