Addition of low levels of modifiers ( sometimes called entrainers ), such as methanol and ethanol, can also significantly increase solubility, particularly of more polar compounds.

Addition of silica fume can yield exceptionally high strengths, and cements containing 5 – 20 % silica fume are occasionally produced.

Addition of copper or manganese oxides can significantly improve the ease of ignition.

Addition and subtraction require the numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted.

Addition of very small numbers is accessible to toddlers ; the most basic task, 1 + 1, can be performed by infants as young as five months and even some animals.

The platted area Cumberland Addition can trace its roots to this early period.

Addition can be performed by repeated subtraction, with no conditional branching ; e. g., the following instructions result in the content at location a being added to the content at location b:

The elements of can be considered as polynomials in of degree less than n. Addition in is given by the rules for polynomial addition and multiplication is given by polynomial multiplication modulo f ( X ).

Addition of lime ( calcium ) can give carminic acid lakes a purple cast.

Addition of tin can play mostly the same role.

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.

Addition chains can be used for addition-chain exponentiation: so for example we only need 7 multiplications to calculate 5 < sup > 31 </ sup >:

Addition of CO < sub > 2 </ sub > to a solution in contact with a solid can affect the alkalinity, especially for carbonate minerals in contact with groundwater or seawater.

* Addition and multiplication of complex numbers and quaternions is associative.

Addition of probability amplitudes as complex numbers

Addition and multiplication are familiar operations in the theory of complex numbers and are given in the figures.

We claim that, as a field, the quotient is isomorphic to the complex numbers, C. A general complex number is of the form, where a and b are real numbers and Addition and multiplication are given by

Addition in the second dimensional cohomology group coincides with tensor product of complex line bundles.

Addition of pyridine, results in the formation of the more stable complex CrO ( O < sub > 2 </ sub >)< sub > 2 </ sub > py.

Addition of chloride ions to a suspension of PbCl < sub > 2 </ sub > gives rise to soluble complex ions.

While new and challenging, the Addition system was criticized for requiring too much precision at times, especially later on near the end of the game where Additions became more complex and required more speed and hand-eye coordination to continue the combo.

The facility, the Engineering Technology Center, covers of land and contains 36 labs, 12 classrooms, two seminar rooms, and a 200-seat lecture room .< ref name =" DPR ">" New Engineering Technology Center and Building I Renovation and Addition.

: Addition of the angles corresponds to multiplication of the elements of SO < sub > 2 </ sub >( R ), and taking the opposite angle corresponds to inversion.

* Addition hybrids, called B < sub > III </ sub > hybrids by Rutishauser: An embryo is formed after a meiotically unreduced egg cell is fertilized.

Addition of hydrogen, acting as a reducing agent, to argon in the plasma displays significantly extends the lifetime of BAM: Eu < sup > 2 +</ sup > phosphor, by reducing the Eu ( III ) atoms back to Eu ( II ).

Addition of a catalytic amount of Pd ( PPh < sub > 3 </ sub >)< sub > 4 </ sub > produces a regiorandom polymer, but treatment with Ni ( dppe ) Cl < sub > 2 </ sub > yields regioregular PAT in quantitative yield.

Addition using the polynomial basis is as simple as addition modulo p. For example, in GF ( 3 < sup > m </ sup >):

: Poems are more regular and correct in the Frame of their Contrivance, and receive less Addition from Events and Episodes than Romances, which are capable of these Accessions, because their Style is not so elevated, and they don't so far di |< 8 > sten'd the Intellect, so that they give it leave to admit a greater Number of different Ideas.

To increase the volatility of polar fragments, various methylating reagents can be added to a sample before pyrolysis.

Furthermore, reflecting the polarizability of divalent sulfur, the S-S bond is susceptible to scission by polar reagents, both electrophiles and especially nucleophiles:

The side-chain can make an amino acid a weak acid or a weak base, and a hydrophile if the side-chain is polar or a hydrophobe if it is nonpolar.

Carnivorans are the most diverse in size of any mammalian order, ranging from the least weasel ( Mustela nivalis ), at as little as and, to the polar bear ( Ursus maritimus ), which can weigh up to, to the southern elephant seal ( Mirounga leonina ), whose adult males weigh up to and measure up to in length.

The five primary classifications can be further divided into secondary classifications such as rain forest, monsoon, tropical savanna, humid subtropical, humid continental, oceanic climate, Mediterranean climate, steppe, subarctic climate, tundra, polar ice cap, and desert.

In the case of a central force, relative to the origin of the polar coordinate system, can be replaced by, meaning the entire force is the component in the radial direction.

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

The above results can be derived perhaps more simply in polar coordinates, and at the same time extended to general motion within a plane, as shown next.

These loops are the closed-magnetic flux cousins of the open-magnetic flux that can be found in coronal hole ( polar ) regions and the solar wind.

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.

This reaction can suffer from anion availability problems and, therefore, can benefit from the addition of phase transfer catalysts or highly polar aprotic solvents such as DMF.

Even when an object's net charge is zero, charge can be distributed non-uniformly in the object ( e. g., due to an external electromagnetic field, or bound polar molecules ).

These channels are gated so they can open and close, thus regulating the flow of ions or small polar molecules.

During solar proton events, ionization can reach unusually high levels in the D-region over high and polar latitudes.

This kind of interaction can be expected between any polar molecule and non-polar / symmetrical molecule.

An example of a dipole – dipole interaction can be seen in hydrogen chloride ( HCl ): the positive end of a polar molecule will attract the negative end of the other molecule and influence their arrangement.

Surface-charge lithography, in fact Plasma desorption mass spectrometry can be directly patterned on polar dielectric crystals via pyroelectric effect,

There is another disturbance of the Earth's rotation called polar motion that can be estimated for only a few months into the future because it is influenced by rapidly and unpredictably varying things such as ocean currents, wind systems, and motions in the liquid nickel-iron outer core of the Earth.

In general, this can be recognized as the equation of a conic section in polar coordinates ( r, θ ).

Polar bears can breed with brown bears to produce fertile grizzly – polar bear hybrids, rather than indicating that they have only recently diverged, the new evidence suggests more frequent mating has continued over a longer period of time, and thus the two bears remain genetically similar.

Collagen exhibits the polar uniaxial orientation of molecular dipoles in its structure and can be considered as bioelectret, a sort of dielectric material exhibiting quasipermanent space charge and dipolar charge.

Therefore, the same point can be expressed with an infinite number of different polar coordinates or, where n is any integer.