This approach requires that: ( 1 ) each text word be separated into smaller elements to establish a correspondence between the occurrence and dictionary entries, and ( 2 ) the information retrieved from several entries in the dictionary be synthesized into a description of the particular word.

To effect these operations, five elements exist ( 1 ) surface, ( 2 ) air, ( 3 ) mines, ( 4 ) submarine, and ( 5 ) fixed installations.

Another 2 KB of vector ROM contains the descriptions of the main graphical elements ( rocks, saucer, player's ship, explosion pictures, letters, and digits ) in the form of DVG commands.

Also, no finite field F is algebraically closed, because if a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > n </ sub > are the elements of F, then the polynomial ( x − a < sub > 1 </ sub >)( x − a < sub > 2 </ sub >) ··· ( x − a < sub > n </ sub >) + 1

The repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons which occupy a complete set of s, p, d and f atomic orbitals, respectively.

Amethyst is a purple variety of quartz ( SiO < sub > 2 </ sub >) and owes its violet color to irradiation, iron impurities ( in some cases in conjunction with transition element impurities ), and the presence of trace elements, which result in complex crystal lattice substitutions.

The elements of battery are ( 1 ) a volitional act ( 2 ) done for the purpose of causing a harmful or offensive contact with another person or under circumstances that make such contact substantially certain to occur and ( 3 ) which causes such contact.

For some elements, allotropes have different molecular formulae which can persist in different phases – for example, two allotropes of oxygen ( dioxygen, O < sub > 2 </ sub > and ozone, O < sub > 3 </ sub >), can both exist in the solid, liquid and gaseous states.

After the acceptance of Avogadro's hypothesis in 1860 it was understood that elements could exist as polyatomic molecules, and the two allotropes of oxygen were recognized as O < sub > 2 </ sub > and O < sub > 3 </ sub >.

For example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at most log < sub > 2 </ sub > n + 1 time units are needed to return an answer.

Many elements of the lament are borne out in the historical narrative in 2 Kings concerning the fall of Jerusalem: Jerusalem lying in ruins ( Lamentations 2: 2 and 2 Kings 25: 9 ), enemies entering the city ( Lamentations 4: 12 and 2 Kings 24: 11 ), people going into exile ( Lamentations 1: 3 and 2 Kings 24: 14 ) and the sanctuary being plundered ( Lamentations 1: 10 and 2 Kings 24: 13 ).

Therefore, after combining like terms, the coefficient of x < sup > n − 2 </ sup > y < sup > 2 </ sup > will be equal to the number of ways to choose exactly 2 elements from an n-element set.

For example, the set with elements 2, 3, and 5 is equal to the set of all prime numbers less than 6.

The two general trends in the remaining stellar-produced elements are: ( 1 ) an alternation of abundance in elements as they have even or odd atomic numbers, and ( 2 ) a general decrease in abundance, as elements become heavier.

The alkali metals are a group of chemical elements in the periodic table with very similar properties: they are all shiny, soft, silvery, highly reactive metals at standard temperature and pressure and readily lose their outermost electron to form cations with charge + 1.

In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, excluding hydrogen ( H ), which is nominally a group 1 element but not normally considered to be an alkali metal as it rarely exhibits behaviour comparable to that of the alkali metals.

As of 2010, elements with atomic numbers 1 to 118 have been observed.

For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by B − 30c, then the indices of those same elements will be 31 to 35.

The intervening elements react differently at different frequencies of light as they whip in and out of view, causing Alioth to have very strange spectral lines that fluctuate over a period of 5. 1 days.

The average adult has a blood volume of roughly 5 liters ( 1. 3 gal ), composed of plasma and several kinds of cells ( occasionally called corpuscles ); these formed elements of the blood are erythrocytes ( red blood cells, RBCs ), leukocytes ( white blood cells ), and thrombocytes ( platelets ).

The first piece to show clear signs of this new interest is the String Quartet No. 1 in A minor ( 1908 ), which contains folk-like elements.

The lightest of the chemical elements are hydrogen and helium, both created by Big Bang nucleosynthesis during the first 20 minutes of the universe in a ratio of around 3: 1 by mass ( approximately 12: 1 by number of atoms ).

Of the 98 naturally occurring elements, those with atomic numbers 1 through 40 are all considered to be stable.

Of the 80 elements with at least one stable isotope, 26 have only one stable isotope, and the mean number of stable isotopes for the 80 stable elements is 3. 1 stable isotopes per element.

The known elements have atomic numbers from 1 through 118, conventionally presented as Arabic numerals.

then there are elements x and y in R such that ax + by = d. The reason: the ideal Ra + Rb is principal and indeed is equal to Rd.

Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

( The elements a + (− b ) and a · b < sup >− 1 </ sup > are also denoted a − b and a / b, respectively.

Two isomorphic constructions of the field with 4 elements are ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) and Z /( 2Z ), where φ =.

Roughly T < sup > 2 </ sup >+ T + 1 = 0 so that T < sup > 2 </ sup >= T + 1 ( since − 1 = 1 in Z / 2Z ) and hence the elements of ( Z / 2Z )/( T < sup > 2 </ sup >+ T + 1 ) are the polynomials of degree up to 1 with coefficients in Z / 2Z, i. e. the set

Corresponding to the Bezout property we may, in any commutative ring, consider the collection of elements of the form pa + qb, where p and q range over the ring.

Like other group 8 elements, iron exists in a wide range of oxidation states, − 2 to + 6, although + 2 and + 3 are the most common.

The term was introduced by Benjamin Peirce in the context of elements of an algebra that remain invariant when raised to a positive integer power, and literally means "( the quality of having ) the same power ", from idem + potence ( same + power ).

In other words, the least element is increased by the corresponding x whereas the rest of the elements pass from X < sup >( m )</ sup > to X < sup >( m + 1 )</ sup > unchanged.

These elements have 6, 5 and 4 f-electrons in the outer shell and thus favor + 6, + 5 and + 4 oxidation states, respectively, and show different physical and chemical properties.

Rational primes ( i. e. prime elements in Z ) of the form 4k + 3 are Gaussian primes, whereas rational primes of the form 4k + 1 are not.

The color of amethyst has been demonstrated to result from substitution by irradiation of trivalent iron ( Fe < sup > 3 +</ sup >) for silicon in the structure, in the presence of trace elements of large ionic radius, and, to a certain extent, the amethyst color can naturally result from displacement of transition elements even if the iron concentration is low.

In a seminal 1986 study, McMillan and Chavis identify four elements of " sense of community ": 1 ) membership, 2 ) influence, 3 ) integration and fulfillment of needs, and 4 ) shared emotional connection.

One way is simply to list all of its elements ; for example, the set consisting of the integers 3, 4, and 5 may be denoted.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

We list the elements of A effectively, n < sub > 0 </ sub >, n < sub > 1 </ sub >, n < sub > 2 </ sub >, n < sub > 3 </ sub >, ...

Salt-like carbides are composed of highly electropositive elements such as the alkali metals, alkaline earths, and group 3 metals including scandium, yttrium and lanthanum.

Carbides of the actinide elements, which have stoichiometry MC < sub > 2 </ sub > and M < sub > 2 </ sub > C < sub > 3 </ sub >, are also described as salt-like derivatives of C < sub > 2 </ sub >< sup > 2 –</ sup >.

Larger amounts of radioactive material were later isolated from coral debris of the atoll, which were delivered to the U. S. The separation of suspected new elements was carried out in the presence of a citric acid / ammonium buffer solution in a weakly acidic medium ( pH ≈ 3. 5 ), using ion exchange at elevated temperatures ; fewer than 200 atoms of einsteinium were recovered in the end.

Theorem 1. 3: For all elements in a group, there exists a unique such that, namely.

This suggested that there might be an unexpected connection between the distribution of primes 2, 3, 5, 7, 11 ,... and the energy levels in the nuclei of heavy elements such as uranium.

For that group all permutations of the three non-identity elements are automorphisms, so the automorphism group is isomorphic to < var > S </ var >< sub > 3 </ sub > and Dih < sub > 3 </ sub >.