Similarly, as an infinite-dimensional example, the Lebesgue space L < sup > p </ sup > is always a Banach space but is only a Hilbert space when p = 2.

Similarly for p ( 2 ), the set of limit points of p ( 1 ), and so on.

Similarly, " They were so farre surprised with his Manifesto, that they would never suffer it to be published " ( p. 103 )

Similarly, cubic reciprocity relates the solvability of x < sup > 3 </ sup > ≡ q ( mod p ) to that of x < sup > 3 </ sup > ≡ p ( mod q ), and biquadratic ( or quartic ) reciprocity is a relation between x < sup > 4 </ sup > ≡ q ( mod p ) and x < sup > 4 </ sup > ≡ p ( mod q ).

If p, q and r are in proportion then q is called a mean proportional to ( or the geometric mean of ) p and r. Similarly, if p, q, r and s are in proportion then q and r are called two mean proportionals to p and s.

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.

Similarly, the 29 minuscule forms ( lowercase or small letters ) are: a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, å, ä, and ö.

* Similarly, the free group F < sub > n </ sub > has p < sup > n </ sup > − 1 subgroups of index p.

Similarly, a fold F < sub > 2 </ sub >( s ) perpendicular to m < sub > 2 </ sub > through its midpoint will place p < sub > 1 </ sub > on the line at location d < sub > 2 </ sub >.

Similarly k = g < sup >– p </ sup > ( mod N ) for any non-zero index k and for a unique p in 0 ,..., N – 2, where the negative exponent denotes the multiplicative inverse of g < sup > p </ sup > modulo N. That means that we can rewrite the DFT using these new indices p and q as:

Similarly, " spin " is a generic term for strategic political communication that attempts to frame or re-frame an event or a statement in a way that is politically profitable for one side and detrimental to another, though at its core it may simply be a red herring ( Bennett 2003, p. 130 ).

Similarly, a Cunningham chain of the second kind of length n is a sequence of prime numbers ( p < sub > 1 </ sub >,..., p < sub > n </ sub >) such that for all 1 ≤ i < n, p < sub > i + 1 </ sub >

Similarly, given any element y of Y, there is a function f < sub > y </ sub >, or f (·, y ), from X to Z, given by f < sub > y </ sub >( x ) := f ( x, y ).

Similarly, relatively little energy is used in producing and combining the raw materials ( although large amounts of CO < sub > 2 </ sub > are produced by the chemical reactions in cement manufacture ).

Similarly, the pentafluoride, DbF < sub > 5 </ sub >, should be even more volatile.

Similarly, the variation in the concentration of gas B is-dC < sub > B </ sub >/ dx.

Similarly, the partial pressure of B changes dP < sub > B </ sub >.

Similarly, for any a in F other than 0, there exists an element a < sup >− 1 </ sup > in F, such that a · a < sup >− 1 </ sup > = 1.

Similarly, < tt >( λx. y ) s → y := s = y </ tt >, demonstrating that < tt > λx. y </ tt > really is a constant function.

Similarly, methyl iodide and methyl triflate are viewed as the equivalent of the methyl cation because they readily undergo S < sub > N </ sub > 2 reactions by weak nucleophiles.

Similarly, for a given vacuum wavelength λ < sub > 0 </ sub >, the wavelength

* Similarly the even-graded element γ = − σ < sub > 1 </ sub > σ < sub > 2 </ sub > corresponds to a vector rotation of 180 °:

Similarly the number for " P " in some countries is actually the weight of an equivalent quantity of P < sub > 2 </ sub > O < sub > 5 </ sub > whereas in others ( including Australia ) it refers to elemental phosphorus.

Similarly, given points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >, z < sub > 1 </ sub >) and ( x < sub > 2 </ sub >, y < sub > 2 </ sub >, z < sub > 2 </ sub >) in three-space, the distance between them is:

Similarly, products of the gammas such as γ < sub > μ </ sub > γ < sub > ν </ sub > represent oriented surface elements, and so on.

To avoid this ambiguity, the number could be represented in scientific notation: 8. 0 × 10 < sup > 3 </ sup > m indicates that the first zero is significant ( hence a margin of 50 m ) while 8. 000 × 10 < sup > 3 </ sup > m indicates that all three zeroes are significant, giving a margin of 0. 5 m. Similarly, it is possible to use a multiple of the basic measurement unit: 8. 0 km is equivalent to 8. 0 × 10 < sup > 3 </ sup > m. In fact, it indicates a margin of 0. 05 km ( 50 m ).

Similarly, metal ion hydrolysis causes ions such as < span style =" white-space: nowrap ;">< sup > 3 +</ sup ></ span > to behave as weak acids :< ref name = Burgess > Section 9. 1 " Acidity of Solvated Cations " lists many pK < sub > a </ sub > values .</ ref >

Similarly, division by any power of two 2 < sup > k </ sup > may be performed by right-shifting k positions.

Similarly IF A > B THEN A ← A − B.

Similarly, all output was scrutinized for a Control-D character ( ASCII 4 ), which BASIC programs would send before seemingly PRINTing a disk command to get DOS's attention ( the disk commands would not really get PRINTed but were intercepted by DOS and prevented from making it to the screen output ).

Similarly, they should not act as directors of competing companies, as their duties to each company would then conflict with each other.

Similarly, the consolidated Teutonic laws of the Germanic tribes, included a complex system of monetary compensations for what courts would consider the complete range of criminal offences against the person, from murder down.

Similarly, Searle concludes, a computer executing the program would not understand the conversation either.

Similarly, during the English Civil War rope-tension drums would be carried by junior officers as a means to relay commands from senior officers over the noise of battle.

Similarly, while having several characters as students in a class taught by Henry Kissinger, the dialogue made up for Kissinger would also come from “ off-panel ” ( although Kissinger had earlier appeared as a character with his face shown in a 1972 series of strips in which he met Mark Slackmeyer while the latter was on a trip to Washington ).

Similarly, if light consisted strictly of classical particles and we illuminated two parallel slits, the expected pattern on the screen would simply be the sum of the two single-slit patterns.

Similarly, if the house was located in an undesirable neighborhood and the Federal Reserve Bank was about to raise interest rates by five percentage points, then the risk factor would be a lot higher than 5 %: it might not be possible for him to predict a profit in discounted terms even if he thinks he could sell the house for $ 200, 000 in three years.

Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm, and so on.

Similarly, since it consists of an estimated 2. 3 million blocks, completing the building in 20 years would involve moving an average of more than 12 of the blocks into place each hour, day and night.

Similarly, jury trials were abolished by the government of India in 1960 ( this was followed by Pakistan soon afterwards ) on the grounds they would be susceptible to media and public influence.

Similarly, if " this sentence is false " is false, then the sentence is true, which would in turn mean that it is actually false, but this would mean that it is true, and so on ad infinitum.

Similarly, there were then several decrees in place aimed at suppressing outward signs of national identity, including decrees against wearing tefillin and tzitzit ; as Conversion to Judaism was against Roman law, Rabbi Judah would not have discussed this.

* Similarly, cloning would violate the no teleportation theorem, which says classical teleportation ( not to be confused with entanglement-assisted teleportation ) is impossible.

Similarly, an observer near the summit would be unaware of standing on a high mountain, as the slope of the volcano would extend beyond the horizon, a mere 3 kilometers away.

Similarly, judges might assume in default of express evidence to the contrary that the place where the cause of action arose would provide certain basic protections, e. g. that the foreign court would provide a remedy to someone who was injured due to the negligence of another.

Similarly, after earning two misses at a height, they could pass to the next height where they would have only one attempt.

Similarly, Internet email users generally consider their emails to be private and hence would be concerned if their email was being accessed, read, stored or forwarded by third parties without their consent.

Similarly, country boogie and Chicago electric blues supplied many of the elements that would be seen as characteristic of rock and roll.