AreaArea is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.
Area of a circleIn geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter pi represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides.
Surface areaThe surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces.
TransaminationTransamination is a chemical reaction that transfers an amino group to a ketoacid to form new amino acids. This pathway is responsible for the deamination of most amino acids. This is one of the major degradation pathways which convert essential amino acids to non-essential amino acids (amino acids that can be synthesized de novo by the organism). Transamination in biochemistry is accomplished by enzymes called transaminases or aminotransferases. α-ketoglutarate acts as the predominant amino-group acceptor and produces glutamate as the new amino acid.
Circular sectorA circular sector, also known as circle sector or disk sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle, the radius of the circle, and is the arc length of the minor sector. The angle formed by connecting the endpoints of the arc to any point on the circumference that is not in the sector is equal to half the central angle.
TransaminaseTransaminases or aminotransferases are enzymes that catalyze a transamination reaction between an amino acid and an α-keto acid. They are important in the synthesis of amino acids, which form proteins. An amino acid contains an amine (NH2) group. A keto acid contains a keto (=O) group. In transamination, the NH2 group on one molecule is exchanged with the =O group on the other molecule. The amino acid becomes a keto acid, and the keto acid becomes an amino acid. Most transaminases are protein enzymes.
Solid angleIn geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle at that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).
Alcoholic liver diseaseAlcoholic liver disease (ALD), also called alcohol-related liver disease (ARLD), is a term that encompasses the liver manifestations of alcohol overconsumption, including fatty liver, alcoholic hepatitis, and chronic hepatitis with liver fibrosis or cirrhosis. It is the major cause of liver disease in Western countries. Although steatosis (fatty liver disease) will develop in any individual who consumes a large quantity of alcoholic beverages over a long period of time, this process is transient and reversible.
Fatty liver diseaseFatty liver disease (FLD), also known as hepatic steatosis, is a condition where excess fat builds up in the liver. Often there are no or few symptoms. Occasionally there may be tiredness or pain in the upper right side of the abdomen. Complications may include cirrhosis, liver cancer, and esophageal varices. There are two types of fatty liver disease: non-alcoholic fatty liver disease (NAFLD) and alcoholic liver disease. NAFLD is made up of simple fatty liver and non-alcoholic steatohepatitis (NASH).
Gram stainIn microbiology and bacteriology, Gram stain (Gram staining or Gram's method), is a method of staining used to classify bacterial species into two large groups: gram-positive bacteria and gram-negative bacteria. The name comes from the Danish bacteriologist Hans Christian Gram, who developed the technique in 1884. Gram staining differentiates bacteria by the chemical and physical properties of their cell walls. Gram-positive cells have a thick layer of peptidoglycan in the cell wall that retains the primary stain, crystal violet.
Cyrillic alphabetsNumerous Cyrillic alphabets are based on the Cyrillic script. The early Cyrillic alphabet was developed in the 9th century AD and replaced the earlier Glagolitic script developed by the Byzantine theologians Cyril and Methodius. It is the basis of alphabets used in various languages, past and present, Slavic origin, and non-Slavic languages influenced by Russian. As of 2011, around 252 million people in Eurasia use it as the official alphabet for their national languages. About half of them are in Russia.
RadianThe radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit, defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as .
SteradianThe steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a length of a circular arc on the circumference, a solid angle in steradians, projected onto a sphere, gives the area of a spherical cap on the surface. The name is derived from the Greek στερεός 'solid' + radian.
Hypercube graphIn graph theory, the hypercube graph Q_n is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q_3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Q_n has 2^n vertices, 2^n – 1n edges, and is a regular graph with n edges touching each vertex. The hypercube graph Q_n may also be constructed by creating a vertex for each subset of an n-element set, with two vertices adjacent when their subsets differ in a single element, or by creating a vertex for each n-digit binary number, with two vertices adjacent when their binary representations differ in a single digit.
Gram-positive bacteriaIn bacteriology, gram-positive bacteria are bacteria that give a positive result in the Gram stain test, which is traditionally used to quickly classify bacteria into two broad categories according to their type of cell wall. Gram-positive bacteria take up the crystal violet stain used in the test, and then appear to be purple-coloured when seen through an optical microscope. This is because the thick peptidoglycan layer in the bacterial cell wall retains the stain after it is washed away from the rest of the sample, in the decolorization stage of the test.
Yo (Cyrillic)Yo, Jo or Io (Ё ё; italics: Ё ё; jɵ) is a letter of the Cyrillic script. In Unicode, the letter is named CYRILLIC CAPITAL/SMALL LETTER IO. In English, the letter Yo is romanized using the Latin ë (according to the ALA–LC and British Standards), ë (yë word-initially) (BGN/PCGN) or yo/jo (orthographic transcription) for Russian, and as i͡o (ALA–LC), yo (BGN/PCGN), or ë (BSI) for Belarusian. In international systems, Yo is romanized as ë (ISO 9). It was derived from the Cyrillic letter Ye (Е е).
Paley graphIn mathematics, Paley graphs are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic tools to be applied to the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally.
Gram-negative bacteriaGram-negative bacteria are bacteria that do not retain the crystal violet stain used in the Gram staining method of bacterial differentiation. They are characterized by their cell envelopes, which are composed of a thin peptidoglycan cell wall sandwiched between an inner cytoplasmic cell membrane and a bacterial outer membrane. Gram-negative bacteria are found in virtually all environments on Earth that support life.
Strongly regular graphIn graph theory, a strongly regular graph (SRG) is defined as follows. Let G = (V, E) be a regular graph with v vertices and degree k. G is said to be strongly regular if there are also integers λ and μ such that: Every two adjacent vertices have λ common neighbours. Every two non-adjacent vertices have μ common neighbours. The complement of an srg(v, k, λ, μ) is also strongly regular. It is a srg(v, v − k − 1, v − 2 − 2k + μ, v − 2k + λ). A strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero.
CylinderA cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces.
