Red-figure potteryRed-figure vase painting is one of the most important styles of figural Greek vase painting. It developed in Athens around 520 BCE and remained in use until the late 3rd century BCE. It replaced the previously dominant style of black-figure vase painting within a few decades. Its modern name is based on the figural depictions in red color on a black background, in contrast to the preceding black-figure style with black figures on a red background. The most important areas of production, apart from Attica, were in Southern Italy.
InducerIn molecular biology, an inducer is a molecule that regulates gene expression. An inducer functions in two ways; namely: By disabling repressors. The gene is expressed because an inducer binds to the repressor. The binding of the inducer to the repressor prevents the repressor from binding to the operator. RNA polymerase can then begin to transcribe operon genes. By binding to activators. Activators generally bind poorly to activator DNA sequences unless an inducer is present.
Fixed point (mathematics)hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.
Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues—of the linearization around the fixed point—crosses the complex plane imaginary axis as a parameter crosses a threshold value.
AllolactoseAllolactose is a disaccharide similar to lactose. It consists of the monosaccharides D-galactose and D-glucose linked through a β1-6 glycosidic linkage instead of the β1-4 linkage of lactose. It may arise from the occasional transglycosylation of lactose by β-galactosidase. It is an inducer of the lac operon in Escherichia coli and many other enteric bacteria. It binds to a subunit of the tetrameric lac repressor, which results in conformational changes and reduces the binding affinity of the lac repressor to the lac operator, thereby dissociating it from the lac operator.
Phase portraitIn mathematics, a phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value.
Adenosine triphosphateAdenosine triphosphate (ATP) is an organic compound that provides energy to drive and support many processes in living cells, such as muscle contraction, nerve impulse propagation, condensate dissolution, and chemical synthesis. Found in all known forms of life, ATP is often referred to as the "molecular unit of currency" of intracellular energy transfer. When consumed in metabolic processes, it converts either to adenosine diphosphate (ADP) or to adenosine monophosphate (AMP). Other processes regenerate ATP.
Bifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
Black-figure potteryBlack-figure pottery painting, also known as the black-figure style or black-figure ceramic (), is one of the styles of painting on antique Greek vases. It was especially common between the 7th and 5th centuries BCE, although there are specimens dating as late as the 2nd century BCE. Stylistically it can be distinguished from the preceding orientalizing period and the subsequent red-figure pottery style. Figures and ornaments were painted on the body of the vessel using shapes and colors reminiscent of silhouettes.
Vector fieldIn vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space . A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.
Fixed-point iterationIn numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.
Complex lamellar vector fieldIn vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different ways, many of which involve the curl. A lamellar vector field is a special case given by vector fields with zero curl. The adjective "lamellar" derives from the noun "lamella", which means a thin layer.
