Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Taylor seriesIn mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
Series (mathematics)In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.
AmpereThe ampere (ˈæmpɛər , ˈæmpɪər ; symbol: A), often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb, or 6.241509074e18 electrons' worth of charge, moving past a point in a second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.
Parallel computingParallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.
Massively parallelMassively parallel is the term for using a large number of computer processors (or separate computers) to simultaneously perform a set of coordinated computations in parallel. GPUs are massively parallel architecture with tens of thousands of threads. One approach is grid computing, where the processing power of many computers in distributed, diverse administrative domains is opportunistically used whenever a computer is available. An example is BOINC, a volunteer-based, opportunistic grid system, whereby the grid provides power only on a best effort basis.
Embarrassingly parallelIn parallel computing, an embarrassingly parallel workload or problem (also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel) is one where little or no effort is needed to separate the problem into a number of parallel tasks. This is often the case where there is little or no dependency or need for communication between those parallel tasks, or for results between them. Thus, these are different from distributed computing problems that need communication between tasks, especially communication of intermediate results.
Ampere-hourAn ampere-hour or amp-hour (symbol: A⋅h or A h; often simplified as Ah) is a unit of electric charge, having dimensions of electric current multiplied by time, equal to the charge transferred by a steady current of one ampere flowing for one hour, or 3,600 coulombs. The commonly seen milliampere-hour (symbol: mA⋅h, mA h, often simplified as mAh) is one-thousandth of an ampere-hour (3.6 coulombs). The ampere-hour is frequently used in measurements of electrochemical systems such as electroplating and for battery capacity where the commonly known nominal voltage is dropped.
DensityDensity (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.
Area densityThe area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the kilogram per square metre (kg·m−2). A related area number density can be defined by replacing mass in by number of particles or other countable quantity. In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (g/m2); for paper in particular, it may be expressed as pounds per ream of standard sizes ("basis ream").
Parallel communicationIn data transmission, parallel communication is a method of conveying multiple binary digits (bits) simultaneously using multiple conductors. This contrasts with serial communication, which conveys only a single bit at a time; this distinction is one way of characterizing a communications link. The basic difference between a parallel and a serial communication channel is the number of electrical conductors used at the physical layer to convey bits. Parallel communication implies more than one such conductor.
Fast-neutron reactorA fast-neutron reactor (FNR) or fast-spectrum reactor or simply a fast reactor is a category of nuclear reactor in which the fission chain reaction is sustained by fast neutrons (carrying energies above 1 MeV or greater, on average), as opposed to slow thermal neutrons used in thermal-neutron reactors. Such a fast reactor needs no neutron moderator, but requires fuel that is relatively rich in fissile material when compared to that required for a thermal-neutron reactor.
Parallel portIn computing, a parallel port is a type of interface found on early computers (personal and otherwise) for connecting peripherals. The name refers to the way the data is sent; parallel ports send multiple bits of data at once (parallel communication), as opposed to serial communication, in which bits are sent one at a time. To do this, parallel ports require multiple data lines in their cables and port connectors and tend to be larger than contemporary serial ports, which only require one data line.
Liquid fluoride thorium reactorThe liquid fluoride thorium reactor (LFTR; often pronounced lifter) is a type of molten salt reactor. LFTRs use the thorium fuel cycle with a fluoride-based molten (liquid) salt for fuel. In a typical design, the liquid is pumped between a critical core and an external heat exchanger where the heat is transferred to a nonradioactive secondary salt. The secondary salt then transfers its heat to a steam turbine or closed-cycle gas turbine. Molten-salt-fueled reactors (MSRs) supply the nuclear fuel mixed into a molten salt.
SuperphénixSuperphénix (Superphoenix) or SPX was a nuclear power station prototype on the Rhône river at Creys-Malville in France, close to the border with Switzerland. Superphénix was a 1,242 MWe fast breeder reactor with the twin goals of reprocessing nuclear fuel from France's line of conventional nuclear reactors, while also being an economical generator of power on its own. Construction began in 1976, the reactor went critical in 1985 and was connected to the grid in 1986. The project suffered cost overruns, delays and enormous public protests.
Electrical resistivity and conductivityElectrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m).
Molten salt reactorA molten salt reactor (MSR) is a class of nuclear fission reactor in which the primary nuclear reactor coolant and/or the fuel is a mixture of molten salt with a fissionable material. Two research MSRs operated in the United States in the mid-20th century. The 1950s Aircraft Reactor Experiment (ARE) was primarily motivated by the technology's compact size, while the 1960s Molten-Salt Reactor Experiment (MSRE) aimed to demonstrate a nuclear power plant using a thorium fuel cycle in a breeder reactor.
Current sourceA current source is an electronic circuit that delivers or absorbs an electric current which is independent of the voltage across it. A current source is the dual of a voltage source. The term current sink is sometimes used for sources fed from a negative voltage supply. Figure 1 shows the schematic symbol for an ideal current source driving a resistive load. There are two types. An independent current source (or sink) delivers a constant current. A dependent current source delivers a current which is proportional to some other voltage or current in the circuit.
Breeder reactorA breeder reactor is a nuclear reactor that generates more fissile material than it consumes. These reactors can be fuelled with more commonly available isotopes of uranium and thorium, such as uranium-238 or thorium-232, as opposed to the rare uranium-235 which is used in conventional reactors. These materials are called fertile materials since they can be bred into fuel by these breeder reactors. Breeder reactors achieve this because their neutron economy is high enough to create more fissile fuel than they use.
