Inserting a new element to a heap can be done by simply creating a new heap containing only this element and then merging it with the original heap.

* Inserting or deleting an element in the middle of the array ( linear time )

* Inserting or deleting an element at the end of the array ( constant amortized time )

Inserting into these summits are 800 – 1000 m high summits of Phu Sinh ( 965m ), Phu Co Tri ( 949m ), Phu On Boi ( 933m ), Phu Tu ( 956m ), Phu Toan ( 905m ), Phu Phong ( 902m ), and Ma Ma ( 835m ).

Inserting the specific heat equation into the thermal efficiency equation ( Equation 1 ) yields.

Inserting a task then requires walking the ready list until reaching either the end of the list, or a task of lower priority than that of the task being inserted.

Inserting a document using a KSK allows the document to be retrieved and decrypted if and only if the requester knows the human-readable string ; this allows for more convenient ( but less secure ) URIs for users to refer to.

Inserting eukaryotic DNA ( instead of mRNA ) into bacteria would not work because it is fragmented, with introns, and would not transcribe successfully using the bacteria's ribosomes.

Inserting this into the formula for the function f one can determine the minimal distance at which the ellipsoid exists.

Inserting a tube that is too large relative to the diameter of the trachea can cause swelling.

Inserting an etalon into the laser cavity, with well-chosen finesse and free-spectral range, can suppress all cavity modes except for one, thus changing the operation of the laser from multi-mode to single-mode.

Inserting the blade perpendicular to the water amounts to ineffective " lily dipping " or " tea-bagging " wherein the blade moves backwards in the water past the paddler's hips simply because the boat is moving forward.

Inserting new data into existing data structures, updating data in existing data structures, deleting data from existing data structures.

Inserting Pamela Pigg into this list makes six-more than the fingers of one hand, unless Adrian is polydactyl.

Inserting these two equations into the cochain homotopy equation proves the Poincaré lemma.

# The programmer types " i ", to begin Inserting source code.

Inserting a very thin graphite extraction foil strips, or removes, the electrons from the H ⁻ ion while allowing the proton to pass through.

Inserting a section can be done by editing either the section before or after it, merging with the previous section by deleting the heading.

Inserting the key into Megatron's tail reveals a firing missile launcher.

Inserting a blatant piece of backmasking in the break between the title track and hard rocker " Judas ' Kiss ," the band's message was less than subtle.

* Inserting vowels into consonant clusters ( epenthesis ): Likewise depending on the social class, every now and then a speaker may insert a vowel ( near-Schwa ) between two following consonants.

Inserting the phrase “ nunc pro tunc ” or similar arguments on a return or other document submitted to the Service has no legal effect, such as reducing a taxpayer ’ s tax liability, and such phrase is described as frivolous in Rev.

Inserting a code for underline would " propagate " to the next display enhancement, while deleting such a code would also have to be propagated to the next display byte or a cursor jump sequence was issued to jump several bytes.

Inserting the figure's Earth Cyber Planet Key into the tail section causes a pair of twin guns to pop up, changing the noise once more, into an explosive blast.

* Inserting and / or mixing in audio from other files.

* Inserting and removing ranks, such as supervisors, assistant managers or regional managers and national managers, is very easy to do.

Image: Knit3. jpg | Inserting the needle

By comparison, the density of lead is 11, 340 kg / m < sup > 3 </ sup >, and that of the densest element, osmium, is 22, 610 kg / m < sup > 3 </ sup >.

Given a set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

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.

For each m and n let s < sub > m, n </ sub > be the n < sup > th </ sup > element of the m < sup > th </ sup > sequence on the list.

A subset T is totally ordered if for any s, t in T we have s ≤ t or t ≤ s. Such a set T has an upper bound u in P if t ≤ u for all t in T. Note that u is an element of P but need not be an element of T. An element m of P is called a maximal element ( or non-dominated ) if there is no element x in P for which m < x.

The map m is the group operation, the map e ( whose domain is a singleton ) picks out the identity element of the group, and the map inv assigns to every group element its inverse.

For example, an array of 10 integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, … 2036, so that the element with index i has the address 2000 + 4 × i.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

Two results which follow from the axiom are that " no set is an element of itself ," and that " there is no infinite sequence ( a < sub > n </ sub >) such that a < sub > i + 1 </ sub > is an element of a < sub > i </ sub > for all i. "

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.

The close relationship of alternative algebras and composition algebras was given by Guy Roos in 2008: He shows ( page 162 ) the relation for an algebra A with unit element e and an involutive anti-automorphism such that a + a * and aa * are on the line spanned by e for all a in A.

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

The analogy in the case of rotating bucket is that the element of water surface will " slide " up or down the surface unless the normal to the surface aligns with the vector resultant formed by the vector addition F < sub > g </ sub > + F < sub > Cfgl </ sub >.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

: There exists an element of F, called the additive identity element and denoted by 0, such that for all a in F, a + 0 = a.

: For every a in F, there exists an element − a in F, such that a + (− a ) = 0.

Less likely is the commonly proposed derivation from Welsh arth " bear " + ( g ) wr " man " ( earlier * Arto-uiros in Brittonic ); there are phonological difficulties with this theory — notably that a Brittonic compound name * Arto-uiros should produce Old Welsh * Artgur and Middle / Modern Welsh * Arthwr and not Arthur ( in Welsh poetry the name is always spelled Arthur and is exclusively rhymed with words ending in-ur-never words ending in-wr-which confirms that the second element cannot be wr " man ").

In that case the invalid location Λ can be any index before the first element ( such as 0 or − 1, respectively ) or after the last one ( n + 1 or n, respectively ).

# If A is Lebesgue measurable and x is an element of R < sup > n </ sup >, then the translation of A by x, defined by A + x =

Furthermore, rather than giving shareholders the slight upper hand as happened in Germany, a debated ' independent ' element would be added to the board, reaching the formula 2x + y.

If x and y are elements of a PID without common divisors, then every element of the PID can be written in the form ax + by.

In each iteration, the PRGA increments i, looks up the ith element of S, S, and adds that to j, exchanges the values of S and S, and then uses the sum S + S ( modulo 256 ) as an index to fetch a third element of S, ( the keystream value K below ) which is XORed with the next byte of the message to produce the next byte of either ciphertext or plaintext.

It is the fourteenth and penultimate element in the lanthanide series, or last element in the f-block, which is the basis of the relative stability of the + 2 oxidation state.