Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.

Analogously, anyone who argues that Einstein's theory of gravitation is simpler than Newton's, must say rather more to explain how it is that the latter is mastered by student-physicists, while the former can be managed ( with difficulty ) only by accomplished experts.

Analogously, prime polynomials ( more correctly, irreducible polynomials ) can be defined as polynomials which cannot be factorized into the product of two non constant polynomials.

Analogously, we can define QL, RQ, and LQ decompositions, with L being a lower triangular matrix.

Addition () is the most basic operation, multiplication () is also a primary operation, though for natural numbers it can be thought of as a chained addition involving n numbers a, and exponentiation () can be thought of as a chained multiplication involving n numbers a. Analogously, tetration () can be thought of as a chained power involving n numbers a.

Analogously, the maximal pressure where a stable SWP can be operated decreases with increasing diameter.

Analogously, one can define Lie algebra homology as

Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.

Analogously, it may ( or may not ) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws.

Analogously, a non-Euclidean plane is said to be elliptic or hyperbolic according as each of its lines contains no point at infinity or two points at infinity.

Analogously, the second law of thermodynamics states that the change in entropy an isolated system will be greater than or equal to 0 for a spontaneous process, suggesting a link between entropy and the area of a black hole horizon.

Analogously to similar results for the more well-known complexity class NP, this transformation together with the Immerman-Szelepcsényi theorem allow any problem in NL to be represented as a second order logic formula with a single existentially quantified predicate with clauses limited to length 2 ; such formulae are known as SO-Krom.

Analogously let a < sub > n </ sub >, b < sub > n </ sub > be in R, 0 ≤ n ≤ N and a < sub > N </ sub > ≠ 0 or b < sub > N </ sub > ≠ 0 then

Analogously an operator A on functions is said to be translation invariant with respect to a translation operator if the result after applying A doesn't change if the argument function is translated.

( Analogously with, given the classical dichotomy, may be factored into a product.

Analogously to the symbol mentioned above, Oxford University Press have devised the non-IPA symbol to represent a vowel which may be either / ʊ / or / ə /, the two being in free variation .. For example awful may be pronounced or.

Analogously, critics of for-profit HMOs argue that such firms disproportionately insure healthy people, while simultaneously eschewing chronically ill patients, who must then by default be cared for disproportionately by public insurance schemes and non-profit providers — thus a so-called " dumping " of undesirable patients.

Analogously, the model produced by SVR depends only on a subset of the training data, because the cost function for building the model ignores any training data close to the model prediction ( within a threshold ).

Analogously, illegitimacy ( or bastardy ) is the status of a child conceived outside of marriage, though the consequences of that definition were ameliorated by legislation.

Analogously to the Riemann zeta function, the values of the Dedekind zeta function at integers encode ( at least conjecturally ) important arithmetic data of the field K. For example, the analytic class number formula relates the residue at s = 1 to the class number h ( K ) of K, the regulator R ( K ) of K, the number w ( K ) of roots of unity in K, the absolute discriminant of K, and the number of real and complex places of K. Another example is at s = 0 where it has a zero whose order r is equal to the rank of the unit group of O < sub > K </ sub > and the leading term is given by

Analogously, the theoretical superior limit for the money held by public is defined by the following series:

Analogously to the unitary case, Steinberg constructed families of groups by taking fixed points of a product of a diagram and a field automorphism.

" Analogously, fads are started by some persons among the crowd, who, even without realizing it, are a little ahead of the rest.

Analogously, many other systems call their printing devices " LP ", " LPT ", or some similar variant, whether these devices are in fact line printers or other types of printers.

Analogously, Rajah Ache was also referred to as Rajah Matanda ( Old Rajah ), while Rajah Sulayman was sometimes referred to as Rajah Muda or Rajamora ( Young Rajah ).

Subtle differences in a compound's partition coefficient result in differential retention on the stationary phase and thus changing the separation.

Chromatography is based on the concept of partition coefficient.

A low blood: gas partition coefficient is therefore necessary for quick removal of the anaesthetic.

For example, many compounds used for medication are weak acids or bases, and a knowledge of the pK < sub > a </ sub > values, together with the water – octanol partition coefficient, can be used for estimating the extent to which the compound enters the blood stream.

Its blood / gas partition coefficient of 2. 4 makes it an agent with moderate induction and recovery time.

The partition coefficient principle has been applied in paper chromatography, thin layer chromatography, gas phase and liquid-liquid applications.

Other constants for dynamic equilibrium involving phase changes include partition coefficient and solubility product.

Chemical potentials are important in many aspects of equilibrium chemistry, including melting, boiling, evaporation, solubility, osmosis, partition coefficient, liquid-liquid extraction and chromatography.

The measurement of this ratio is known as the partition coefficient.

Each partition of n into an even number of distinct parts contributes + 1 to the coefficient of x < sup > n </ sup >; each partition into an odd number of distinct parts contributes − 1.

However, the coefficient of x < sup > 12 </ sup > is − 1 because there are seven ways to partition 12 into an even number of distinct parts, but there are eight ways to partition 12 into an odd number of distinct parts.

The distribution of a compound between water and octanol is used to calculate the partition coefficient ' P ' of that molecule ( often expressed as its logarithm to the base 10, log P ).

Many dermal absorption models consider the stratum corneum / water partition coefficient to be well approximated by a function of the water / octanol partition coefficient of the form:

Where a and b are constants, is the stratum corneum / water partition coefficient, and is the water / octanol partition coefficient.

If the integer n is partitioned into a sum in which " 1 " appears j < sub > 1 </ sub > times, " 2 " appears j < sub > 2 </ sub > times, and so on, then the number of partitions of a set of size n that collapse to that partition of the integer n when the members of the set become indistinguishable is the corresponding coefficient in the polynomial.

Meyer compared the potency of many agents, defined as the reciprocal of the molar concentration required to induce anaesthesia in tadpoles, with their olive oil / water partition coefficient.

He found a nearly linear relationship between potency and the partition coefficient for many types of anaesthetic molecules such as alcohols, aldehydes, ketones, ethers, and esters.