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Transformative research is a term that became increasingly common within the science policy community in the 2000s for research that shifts or breaks existing scientific paradigms. The idea has its provenance in Thomas Kuhn's notion of scientific revolutions, where one scientific paradigm is overturned for another.
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory .
Transmutation had previously been used as a term in alchemy to describe the transformation of base metals into gold. Other names for evolutionary ideas used in this period include the development hypothesis (one of the terms used by Darwin) and the theory of regular gradation , used by William Chilton in the periodical press such as The Oracle ...
Transformation (function), concerning functions from sets to themselves; Transform theory, theory of integral transforms List of transforms, a list of mathematical transforms; Integral transform, a type of mathematical transform
A paradigm shift is a fundamental change in the basic concepts and experimental practices of a scientific discipline.It is a concept in the philosophy of science that was introduced and brought into the common lexicon by the American physicist and philosopher Thomas Kuhn.
A scientific theory is an explanation of an aspect of the natural world and universe that can be (or a fortiori, that has been) repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science.
In transform theory, optics and quantum mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has 4 parameters and 1 constraint, so it is a 3-dimensional family, and can be visualized as the action of the special linear group SL 2 (R) on the time–frequency plane (domain).