(mathematics) A transform used in Borel summation. / (mathematics) A generalization of this in Nachbin's theorem.

plural of Borel transform

(linguistics) A generative grammar, especially of a natural language, developed in the Chomskyan tradition of phrase structure grammars (as opposed to dependency grammars), and involving the use of defined operations called transformations to produce new sentences from existing ones.

plural of transformational grammar

plural of Helmert transformation

A kind of transformation in three-dimensional space, frequently used in geodesy to avoid distortion when converting from one datum to another.

Synonym of Hadamard transform

(mathematics) Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)

An electrical transformer that reduces voltage from an electrical grid before being distributed to customers.

A transformer used to transfer electrical power from a source of alternating current (AC) power to some equipment or device while galvanically isolating the device from the power source, usually for safety reasons.