For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;

Combinatorics is an example of a field of mathematics which does not, in general, follow the axiomatic method.

As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.

Another example of an algebraically closed field is the field of ( complex ) algebraic numbers.

This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

Scientists dismiss these mechanisms as implausible since, for example, the magnetic field, when measured from earth, of a large but distant planet such as Jupiter is far smaller than that produced by ordinary household appliances.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

An example is the field of complex numbers.

For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension.

For example, it also predicts the variation of the particle density in a gravitational field with height, if.

For example, the CIA World Factbook uses the word in its " Country name " field to refer to " a wide variety of dependencies, areas of special sovereignty, uninhabited islands, and other entities in addition to the traditional countries or independent states ".< sup id = Note_1 >

For example, a 1039 bit integer was factored with the special number field sieve using 400 computers over 11 months.

For example, if an electric field is placed across a solution of Na < sup >+</ sup > and Cl < sup >−</ sup > ( and conditions are right ) the sodium ions move towards the negative electrode ( cathode ), while the chloride ions move towards the positive electrode ( anode ).

The authors of the study interpreted this as being the result of the ease by which primary commodities may be extorted or captured compared to other forms of wealth, for example, it is easy to capture and control the output of a gold mine or oil field compared to a sector of garment manufacturing or hospitality services.

For example, there are slow-conducting unmyelinated C fibers and faster-conducting myelinated Aδ fibers.

If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

This is seen in, for example, phenol ( C < sub > 6 </ sub > H < sub > 5 </ sub >- OH ), which is acidic at the hydroxyl ( OH ), since a charge on this oxygen ( alkoxide-O < sup >–</ sup >) is partially delocalized into the benzene ring.

As an example consider the C declaration

The C and C ++ programming languages, for example, define byte as an " addressable unit of data storage large enough to hold any member of the basic character set of the execution environment " ( clause 3. 6 of the C standard ).

" Historian and novelist C. S. Forester, writing in 1929, compared the Nile to the great naval actions in history and concluded that " it still only stands rivalled by Tsu-Shima as an example of the annihilation of one fleet by another of approximately equal material force ".

An important example of such an algebra is a commutative C *- algebra.

One modern example of such an ascending valve is the Yamaha YSL-350C trombone, in which the extra valve tubing is normally engaged to pitch the instrument in Bb, and pressing the thumb lever removes a whole step to pitch the instrument in C. Valves require regular lubrication.

E. C. Segar's 1916 comic strip " Charlie Chaplin's Comedy Capers " is an early example.

There is no consensus on some terms describing carbon nanotubes in scientific literature: both "- wall " and "- walled " are being used in combination with " single ", " double ", " triple " or " multi ", and the letter C is often omitted in the abbreviation ; for example, multi-walled carbon nanotube ( MWNT ).

For example kidney beans are toxic when raw or improperly cooked, due to the presence of phytohaemagglutinin which can be inactivated after cooking for at least ten minutes at 100 ° C.

IUPAC prefers that isotope symbols be written in superscript notation when practical, for example < sup > 12 </ sup > C and < sup > 235 </ sup > U. However, other notations, such as carbon-12 and uranium-235, or C-12 and U-235, are also used.

For example, trace ( but detectable ) amounts of carbon-14 (< sup > 14 </ sup > C ) are continually produced in the atmosphere by cosmic rays impacting nitrogen atoms, and argon-40 (< sup > 40 </ sup > Ar ) is continually produced by the decay of primordially occurring but unstable potassium-40 (< sup > 40 </ sup > K ).

( Some exceptions exist ; for example, deoxyribose, a component of DNA, has the empirical formula C < sub > 5 </ sub > H < sub > 10 </ sub > O < sub > 4 </ sub >.

The aldohexose D-glucose, for example, has the formula ( C · H < sub > 2 </ sub > O ) < sub > 6 </ sub >, of which all but two of its six carbons atoms are stereogenic, making D-glucose one of 2 < sup > 4 </ sup > = 16 possible stereoisomers.

This is achieved by scaling the number of involved molecules ( A, B, C and D in a schematic example below ) by the appropriate integers a, b, c and d.

As an example of a conditional proof in symbolic logic, suppose we want to prove A → C ( if A, then C ) from the first two premises below:

For example, consider the following C ++ function:

In Arthur C. Clarke's short story " Technical Error " there is an example of differing chirality.

For example, ethyl alcohol and water form an azeotrope of 95. 6 % at 78. 1 ° C.

For example, if a closed string splits, its worldsheet will look like a single pipe splitting ( or connected ) to two pipes ( often referred to as a pair of pants — see drawing at right ).

During allopatric ( from the ancient Greek allos, " other " + Greek patrā, " fatherland ") speciation, a population splits into two geographically isolated populations ( for example, by habitat fragmentation due to geographical change such as mountain building ).

This reaction example is the opposite of hydrolysis, which splits a chemical entity into two parts through the action of the polar water molecule, which itself splits into hydroxide and hydrogen ions.

They have assumed, for example, that the Hilbert space of the universe splits naturally into a tensor product structure compatible with the measurement under consideration.

For example, Alice acquires a lot by mortgage then splits up the lot into three lots ( X, Y, and Z ), and sells lot Y to Bob, and then lot Z to Charlie, retaining lot X for herself.

The group CLAMP for example, splits the duties between its members, but does not use additional assistants.

In English, for example, the groups and are consonant clusters in the word splits.

Splits are usually done as floor work, barre work or incorporated into dances ; the ability to do splits is critical to ballet dancers as it allows for proper execution of certain movements, for example, the Grand Jeté, Arabesque Penchée and many other movements.

Furthermore, there have been splits in many of the off-shoot churches ; for example, the church founded by Sherrod C. Johnson ( Church of the Lord Jesus Christ of the Apostolic Faith, also referred to as CLJC ) has splintered and re-emerged as the Holy Temple Church of the Lord Jesus Christ of the Apostolic Faith ; the Apostolic Ministries of America ; and the, all of which are actively evangelizing North America, the Caribbean, Europe, and West Africa.

For example, if p is an odd prime not dividing D, then p splits if and only if D is congruent to a square modulo p. The first two cases are in a certain sense equally likely to occur as p runs through the primes, see Chebotarev density theorem.

For example, the block cipher TEA simply splits the 128-bit key into four 32-bit pieces and uses them repeatedly in successive rounds.

For example, if user Sara is connected to server A, user Bob is connected to server B, and user Joe is connected to C, and C splits, or disconnects, from A, it will appear to Joe as if Sara and Bob both quit ( disconnected from the network ), and it will appear to both Sara and Bob that Joe quit.

Clearly a die could roll too few sixes as easily as too many and we would be just as suspicious, so we should use the two-tailed test which ( for example ) splits the 5 % probability across the two tails.

Also, the level set method makes it very easy to follow shapes that change topology, for example when a shape splits in two, develops holes, or the reverse of these operations.

William Greener, for example, splits British sporting rifles at the turn of the 20th century into four classes:

Placental and marsupial mammals are an example of divergent evolution, an evolutionary concept occurring when a single group of organisms splits into two groups and each group evolves in increasingly different directions.

In accordance with the decomposition of the regular representation into irreducible representations, such a zeta-function splits into a product of Artin L-functions, for each irreducible representation of G. For example, the simplest case is when G is the symmetric group on three letters.