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

Since symbols ( for example, alphanumeric characters ) are not continuous, representing symbols digitally is rather simpler than conversion of continuous or analog information to digital.

Since classical analog filters are IIR filters, there has been a long history of studying the range of possible transfer functions implementing various of the above desired filter responses in continuous time systems.

Since the publication of the History of Trade Unionism ( 1894 ) by Sidney and Beatrice Webb, the predominant historical view is that a trade union " is a continuous association of wage earners for the purpose of maintaining or improving the conditions of their employment.

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 the Heisenberg principle limits the precision of any measurement of the combination of an electron's momentum ( related to energy ) and its position, in a crystal effectively the available energy levels form a continuous band of allowed energy levels.

Since its first meeting, the Council, which exists in continuous session, has travelled widely, holding meetings in many cities, such as Paris and Addis Ababa, as well as at its current permanent home at the United Nations Headquarters in New York City.

Since electromagnetism was known to be a wave generated by a changing electric or magnetic field ( a continuous, wave-like entity itself ) an atomic / particle description of electricity and charge was a non sequitur.

Since adjoint functors exist in abundance, this gives numerous examples of continuous and cocontinuous functors.

Since a convolutional code doesn't use blocks, processing instead a continuous bitstream, the value of t applies to a quantity of errors located relatively near to each other.

Since this force varies with the position of the charge and by Coloumb's Law it is defined at all points in space, is a continuous function of the charge's position ( x, y, z ).

Since becoming operational in Normandy on August 1, 1944 until May 9, 1945, the Third Army was in continuous combat for 281 days.

Since the electrode is continuous, welding speeds are greater for GMAW than for SMAW.

Since 1866 Dargomïzhsky had been working on his opera The Stone Guest, a version of the Don Juan story with a Pushkin text that he declared would be set " just as it stands, so that the inner truth of the text should not be distorted ", and in a manner that abolished the ' unrealistic ' division between aria and recitative in favour of a continuous mode of syllabic but lyrically heightened declamation somewhere between the two.

Since around the 1950s and the rise of bebop, continuous use of vibrato has largely fallen out of style in favor of more selective use.

Since that replacement, the great expansion of total power was driven by continuous improvements in energy conversion efficiency.

Since then, papyrus finds have greatly added to the store of Ibycean verses-notably, and controversially, forty-eight continuous lines addressed to Polycrates, whose identification with Polycrates of Rhodes ( son of Polycrates, the Samian tyrant ) requires a careful selection of historical sources.

Since many of the events were reused in the 2001 film Jay and Silent Bob Strike Back, not all the events depicted here are necessarily continuous with those depicted elsewhere in the View Askewniverse.

Since then there has been a continuous loss of territory to the neighbouring cities of Altona ( later itself a part of Hamburg ), Hamburg and Norderstedt.

Since July 15, 1929, the choir has performed a weekly radio broadcast called Music and the Spoken Word, which is one of the longest-running continuous radio network broadcasts in the world.

Since the division has been eliminated and we have a continuous function, we can freely substitute to find the limit:

Since the 1960s, there has been a long and continuous tradition of squatted social centers in the Netherlands, particularly in the capital, Amsterdam.

Since quantitative measurements are essential in all sciences, there is a continuous effort by computer science practitioners and theoreticians to bring similar approaches to software development.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero.

Since bottled water processed with distillation or reverse osmosis lacks fluoride ions which are present in some natural ground water, it is possible that the drinking of distilled water may increase the risk of tooth decay due to a lack of this element now added to many water supplies.

Since ethyl alcohol boils at a lower temperature than water, a common application of the process of distillation is to produce strong alcoholic drinks.

Since each component of the mixture evaporates at slightly different temperatures and the goal of reduction is to drive away those with lowest points of evaporation, it is – in a way – a form of distillation.

Since the mixture is already above the 96 % azeotrope, the distillation will not get " stuck " at that point and the ethanol can be distilled to whatever concentration is needed.

Since Ca < sup > 2 +</ sup > and Mg < sup > 2 +</ sup > exist as nonvolatile salts, they can be removed by distilling the water, but distillation is too expensive in most cases ( rainwater is soft because it is, in effect, distilled.

Since the solution boils over a range of temperatures as in distillation, more of the heat can be extracted from the source than with a pure working fluid.

Since it was illegally produced, the proof was dependent on the efficiency of the distillation process.

Since ancient perfumers and apothecaries never compounded their fragrances by mixing essential oils in such large ratio with respect to carrier oils — because the original formula was to be distilled after maceration, not before — it is possible to restore the proportions to something like what they might have been if maceration and distillation had occurred " according to the art of the apothecary ":

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 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.