Arc lengthArc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) , then the curve is rectifiable (i.
Supply and demandIn microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted.
Foot (unit)The foot ( () feet), standard symbol: ft, is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, , is a customarily used alternative symbol. In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Historically, the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
BIBO stabilityIn signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is For discrete-time signals: For continuous-time signals: For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.
Alpha-1 antitrypsinAlpha-1 antitrypsin or α1-antitrypsin (A1AT, α1AT, A1A, or AAT) is a protein belonging to the serpin superfamily. It is encoded in humans by the SERPINA1 gene. A protease inhibitor, it is also known as alpha1–proteinase inhibitor (A1PI) or alpha1-antiproteinase (A1AP) because it inhibits various proteases (not just trypsin). In older biomedical literature it was sometimes called serum trypsin inhibitor (STI, dated terminology), because its capability as a trypsin inhibitor was a salient feature of its early study.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
StructureA structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.
Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
Alpha-1 antitrypsin deficiencyAlpha-1 antitrypsin deficiency (A1AD or AATD) is a genetic disorder that may result in lung disease or liver disease. Onset of lung problems is typically between 20 and 50 years of age. This may result in shortness of breath, wheezing, or an increased risk of lung infections. Complications may include chronic obstructive pulmonary disease (COPD), cirrhosis, neonatal jaundice, or panniculitis. A1AD is due to a mutation in the SERPINA1 gene that results in not enough alpha-1 antitrypsin (A1AT).
