Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic ( initial, linear ) portion of the stress-strain curve:

This follows from the previous result, using the fact that the Picard group of a curve is the points of its Jacobian variety, an abelian variety of dimension g, and if n is coprime to the characteristic then the points of order dividing n in an abelian variety of dimension g over an algebraically closed field form a group isomorphic to ( Z / nZ )< sup > 2g </ sup >.

Suppose that E is a modular elliptic curve, then we can perform a level descent modulo primes ℓ dividing one of the exponents δ < sub > p </ sub > of a prime dividing the discriminant.

Suppose that the Fermat equation with exponent &# 8467 ; ≥ 3 had a solution in non-zero integers a, b, c. Let us form the corresponding Frey curve E. It is an elliptic curve and one can show that its discriminant Δ is equal to 16 ( abc )< sup > 2 &# 8467 ;</ sup > and its conductor N is the radical of abc, i. e. the product of all distinct primes dividing abc.

The effect of temperature can be removed from THEMIS infrared data by dividing the image by a black body curve.

The Paraguay makes a long, gentle curve to the south-southeast before resuming a more south-southwest course, dividing the country of Paraguay into two distinct halves: the Gran Chaco region to the west, a largely uninhabited semi-arid region ; and the eastern forested departments of the country, accounting for some 98 % of the country's inhabitants.

In mathematics, the Weil pairing is a pairing ( bilinear form, though with multiplicative notation ) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity.

Let E be an elliptic curve over Q of conductor N. Then, E has good reduction at all primes p not dividing N, it has multiplicative reduction at the primes p that exactly divide N ( i. e. such that p divides N, but p < sup > 2 </ sup > does not ; this is written p || N ), and it has additive reduction elsewhere ( i. e. at the primes where p < sup > 2 </ sup > divides N ).

Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.

The number of UK units of alcohol in a drink can be determined by multiplying < var > the volume of the drink ( in milliliters )</ var > by its < var > percentage ABV </ var >, and dividing by 1000.

* The Ham sandwich theorem: For any compact sets A < sub > 1 </ sub >,..., A < sub > n </ sub > in ℝ < sup > n </ sup > we can always find a hyperplane dividing each of them into two subsets of equal measure.

During interphase ( the period of the cell cycle where the cell is not dividing ), two types of chromatin can be distinguished:

Medications that kill rapidly dividing cells or blood cells are likely to reduce the number of platelets in the blood, which can result in bruises and bleeding.

This operation can be thought of ( very informally ) as the act of dividing the input set by the equivalence relation, hence both the name " quotient ", and the notation, which are both reminiscent of division.

One way in which the quotient set resembles division is that if is finite and the equivalence classes are all equinumerous, then the number of equivalence classes in can be calculated by dividing the number of elements in by the number of elements in each equivalence class.

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

For example,, by dividing both terms by can be written as

We can check this answer by dividing each of our original numbers by 51 and verify that indeed:

From the radian frequency, the natural frequency, f < sub > n </ sub >, can be found by simply dividing ω < sub > n </ sub > by 2π.

For the sake of simplicity, we might assume that the weights are normalized so that they sum up to 1 ( which can be easily done by dividing each weight by their sum ), thus allowing some terms in the above formulae to be omitted:

Glucose concentrations expressed as mg / dL can be converted to mmol / L by dividing by 18. 0 g / dmol ( the molar mass of glucose ).

This can be done in a number of ways, of which the simplest is impalement: dividing the field per pale and putting one whole coat in each half.

A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor.

The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain: any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor.

The normal form can be derived from the general form by dividing all of the coefficients by

The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them.

Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial.

Electricity permits control by dividing the layout into isolated blocks, where trains can be slowed or stopped by lowering or cutting power to a block.

Mergers and acquisitions ( abbreviated M & A ) is an aspect of corporate strategy, corporate finance and management dealing with the buying, selling, dividing and combining of different companies and similar entities that can help an enterprise grow rapidly in its sector or location of origin, or a new field or new location, without creating a subsidiary, other child entity or using a joint venture.

A radar's maximum range can be determined by dividing the listening time ( pulse repetition time minus pulsewidth ) by a radar mile.

By successively dividing out factors x − a, one sees that any polynomial with complex coefficients can be written as a constant ( its leading coefficient ) times a product of such polynomial factors of degree 1 ; as a consequence the number of ( complex ) roots counted with their multiplicities is exactly equal to the degree of the polynomial.

The number of outs can be converted to the probability of making the hand on the next card by dividing the number of outs by the number of unseen cards.

It can be verified by dividing the polygon into triangles, but it can also be seen as a special case of Green's theorem.

However, in this case as elsewhere it was necessary to arrive at a single standard to be applied to all situations, representing an averaging of conditions, and thus to fix particular points in time which would be considered the dividing points between daytime and nighttime conditions.

This would be reduced by multiplying 8 times 6 and then dividing the product by 12.

The plan calls for dividing the project into 16 sectors which would be barred to vehicular traffic.

They may be propagated from offsets or by dividing the rootstock in early spring or autumn.

Apart from the lowlands and the Atlas mountain range, the continent may be divided into two regions of higher and lower plateaus, the dividing line ( somewhat concave to the north-west ) running from the middle of the Red Sea to about 6 deg.

After the November 2000 G8 protest in Montreal, at which many protesters were beaten, trampled, and arrested in what was intended to be a festive protest, the tactic of dividing protests into " green " ( permitted ), " yellow " ( not officially permitted but with little confrontation and low risk of arrest ), and " red " ( involving direct confrontation ) zones was introduced.

Now the remainder of dividing either a or b by d is also of the form ax + by since it is obtained by subtracting a multiple of from a or b, and on the other hand it has to be strictly smaller in absolute value than d. This leaves 0 as only possibility for such a remainder, so d divides a and b exactly.

The process could then be repeated by dividing the resulting smaller interval into smaller and smaller parts until it closes down on the desired limit point.

While at the basic levels, meditation is geared toward relaxation, the practice of advanced meditators may be aimed toward the purpose of dividing one from their awareness of " self ," to a certain degree, and for a certain time.

An " ink spot " clear and hold strategy must be used by the counter-insurgent regime, dividing the conflict area into sectors, and assigning priorities between them.

However, a single computer network may be converted into an internetwork by dividing the network into segments and logically dividing the segment traffic with routers.