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Page "Analyticity of holomorphic functions" ¶ 17
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Since and factor
Since 2005, the Bengals wear white for September home games where the heat could become a factor.
Since the definition of the equivalence factor may not be unequivocal, IUPAC and NIST discourage the use of normality.
Since blunt-ended DNA fragments have no cohesive ends to anneal, the melting temperature is not a factor to consider within the normal temperature range of the ligation reaction.
Since the inverse DFT is the same as the DFT, but with the opposite sign in the exponent and a 1 / N factor, any FFT algorithm can easily be adapted for it.
Since the stopping force F times that distance must be equal to the head's kinetic energy, it follows that F will be much greater than the original driving force f — roughly, by a factor D / d.
Since the Confederacy was founded, among other things, on states ’ rights, one important factor in Davis ’ choice of cabinet members was representation from the various states.
Since 1970, the government has given high priority to education in order to develop a domestic work force, which the government considers a vital factor in the country's economic and social progress.
Since this is negative, that factor is imaginary.
Since the units are consistent, the power factor is by definition a dimensionless number between 0 and 1.
Since the regulation of vascularization in the mature retina involves a balance between endogenous positive growth factors, such as vascular endothelial growth factor ( VEGF ) and inhibitors of angiogenesis, such as pigment epithelium-derived factor ( PEDF ), rAAV-mediated expression of PEDF, angiostatin, and the soluble VEGF receptor sFlt-1, which are all antiangiogenic proteins, have been shown to reduce aberrant vessel formation in animal models.
Since specific gene therapies cannot readily be used to treat a significant fraction of patients with retinal dystrophy, there is a major interest in developing a more generally applicable survival factor therapy.
Multiply by the switching frequency on the load capacitances to get the current used, and multiply by voltage again to get the characteristic switching power dissipated by a CMOS device:. Since most gates do not operate / switch at every clock cycle, they are often accompanied by a factor, called the activity factor.
Since the molar volume of gases is very roughly 1000 times that of solids and liquids, this results in a factor of about 1000 loss in volumetric heat capacity for gases, as compared with liquids and solids.
One performance issue is the 1 / 2 factor in the initial value of D. Since all of this is about the sign of the accumulated difference, then everything can be multiplied by 2 with no consequence.
Since the most important source of thermal energy is from the Sun, the ratio of glazing to thermal mass is an important factor to consider.
Since the Industrial Revolution, a major factor of productivity was the substitution of energy from, human and animal labor, water and wind power to electric power and internal combustion.
Since 2006, natural growth has been positive, but the most important factor for the recent population of the Czech Republic has been immigration, approximately 300, 000 during the last decade.
Since the square root of an algebraic integer is again an algebraic integer, it is not possible to factor any nonzero nonunit algebraic integer into a finite product of irreducible elements, which implies that is not Noetherian!
Since this is a limiting factor a robot may not be able to reach its specified maximum speed for movements over a short distance or a complex path requiring frequent changes of direction.
Since energy in quantum mechanics is defined as the phase factor exp (- iEt ) that one gets when one moves forward in time, the way to reverse time while preserving the sign of the energy is to reverse the sense of " i ", so that the sense of phases is reversed.
# Since r has been found, we can factor ( x r ) out of p ( x ) repeatedly until we have removed all of the roots at r. Repeat this for any other multiple roots until there are no more multiple roots.
Since the Supreme Court decided Bakke, California banned the state's use of race as a factor to consider in public schools ' admission policies.
Since large amounts of water are used during the process of whisky production, water supplies are a key factor for the location of any distillery.

Since and z
Since TPF can run as a second level guest under IBM's z / VM, a user can employ the VM trace facility to closely follow the execution of code.
However, C language programming is much easier to obtain skilled people in, so most if not all new development is done in C. Since z / TPF allows assembler programs to be repackaged into 1 logical file, critical legacy applications can be maintained and actually improve efficiency-the cost of entering one of these programs will now come at the initial enter when the entire program is fetched into core and logical flow through the program is accomplished via simple branch instructions, instead of a dozen or so IBM instructions previously needed to perform what is known as ' core resident enter / back '.
Since z / VSE 3. 1, Fibre Channel access to storage devices is supported, although only on IBM's Enterprise Storage Server ( ESS ) and its successors.
Since it is nonnegative it has at most one real root in z, whence its discriminant is less than or equal to zero, that is,
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 this * z changed to * r in the Scandinavian languages and in West Germanic ( German, Dutch, English, Frisian ), Verner's Law resulted in alternation of * s and * r in some inflectional paradigms, known as grammatischer Wechsel.
Since an nth degree polynomial equation can only have n distinct roots, this implies that the powers of a primitive root z, z < sup > 2 </ sup >, ... z < sup > n 1 </ sup >, z < sup > n </ sup >
Since all z / OS installations usually have both TSO and TSO / E functions installed, it is normal to refer to both TSO and TSO / E as " TSO ".
Since all its poles lie on the negative real axis, from z
Since, for a free-electron model, the contribution to the current density is directly proportional to the area in energy space ( with the Sommerfeld supply density z < sub > S </ sub > as the constant of proportionality ), it is useful to think of the ECD as drawn from electron states in an area of size d < sub > F </ sub >< sup > 2 </ sup > ( measured in eV < sup > 2 </ sup >) in the energy-space diagram.
Since root locus is a graphical angle technique, root locus rules work the same in the z and s planes.
Since z < sup > 1 / 2 </ sup > = e < sup > 1 / 2 Log ( z )</ sup >, on the contour outside the branch cut, we have gained 2π in argument along γ ( by Euler's Identity, represents the unit vector, which therefore has as its log.
Since the motion is planar, and p and L are perpendicular, p < sub > z </ sub >
Since rays in space can be parameterized by three coordinates, x, y, and z and two angles and, as shown at left, it is a five-dimensional function.
Since z < sub > 0 </ sub > is a local maximum for this function also, it follows from the maximum principle that | f ( z )| is constant.
Since λ has modulus 1, multiplying any split-complex number z by λ preserves the modulus of z and represents a hyperbolic rotation ( also called a Lorentz boost or a squeeze mapping ).
Since g ( z < sub > N </ sub >) ≠ 0, it follows that g ' ( z )/ g ( z ) has no singularities at z < sub > N </ sub >, and thus is analytic at z < sub > N </ sub >, which implies that the residue of f ′( z )/ f ( z ) at z < sub > N </ sub > is k.

Since and
Since p ( x ) is irreducible, this means that p ( x ) = k ( x a ), for some k ∈ F
Since 612 255 = 357 our next pair is
Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k 1 </ sub > is less than its predecessor r < sub > k 2 </ sub >.
In the first step, the final nonzero remainder r < sub > N 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N 1 </ sub >; therefore, g must be less than or equal to r < sub > N 1 </ sub >.
Since r < sub > N 1 </ sub > is a common divisor of a and b, r < sub > N 1 </ sub > ≤ g.
Since the first part of the argument showed the reverse ( r < sub > N 1 </ sub > ≤ g ), it follows that g = r < sub > N 1 </ sub >.
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 2 < sup >( q 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.
Since p is prime q 1 must be a multiple of p. Of course, if the number m = < sup >( q 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.
Since ω = dΦ / dt and k = + dΦ / dx, the wave velocity is v = dx / dt = ω / k.
Since the r < sup > th </ sup > failure comes last, it remains to choose the k trials with successes out of the remaining k + r 1 trials.
Since 2000, a small amateur experimental planting has been underway in the Lake Champlain valley of Vermont at the Vermont Experimental Cold-Hardy Cactus Garden where winter temperatures can reach 37 ° C with variable snowcover.
Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k 1 </ sup > of them.
Since methane clathrates are stable at a higher temperature than liquefied natural gas ( LNG ) (− 20 vs 162 ° C ), there is some interest in converting natural gas into clathrates rather than liquifying it when transporting it by seagoing vessels.
Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.
Since the topology on R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ( X )- adic topology and R < nowiki ></ nowiki > X < nowiki ></ nowiki > is complete, we can in particular apply power series to other power series, provided that the arguments don't have constant coefficients ( so that they belong to the ideal ( X )): f ( 0 ), f ( X < sup > 2 </ sup >− X ) and f ( ( 1 X )< sup >− 1 </ sup > 1 ) are all well defined for any formal power series f ∈ R < nowiki ></ nowiki > X < nowiki ></ nowiki >.

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