However, it is also the form where the parameters have the least physical interpretation and is generally reserved for theoretical treatment of the PID controller.The standard form, despite being slightly more complex mathematically, is more common in industry.In many cases, the manipulated variable output by the PID controller is a dimensionless fraction between 0 and 100% of some maximum possible value, and the translation into real units (such as pumping rate or watts of heater power) is outside the PID controller.…
Mathematically, those elements can be connected in any order without changing the end-result.As digital computers use a finite approximation to numerical computing, this is in practice not true.…
Previously, the champion may have been decided before the last race (or even several races before the end of the season) because it was mathematically impossible for any other driver to gain enough points to overtake the leader.Although this is still mathematically possible going into the last two events, it has yet to occur.On November 20, 2011, Tony Stewart and Carl Edwards ended the season in a first-ever points tie.…
In electronics, Complex gain is the effect circuitry has on the amplitude and phase of a sine wave signal.The term complex is used because mathematically this effect can be expressed as a complex number.…
It is widely used in the context of resource allocation and payoff distribution.Mathematically, there are m types of resources and n products can be produced out of them.…
If the barley was not ripe, or various other phenomena indicated that spring was not yet imminent, an intercalary month (Adar II) would be added.However, since at least the 4th century, the date has been fixed mathematically.…
Mathematically, it is the size of an order needed to move the market price by a given amount.If the market is deep, a large order is needed to change the price.…
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable.Many important properties of physical systems can be represented mathematically as matrix problems.For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.…
Markopolos later said that he knew within five minutes that Madoff's numbers didn't add up.It took him another four hours to mathematically prove that they could have only been obtained by fraud.Despite this, Markopolos' bosses at Rampart asked Markopolos to deconstruct Madoff's strategy to see if he could replicate it.…
In a very abstract setting, the principle of inclusion-exclusion amounts to no more than the calculation of the inverse of a certain matrix.From this point of view, there is nothing mathematically interesting about the principle.However, the wide applicability of the principle makes it an extremely valuable technique in combinatorics and related areas of mathematics.…
Public-key cryptography, also known as asymmetric cryptography, is a class of cryptographic algorithms which requires two separate keys, one of which is secret (or private) and one of which is public.Although different, the two parts of this key pair are mathematically linked.The public key is used to encrypt plaintext or to verify a digital signature; whereas the private key is used to decrypt ciphertext or to create a digital signature.…
Aggregating reviews and playlists from over 150 publications, both print and online, the site also encompassed historical sources.The site then ranked the songs mathematically, based on the information gathered.With a methodology based in the fields of bibliometrics and sentiment analysis, Critical Metrics quantified these positive citations and sentiments into indices for media playlisting and consumption.…
They are either knowledge-based (for example, written tests on earth science, physics, astronomy, or biology), hands-on (for example, chemistry lab practicals), or engineering-based (participants construct a device to do specified tasks).Knowledge-based events generally have two participants either taking a test or mathematically analyzing data.…
The win mathematically ensured that no team could finish ahead of them in points.On April 4, 2011, goaltender Brad Thiessen was named the recipient of the Aldege "Baz" Bastien Award, an annual award given to the AHL's outstanding goaltender for each season, as voted by coaches, players and members of the media in each of the league's 30 cities.…
Petzval tried to represent practically everything in his environment mathematically.Thus he tried to mathematically model fencing or the course of the horse.His obsession with mathematics finally led to the discovery of the portrait objective.…
If there is no scoring in the five-minute overtime, the game goes into a three-round shootout with the home team given the choice of shooting or defending first.This sequence ends when one team mathematically has more shootout goals than the other, thus winning the game.If neither team emerges victorious, the shootout continues one frame at a time until one team scores and the other does not, in which case the team that scores is given the win.…
Initially the classifiers or rules were binary, but recent research has expanded this representation to include real-valued, neural network, and functional (S-expression) conditions.Learning classifier systems are not fully understood mathematically and doing so remains an area of active research.…
Many forces (particularly those that depend on velocity) are not force fields.In these cases, the above three conditions are not mathematically equivalent.For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl).…
In that situation, a list of the winning members of America's team was shown, similar to a credit roll, and the studio contestant won a Trivial Pursuit board game.At any point, if it became mathematically impossible for one bank to overtake the other, the final round stopped.If the studio bank won in this situation, the studio player had the chance to play the next unused question as a double-or-nothing wager, or decline to do so.…
This field has grown into another sub-discipline of network science called dynamic network analysis.More recently other network science efforts have focused on mathematically describing different network topologies.Duncan Watts reconciled empirical data on networks with mathematical representation, describing the small-world network.…