Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
Scholarly peer reviewScholarly peer review or academic peer review (also known as refereeing) is the process of having a draft version of a researcher's methods and findings reviewed (usually anonymously) by experts (or "peers") in the same field. Peer review is widely used for helping the academic publisher (that is, the editor-in-chief, the editorial board or the program committee) decide whether the work should be accepted, considered acceptable with revisions, or rejected for official publication in an academic journal, a monograph or in the proceedings of an academic conference.
Gröbner basisIn mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.
Representable functorIn mathematics, particularly , a representable functor is a certain functor from an arbitrary into the . Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory.
Evidence-based practiceEvidence-based practice (EBP) is the idea that occupational practices ought to be based on scientific evidence. While seemingly obviously desirable, the proposal has been controversial, with some arguing that results may not specialize to individuals as well as traditional practices. Evidence-based practices have been gaining ground since the formal introduction of evidence-based medicine in 1992 and have spread to the allied health professions, education, management, law, public policy, architecture, and other fields.
Evidence-based policyEvidence-based policy is a concept in public policy that advocates for policy decisions to be grounded on, or influenced by, rigorously established objective evidence. This concept presents a stark contrast to policymaking predicated on ideology, 'common sense,' anecdotes, or personal intuitions. The approach mirrors the effective altruism movement's philosophy within governmental circles. The methodology employed in evidence-based policy often includes comprehensive research methods such as randomized controlled trials (RCT).
Case reportIn medicine, a case report is a detailed report of the symptoms, signs, diagnosis, treatment, and follow-up of an individual patient. Case reports may contain a of the patient, but usually describe an unusual or novel occurrence. Some case reports also contain a literature review of other reported cases. Case reports are professional narratives that provide feedback on clinical practice guidelines and offer a framework for early signals of effectiveness, adverse events, and cost.
Functor represented by a schemeIn algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of .
EnergiewendeThe Energiewende (ʔɛnɐˈɡiːˌvɛndə) is the ongoing transition by Germany to a low carbon, environmentally sound, reliable, and affordable energy supply. The new system intends to rely heavily on renewable energy (particularly wind, photovoltaics, and hydroelectricity), energy efficiency, and energy demand management. The last nuclear power plants were shut down in 2023; all existing coal-fired generation will be retired by 2038.
Evidence-based educationEvidence-based education (EBE) is the principle that education practices should be based on the best available scientific evidence, rather than tradition, personal judgement, or other influences. Evidence-based education is related to evidence-based teaching, evidence-based learning, and school effectiveness research. For example, research has shown that spaced repetition (also spaced training, spacing effect and spaced learning) "leads to more robust memory formation than massed training does, which involves short or no intervals".
