Order theoryOrder theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Newton's method in optimizationIn calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function F, which are solutions to the equation F (x) = 0. As such, Newton's method can be applied to the derivative f ′ of a twice-differentiable function f to find the roots of the derivative (solutions to f ′(x) = 0), also known as the critical points of f. These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article.
Paroxysmal supraventricular tachycardiaParoxysmal supraventricular tachycardia (PSVT) is a type of supraventricular tachycardia, named for its intermittent episodes of abrupt onset and termination. Often people have no symptoms. Otherwise symptoms may include palpitations, feeling lightheaded, sweating, shortness of breath, and chest pain. The cause is not known. Risk factors include alcohol, caffeine, nicotine, psychological stress, and Wolff-Parkinson-White syndrome, which often is inherited. The underlying mechanism typically involves an accessory pathway that results in re-entry.
Motor–generatorA motor–generator (an M–G set) is a device for converting electrical power to another form. Motor–generator sets are used to convert frequency, voltage, or phase of power. They may also be used to isolate electrical loads from the electrical power supply line. Large motor–generators were widely used to convert industrial amounts of power while smaller motor–generators (such as the one shown in the picture) were used to convert battery power to higher DC voltages.
Linear congruential generatorA linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation.
Radiofrequency ablationRadiofrequency ablation (RFA), also called fulguration, is a medical procedure in which part of the electrical conduction system of the heart, tumor or other dysfunctional tissue is ablated using the heat generated from medium frequency alternating current (in the range of 350–500 kHz). RFA is generally conducted in the outpatient setting, using either local anesthetics or twilight anesthesia. When it is delivered via catheter, it is called radiofrequency catheter ablation.
Multiprotocol Label SwitchingMultiprotocol Label Switching (MPLS) is a routing technique in telecommunications networks that directs data from one node to the next based on labels rather than network addresses. Whereas network addresses identify endpoints the labels identify established paths between endpoints. MPLS can encapsulate packets of various network protocols, hence the multiprotocol component of the name. MPLS supports a range of access technologies, including T1/E1, ATM, Frame Relay, and DSL. In an MPLS network, labels are assigned to data packets.
Cutting-plane methodIn mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
