For an arbitrary, we define the following elementary transformation, which is denoted by : (i) if, then is transformed to another ordered partition from, say, such that the conditions and from Lemma 4 are satisfied; (ii) otherwise, the ordered partition remains unchanged. .
By employing shell transformation properly, a mesh that intersects predefined constraints intensively can be transformed to another one with much fewer intersections, thus remarkably reducing the occasions of Steiner point insertion.
What the artist says: "I'm interested in a state of between-ness, and that state you find if one thing transforms to another".
Some of the clay minerals can serve as catalysts for reactions in which one organic substance is transformed to another on the mineral's surface.
In the composition range (Mg0.8Fe0.2 2SiO4 to Mg2SiO4, however, the olivines were transformed to another orthorhombic structure (called β-orthosilicate) at a pressure of about 130 kilobars and a temperature of 1,000° C.
Equation (1.1) can be transformed to another form which has equivalent properties.
The task of polar coordinate transform is that an image under the Cartesian coordinate (x - y) space is transformed to another image under polar coordinate (ϕ- r) space.
if, then is transformed to another ordered partition from, say, such that the conditions and from Lemma 4 are satisfied; otherwise, the ordered partition remains unchanged.
This suggestion is supported by differential scanning calorimetry data presented by Parkin [3], which show that piperidine appears to form one phase on cooling from the liquid, which then transforms to another phase at 239 K.
Also, in the case of PCA, when dataset is transformed to another space, position of the original dataset changes, whereas in the case of LDA, the position remains the same.
