There is no known useful formula that yields all of the prime numbers and no composites.

Electrolytic conductors are used in electronic devices where the chemical reaction at a metal / electrolyte interface yields useful effects.

* Forest gardening – low-maintenance organic plant-based food production and agroforestry system based on woodland ecosystems, incorporating fruit and nut trees, shrubs, herbs, vines and perennial vegetables which have yields directly useful to humans.

Forest gardening is a low-maintenance sustainable plant-based food production and agroforestry system based on woodland ecosystems, incorporating fruit and nut trees, shrubs, herbs, vines and perennial vegetables which have yields directly useful to humans.

Effectively, this means that each muon catalyzing d-d muon-catalyzed fusion reactions in pure deuterium is only able to catalyze about one-tenth of the number of d-t muon-catalyzed fusion reactions that each muon is able to catalyze in a mixture of equal amounts of deuterium and tritium, and each d-d fusion only yields about one-fifth of the yield of each d-t fusion, thereby making the prospects for useful energy release from d-d muon-catalyzed fusion at least 50 times worse than the already dim prospects for useful energy release from d-t muon-catalyzed fusion.

The book goes on to point out the role of bottlenecks ( constraints ) in a manufacturing process, and how identifying them not only makes it possible to reduce their impact, but also yields a useful tool for measuring and controlling the flow of materials.

Rauvolfia serpentina, or Indian Snakeroot, yields the alkaloids reserpine and rescinnamine, which are useful tools in the treatment of high blood pressure and even some forms of psychosis.

Hartlib valued useful knowledge: anything that could increase crop yields, or cure disease.

Tertiary alcohols are prone to elimination, and phenols are usually too unreactive to give useful yields.

Some research into original design still yields useful results, for example genetic algorithms have been used to design logic systems with integrated fault detection that outperform hand designed equivalents.

In the case of the slice or coslice category, the identity functor may be replaced with some other functor ; this yields a family of categories particularly useful in the study of adjoint functors.

In contrast to monolayer cultures, however, the spheroid structures that are formed when ESCs aggregate enables the non-adherent culture of EBs in suspension, making EB cultures inherently scalable, which is useful for bioprocessing approaches, whereby large yields of cells can be produced for potential clinical applications.

Also, many useful Lewis acid-catalyzed ene reactions have been developed which can afford high yields and selectivities at significantly lower temperatures, making the ene reaction a useful C – C forming tool for the synthesis of complex molecules and natural products.

On the other hand, the paramethylbenzhydrylamine ( pMBHA ) resin yields a C-terminal amide, which is useful in mimicking the interior of a protein.

To be useful, these methods need to give high yields, and to be reliable for a broad range of substrates.

The above description assumes that the waveform of the transmitter being exploited possesses a usable radar ambiguity function and hence cross-correlation yields a useful result.

In more than 90 % of cases analysis of pleural fluid yields clinically useful information.

Dividing the entire expression above by log < sub > e </ sub > 2 yields the divergence in bits.

The expression for yields the equivalent time constant in terms of the sampling period and smoothing factor:

The expression for parameter yields the equivalent time constant in terms of the sampling period and:

yields an integral expression for w ( r ):

In statistical mechanics, a semi-classical derivation of the entropy that doesn't take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive ( is not proportional to the amount of substance in question ).

Substituting this expression into the wave equation yields the time-independent form of the wave equation, also known as the Helmholtz equation:

The above expression yields the poles of the gain G. For each complex pole, there is another which is the complex conjugate, and for each conjugate pair there are two more that are the negatives of the pair.

Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles somewhat an expression describing the interaction between instantaneous multipoles ( see the qualitative description above ).

They have become the mammalian equivalent of E. coli in research and biotechnology today, especially when long-term, stable gene expression and high yields of proteins are required.

While bc can work with arbitrary precision, it actually defaults to zero digits after the decimal point-so the expression 2 / 3 yields 0.

Setting and equating the above two expression yields that

An atomic parsing expression consisting of a single terminal ( i. e. literal ) succeeds if the first character of the input string matches that terminal, and in that case consumes the input character ; otherwise the expression yields a failure result.

Applying the Cauchy-Bunyakowski-Schwartz inequality to each term of the last expression yields

An expression-oriented programming language is a programming language where every ( or nearly every ) construction is an expression and thus yields a value.

In C and C ++, evaluating such an expression yields undefined behavior.

Character defines a function associated by convention with an expression, which takes contextual elements as arguments and yields content as values.

We can say that an expression is context-sensitive if and only if its character defines a non-constant function ( i. e., just in case it yields different content-values given different context-element-arguments ).

Dividing the expression by yields:

Expression yields in Pichia vary between different clones, and usually a large number of clones needs to be screened for protein expression before a good producer is found.

Compared to other expression systems such as S2-cells from Drosophila melanogaster or Chinese Hamster Ovary cells, Pichia usually gives much better yields.

Cultured cells expressing the aequorin gene can effectively synthesize aequorin: however, recombinant expression yields only the apoprotein, therefore it is necessary to add coelenterazine into the culture medium of the cells to obtain a functional protein and thus use its blue light emission to measure Ca < sup > 2 +</ sup > concentration.

While Nicomachus ' algorithm is the same as Euclid's, when the numbers are prime to one another it yields the number " 1 " for their common measure.

However, actual rainfall from year to year is irregular and occasionally may be less than, leading to severe reductions in crop yields for both rain-fed and irrigated agriculture.

Low concentrations are not a problem for bacteria because they simply ignore the waste that surrounds the metals, attaining extraction yields of over 90 % in some cases.

Botanists also study how plants produce food we can eat and how to increase yields and therefore their work is important in mankind's ability to feed the world and provide food security for future generations, for example, through plant breeding.

Shotgun sequencing yields sequence data quickly, but the task of assembling the fragments can be quite complicated for larger genomes.

Equating these two expressions yields a formula for the diffusivity:

Owing to this local dealing, the city dwellers find that their grain yields are the best, and for the first time make deliberate and conscious selection.

The formula that yields this temperature is based on the first law of thermodynamics and takes note of the fact that the heat of combustion is used entirely for heating the fuel, the combustion air or oxygen, and the combustion product gases ( commonly referred to as the flue gas ).

Substituting into the above formula for | F < sub > h </ sub >| yields a horizontal force to be:

The harvest yields for Chianti Classico are restricted to no more than 3 tonnes per acre ( 7. 5 tonnes / hectare ).

Integrating + 1. 7 ms / d / cy and centering the resulting parabola on the year 1820 yields ( to a first approximation ) 31 ×(( Year − 1820 )/ 100 )< sup > 2 </ sup > seconds for ΔT.

He puts forward the idea that when men have the opportunity to possess property and work on it, they will “ learn to love the very soil which yields in response to the labor of their hands, not only food to eat, but an abundance of the good things for themselves and those that are dear to them .” He states also that owning property is not only beneficial for a person and their family, but is in fact a right, due to God having “... given the earth for the use and enjoyment of the whole human race ”.

For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

Using this diazomethane, mixtures of carboxylic acids can be converted to their methyl esters in near quantitative yields, e. g., for analysis by gas chromatography.

Substitution into the equation above for the control volume cv yields:

This ring is a field because it contains a multiplicative inverse for each element N other than zero ( an integer that, multiplied by the element modulo p yields 1 ), and it has a finite number of elements ( p ), making it a finite field.

How Gerrymandering can influence electoral results on a Voting system # Nonproportional and semiproportional methods | non-proportional system. Example for a state with 3 equally sized districts, 15 voters and 2 parties: Plum ( squares ) and Orange ( circles ). In ( a ), creating 3 mixed-type districts yields a 3 – 0 win to Plum — a disproportional result considering the state-wide 9: 6 Plum majority. In ( b ), Orange wins the urban district while Plum wins the rural districts — the 2-1 result reflects the state-wide vote ratio. In ( c ), gerrymandering techniques ensure a 2-1 win to the state-wide minority Orange party.

The solution of the Schrödinger equation goes much further than the Bohr model, because it also yields the shape of the electron's wave function (" orbital ") for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds.

Combining these together yields the Schrödinger Hamilton for the N-particle case:

Rainfall is not always adequate for rice cultivation, however, and the relatively high average precipitation conceals years where rainfall may be only half or less of the norm, causing significant declines in rice yields.