Stationary pointIn mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient is zero).
Fermat's theorem (stationary points)In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function , with derivative , are found by solving an equation in .
Inflection pointIn differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.
Y chromosomeThe Y chromosome is one of two sex chromosomes in therian mammals and other organisms. The other sex chromosome is the X chromosome. Y is normally the sex-determining chromosome in many species, since it is the presence or absence of Y that determines the male or female sex of offspring produced in sexual reproduction. In mammals, the Y chromosome contains the gene SRY, which triggers male development. The DNA in the human Y chromosome is composed of about 62 million base pairs, making it similar in size to chromosome 19.
Saddle pointIn mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis. However, a saddle point need not be in this form.
X chromosomeThe X chromosome is one of the two sex chromosomes in many organisms, including mammals, and is found in both males and females. It is a part of the XY sex-determination system and XO sex-determination system. The X chromosome was named for its unique properties by early researchers, which resulted in the naming of its counterpart Y chromosome, for the next letter in the alphabet, following its subsequent discovery. It was first noted that the X chromosome was special in 1890 by Hermann Henking in Leipzig.
InfluenzaInfluenza, commonly known as "the flu", is an infectious disease caused by influenza viruses. Symptoms range from mild to severe and often include fever, runny nose, sore throat, muscle pain, headache, coughing, and fatigue. These symptoms begin from one to four days after exposure to the virus (typically two days) and last for about 2–8 days. Diarrhea and vomiting can occur, particularly in children. Influenza may progress to pneumonia, which can be caused by the virus or by a subsequent bacterial infection.
Jacobian matrix and determinantIn vector calculus, the Jacobian matrix (dʒəˈkəʊbiən, dʒᵻ-,_jᵻ-) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature.
Spanish fluThe 1918-20 flu pandemic, also known as the Great Influenza epidemic or by the common misnomer of the Spanish flu, was an exceptionally deadly global influenza pandemic caused by the H1N1 influenza A virus. The earliest documented case was March 1918 in the state of Kansas in the United States, with further cases recorded in France, Germany and the United Kingdom in April. Two years later, nearly a third of the global population, or an estimated 500 million people, had been infected in four successive waves.
Gaussian eliminationIn mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855).
Veterans DayVeterans Day (originally known as Armistice Day) is a federal holiday in the United States observed annually on November 11, for honoring military veterans of the United States Armed Forces (who were discharged under conditions other than dishonorable). It coincides with other holidays including Armistice Day and Remembrance Day which are commemorated in other countries that mark the anniversary of the end of World War I. Major hostilities of World War I were formally ended at the 11th hour of the 11th day of the 11th month of 1918 when the Armistice with Germany went into effect.
Cartesian coordinate systemIn geometry, a Cartesian coordinate system (UKkɑːrˈtiːzjən, USkɑːrˈtiʒən) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where they meet is called the origin and has (0, 0) as coordinates.
Hong Kong fluThe Hong Kong flu, also known as the 1968 flu pandemic, was a flu pandemic whose outbreak in 1968 and 1969 killed between one and four million people globally. It is among the deadliest pandemics in history, and was caused by an H3N2 strain of the influenza A virus. The virus was descended from H2N2 (which caused the Asian flu pandemic in 1957–1958) through antigenic shift, a genetic process in which genes from multiple subtypes are reassorted to form a new virus.
X-rayX-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.
Remembrance DayRemembrance Day (also known as Poppy Day owing to the tradition of wearing a remembrance poppy) is a memorial day observed in Commonwealth member states since the end of the First World War in 1919 to honour armed forces members who have died in the line of duty. The day is also marked by war remembrances in several other non-Commonwealth countries. In most countries, Remembrance Day is observed on 11 November to recall the end of First World War hostilities.
X-ray tubeAn X-ray tube is a vacuum tube that converts electrical input power into X-rays. The availability of this controllable source of X-rays created the field of radiography, the imaging of partly opaque objects with penetrating radiation. In contrast to other sources of ionizing radiation, X-rays are only produced as long as the X-ray tube is energized. X-ray tubes are also used in CT scanners, airport luggage scanners, X-ray crystallography, material and structure analysis, and for industrial inspection.
Proper velocityIn relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector and proper time τ elapsed on the clocks of the traveling object: It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer. The two types of velocity, ordinary and proper, are very nearly equal at low speeds. However, at high speeds proper velocity retains many of the properties that velocity loses in relativity compared with Newtonian theory.
Dependent and independent variablesDependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.
Proper accelerationIn relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, because the same gravity acts equally on the inertial observer. As a consequence, all inertial observers always have a proper acceleration of zero.
Eigenvalues and eigenvectorsIn linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.
