CurveIn mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...
Derived categoryIn mathematics, the derived category D(A) of an A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology.
Chord (music)A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and other types of broken chords (in which the chord tones are not sounded simultaneously) may also be considered as chords in the right musical context. In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note.
Differentiable curveDifferential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.
Algebraic curveIn mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0.
Derived functorIn mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. It was noted in various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of these observations. Suppose we are given a covariant left exact functor F : A → B between two A and B.
Plane curveIn mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions. A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form for some specific function f.
RNA polymerase IIIIn eukaryote cells, RNA polymerase III (also called Pol III) is a protein that transcribes DNA to synthesize 5S ribosomal RNA, tRNA and other small RNAs. The genes transcribed by RNA Pol III fall in the category of "housekeeping" genes whose expression is required in all cell types and most environmental conditions. Therefore, the regulation of Pol III transcription is primarily tied to the regulation of cell growth and the cell cycle, and thus requires fewer regulatory proteins than RNA polymerase II.
Generation III reactorGeneration III reactors, or Gen III reactors, are a class of nuclear reactors designed to succeed Generation II reactors, incorporating evolutionary improvements in design. These include improved fuel technology, higher thermal efficiency, significantly enhanced safety systems (including passive nuclear safety), and standardized designs intended to reduce maintenance and capital costs. They are promoted by the Generation IV International Forum (GIF).
Root cause analysisIn science and engineering, root cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. It is widely used in IT operations, manufacturing, telecommunications, industrial process control, accident analysis (e.g., in aviation, rail transport, or nuclear plants), medicine (for medical diagnosis), healthcare industry (e.g., for epidemiology), etc. Root cause analysis is a form of inductive (first create a theory [root] based on empirical evidence [causes]) and deductive (test the theory [underlying causal mechanisms] with empirical data) inference.
New DealThe New Deal was a series of programs, public work projects, financial reforms, and regulations enacted by President Franklin D. Roosevelt in the United States between 1933 and 1939. Major federal programs and agencies included the Civilian Conservation Corps (CCC), the Works Progress Administration (WPA), the Civil Works Administration (CWA), the Farm Security Administration (FSA), the National Industrial Recovery Act of 1933 (NIRA) and the Social Security Administration (SSA).
