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In a second approach a new interpretation of the classical projection of space domain responses on an Hilbertian base is used for prediction of global resonances.
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The resulting 'map', which is a projection of multidimensional space not geographic space, reveals interrelationships between classes and has proven beneficial in a variety of environmental settings [ 16, 17].
The Results and Discussion section presents a definition of tree space and an elegant projection of that space that has all four of these desirable properties.
As video frame is a projection of 3D space, extraction of key information is a challenging task.
By making an adequate projection of measurement space, the mode-common subspace is separated and can be represented by a robust statistical model.
Although we have tried to explain most of the diagrams using the three-dimensional eigenvalue space (left( {lambda_{1}, lambda_{2}, lambda_{3} } right)), some representations cannot be written as a one-to-one projection of this space.
which is an orthogonal projection projecting space to of the matrix where is an identity matrix and an -dimensional matrix (3.18).
which is an orthogonal projection projecting space to of the transposed matrix where is an identity matrix and is an -dimensional matrix pseudoinverse to the -dimensional matrix.
These bounds are related to the distance between the projections of the space curves onto a plane (say, z= 0), and the distance between the z-coordinates of points in the original curves.
Similarly, absolute space arises from a projection of spacetime onto space, i.e. a function that identifies spacetime points that have the same spatial coordinates.
Continuing with the monotonicity of the Apriori principle, a set of dense points in an k-dimensional space S is dense in all the lower dimensional projections of this space [33].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com