Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.

Since the introduction of the first commercially available microprocessor ( the Intel 4004 ) in 1970, and the first widely used microprocessor ( the Intel 8080 ) in 1974, this class of CPUs has almost completely overtaken all other central processing unit implementation methods.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Since the 2011 local government reform it is part of the municipality Corinth, of which it is the seat and a municipal unit.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since such radiation can produce severe damage to life at powers that produce very little heating, it is considered far more dangerous ( in terms of damage-produced per unit of energy, or power ) than the rest of the electromagnetic spectrum.

Since bosons carry one unit of angular momentum, the fermion's spin direction will flip from + to − ( or vice versa ) during such an exchange ( in units of the reduced Planck's constant ).

Since the joule is also a Watt-second and the common unit for electricity sales to homes is the kWh ( kilo-Watt-hour ), a kWh is thus 1000 ( kilo ) x 3600 seconds

Since each chromosome has only one functional unit of a pair of kinetochores, whole chromosomes are pulled toward opposing poles, forming two haploid sets.

Since local government reorganisation, the unit in England, Northern Ireland and Wales is known as a district, and in Scotland as a council area.

* The atomic mass unit ( u ) is defined so that a single carbon-12 atom has a mass of 12 u ; 1 u is approximately .< ref group =" note "> Since the Avogadro constant N < sub > A </ sub > is defined as the number of atoms in 12 g of carbon-12, it follows that 1 u is exactly 1 /( 10 < sup > 3 </ sup > N < sub > A </ sub >) kg .</ ref > The atomic mass unit is convenient for expressing the masses of atoms and molecules.

Since he was no longer physically qualified for flying, he was transferred to RAF Intelligence and seconded to MI9, a unit that was dedicated to supporting resistance movements and helping prisoners escape.

Since the standard unit for expressing the mass of molecules or atoms ( the dalton or atomic mass unit ) is defined as 1 / 12 of the mass of a < sup > 12 </ sup > C atom, it follows that the molar mass of a substance, measured in grams per mole, is exactly equal to its mean molecular or atomic mass, measured in daltons ; which is to say, to the substance's mean molecular or atomic weight.

Since it is referenced to the watt, it is an absolute unit, used when measuring absolute power.

Since the surface area of a sphere of radius r is A = 4πr < sup > 2 </ sup >, then intensity I ( power per unit area ) of radiation at distance r is

Since healing is a rare ability, units do not regenerate health, and there is no way to construct new units, hit and run skirmishes are effective and unit conservation is essential.

Since the " band " as a unit was much more important than " tribe " in Chiricahua culture, the Chiricahua had no name for themselves ( autonym ) as a people.

Since the 2011 local government reform it is part of the municipality Pylos-Nestoras, of which it is the seat and a municipal unit.

Since payment by commodity generally provides a useful good, commodity money is similar to barter, but is distinguishable from it in having a single recognized unit of exchange.

Since ε < sub > 0 </ sub >, the vacuum permittivity, is not dimensionless, the coulomb ( the SI unit of charge ) is not dimensionally equivalent to < sup > 1 / 2 </ sup > < sup > 3 / 2 </ sup > < sup >− 1 </ sup >, unlike the statcoulomb.

Since the 2011 local government reform it is part of the municipality Argos-Mykines, of which it is a municipal unit.

Since 1965, when the latter unit of local government was dissolved, it has been more fuzzily defined.

Since the 2011 local government reform it is part of the municipality Vari-Voula-Vouliagmeni, of which it is a municipal unit.

Since relativity postulates that the speed of light is the same for all observers, the Lorentz transformation must preserve the spacetime interval between any two events in Minkowski space.

Since 1983, it has been defined as " the length of the path travelled by light in vacuum during a time interval of of a second.

Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.

Since a Fahrenheit-sized interval of temperature is only < sup > 5 </ sup >⁄< sub > 9 </ sub > that of a Celsius-sized interval, the value is typically expressed as 10. 4 ( µin / in )/° F rather than 18. 7 ( µin / in )/° C .< sub > </ sub ></ ref > Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Q < sub > p </ sub > = 125 ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125 µL / L, 125 µgal / gal, 125 cm < sup > 3 </ sup >/ m < sup > 3 </ sup >, etc.

Since TV screens hide the vertical blanking interval of a composite video signal and even crop the edges of the picture, extensions have been implemented by taking advantage of these unseen parts of the signal.

Since it reports order statistics ( rather than, say, the mean ) the five-number summary is appropriate for ordinal measurements, as well as interval and ratio measurements.

Since again, quality is uniformly distributed over the interval from 0 to this, the average quality of the cars offered for sale at will be worth only.

Since fifths and fourths are intervals composed respectively of 7 and 5 semitones, the circumference of a circle of fifths is an interval as large as 7 octaves ( 84 semitones ), while the circumference of a circle of fourths equals only 5 octaves ( 60 semitones ).

Since the function of pitch classes is a key element, the problem of compound intervals with interval recognition is not an issue — whether the notes in a melody are played within a single octave or over many octaves is irrelevant.

Since the first coefficient a < sub > 0 </ sub > of the continued fraction of x plays no role in Khinchin's theorem and since the rational numbers have Lebesgue measure zero, we are reduced to the study of irrational numbers in the unit interval, i. e., those in.

Since is defined over an interval,

Since the initial rollout of Fastpass, the rules have been relaxed a bit, and now additional Fastpasses can be had sooner after one another ( maximum 2 hour interval between obtaining two Fastpasses ), but still only one Fastpass per attraction per park ticket in every interval.

Since the Chinese system is not an equal tempered tuning, playing a melody starting from the lǜ nearest to A will not necessarily sound the same as playing the same melody starting from some other lǜ, since the wolf interval will occupy a different point in the scale.

Since the kotekan patterns are either three notes ( telu ) or three sounds ( the kotekan empat has two solo pitches plus the open interval ), the simple patterns do not repeat every four or eight notes.

Since 2005, the FDA and European regulators have required that nearly all new molecular entities are evaluated in a Thorough QT ( TQT ) study to determine a drug's effect on the QT interval.

Since a musical interval is a ratio of frequencies, the equal-tempered chromatic scale divides the octave ( which has a ratio of 2: 1 ) into twelve equal parts.

Since each modulator is very slow, we can afford to insert a guard interval between the symbols, and thus eliminate the ISI.

Since the required confidence interval to establish a relationship between two parameters is usually chosen to be 95 % ( meaning that there is a 95 % chance that the relationship observed is not due to random chance ), there is a thus a 5 % chance of finding a correlation between any two sets of completely random variables.

Since a query may return all intervals, for example if the query is a large interval intersecting all intervals in the collection, this is asymptotically optimal ; however, we can do better by considering output-sensitive algorithms, where the runtime is expressed in terms of m, the number of intervals produced by the query.

Since we only care about the interval beginnings in this scenario, we can consult the list sorted by beginnings.

Since each node stores the intervals that overlap it, with all intervals completely to the left of its center point in the left subtree, similarly for the right subtree, it follows that each interval is stored in the node closest to the root from the set of nodes whose center point it overlaps.

Since BHM takes place in an " open hole ", the casing shoe is located just above the upper border of the production interval ( ore body ) leaving the rest open.