TemperatureTemperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Negative temperatureCertain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. The absolute temperature (Kelvin) scale can be understood loosely as a measure of average kinetic energy. Usually, system temperatures are positive.
Absolute zeroAbsolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.
Integer programmingAn integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Scale of temperatureScale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to convenient and stable parameters or reference points, such as the freezing and boiling point of water. Absolute temperature is based on thermodynamic principles: using the lowest possible temperature as the zero point, and selecting a convenient incremental unit. Celsius, Kelvin, and Fahrenheit are common temperature scales.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Orthonormal basisIn mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.
