In differential cryptanalysis, an attacker exploits how differences in the input to a cipher ( the plaintext ) can affect the resultant difference at the output ( the ciphertext ).

The resultant force, or resultant force-torque, fully replaces the effects of all forces on the motion of the rigid body they act upon.

Eysenck, along with another contemporary in trait psychology named J. P. Guilford ( 1959 ), believed that the resultant trait factors obtained from factor analysis should be statistically independent of one another — that is, the factors should be arranged ( rotated ) so that they are uncorrelated or orthogonal ( at right angles ) to one another.

As the gas is compressed the work done on the gas is P < sub > 1 </ sub > V < sub > 1 </ sub > and the resultant work done by the gas during this expansion is P < sub > 2 </ sub > V < sub > 2 </ sub >.

Another realization of intersection multiplicity comes from the resultant of the two polynomials P and Q.

In coordinates where p is ( 0, 0 ), the curves have no other intersections with y = 0, and the degree of P with respect to x is equal to the total degree of P, I < sub > p </ sub >( P, Q ) can be defined as the highest power of y that divides the resultant of P and Q ( with P and Q seen as polynomials over K ).

For univariate monic polynomials < var > P </ var > and < var > Q </ var > over a field < var > k </ var >, the resultant res (< var > P </ var >,< var > Q </ var >) is a polynomial function of their coefficients.

* Since the resultant is a polynomial with integer coefficients in term of the coefficients of < var > P </ var > and < var > Q </ var >, it follows that

** If < var > h </ var > is a homomorphism of the ring of the coefficients into another commutative ring, which preserve the degrees of < var > P </ var > and < var > Q </ var >, then the resultant of the image by < var > h </ var > of < var > P </ var > and < var > Q </ var > is the image by < var > h </ var > of the resultant of < var > P </ var > and < var > Q </ var >.

Since the resultant depends polynomially ( with integer coefficients ) on the roots of < var > P </ var > and < var > Q </ var >, and it is invariant with respect to permutations of each set of roots, it must be possible to calculate it using an ( integer ) polynomial formula on the coefficients of < var > P </ var > and < var > Q </ var >.

More concretely, the resultant is the determinant of the Sylvester matrix ( and of the Bézout matrix ) associated to < var > P </ var > and < var > Q </ var >.

By the symmetry of the defining formula, this shows that the resultant is a polynomial expression of the coefficients of both < var > P </ var > and < var > Q </ var >.

The sum, difference, product and quotient of two algebraic numbers is again algebraic ( this fact can be demonstrated using the resultant ), and the algebraic numbers therefore form a field, sometimes denoted by A ( which may also denote the adele ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

A popular application was use in home theater PC systems due to high performance and low heat output resultant from low V < sub > core </ sub > settings.

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 resultant common structural element is the < sup > 6 -</ sup > group. The most common disilicates by far are members of the epidote group.

The resultant nitric acid was then used as a source of nitrate ( NO < sub > 3 </ sub >< sup >-</ sup >) in the reaction

At higher temperatures ( 10 K < T < Θ ), the conservation of energy and quasimomentum, where q < sub > 1 </ sub > is wave vector of the incident phonon and q < sub > 2 </ sub >, q < sub > 3 </ sub > are wave vectors of the resultant phonons, may also involve a reciprocal lattice vector G complicating the energy transport process.

For example, if x < sup > 2 </ sup > − x − 1 = 0, y < sup > 3 </ sup > − y − 1 = 0 and z = xy, then eliminating x and y from z − xy and the polynomials satisfied by x and y using the resultant gives z < sup > 6 </ sup > − 3z < sup > 4 </ sup > − 4z < sup > 3 </ sup > + z < sup > 2 </ sup > + z − 1, which is irreducible, and is the monic polynomial satisfied by the product.

( To see that the xy is a root of the x-resultant of z − xy and x < sup > 2 </ sup > − x − 1, one might use the fact that the resultant is contained in the ideal generated by its two input polynomials.

However, when forming a bulk metal, Li atoms come to a resonance structure by taking 1 electron from its neighbouring Li atom and the resultant electronic configuration becomes 1s < sup > 2 </ sup > 2s < sup > 1 </ sup > 2p < sup > 1 </ sup > ( e < sup >-</ sup >).

The right sub tree is made the right child of the resultant left sub tree ( for METHOD 1 ).

The resultant length of the flood-protected river comprises 2, 940 km ( out of 4, 220 km of all Hungarian protected rivers ) which forms one of the largest flood protection systems in Europe ; larger than the Netherlands ' 1, 500 km, the Po River's 1, 400 km, or the Loire Valley's 480 km.

A resultant collection of less than 1. 5 mL is considered a positive result.

Thus, Lester Grabbe points to a number of parallels between the Azazel narrative in 1 Enoch and the wording of Leviticus 16, including “ the similarity of the names Asael and Azazel ; the punishment in the desert ; the placing of sin on Asael / Azazel ; the resultant healing of the land .” Daniel Stökl also observes that “ the punishment of the demon resembles the treatment of the goat in aspects of geography, action, time and purpose .” Thus, the place of Asael ’ s punishment designated in 1 Enoch as Dudael is reminiscent of the rabbinic terminology used for the designation of the ravine of the scapegoat in later rabbinic interpretations of the Yom Kippur ritual.

The resultant paradox is famously articulated by Moshe Chaim Luzzatto ( Derekh Hashem I: 1: 5 ), describing the dichotomy as arising out of our inability to comprehend the idea of absolute unity:

The resultant bite forces calculated for Stegosaurus were 140. 1 N ( Newton ), 183. 7 N, and 275 N ( for anterior, middle and posterior teeth, respectively ), which means that its bite force was less than half that of a Labrador retriever.

Banbury has one of the UK's lowest unemployment rates, dipping as low as 1 % in 2005, although it has since risen due to the recession which began in 2008. with a resultant high demand for labour.

If the same signal is sent to both inputs of a ring modulator, the resultant harmonic spectrum is the original frequency domain doubled ( if f < sub > 1 </ sub >

Dunlop assigned his patent to William Harvey Du Cros, in return for 1, 500 shares in the resultant company and in the end did not make any great fortune by his invention.

This procedure can be repeated to add F < sub > 3 </ sub > to the resultant F < sub > 1 </ sub > + F < sub > 2 </ sub >, and so forth.

The resultant force and torque on a rigid body obtained from a system of forces F < sub > i </ sub > i = 1 ,..., n, is simply the sum of the individual wrenches W < sub > i </ sub >, that is

The resultant images show Geographos to be the most elongated object in the solar system ; it measures 5. 1 × 1. 8 km.

Calcium carbonate is used as the source of CO < sub > 2 </ sub > and the resultant calcium oxide is used to recover the ammonia from the ammonium chloride.

After eliminating the meaning-laden syllables, Ebbinghaus ended up with 2, 300 resultant syllables.

The resultant theory copes with experiment better than classical mechanics, e. g. in the Michelson – Morley experiment that supports postulate 2, but also has many surprising consequences.

The LMDC was funded through the disbursement of Community Development Block Grants-amounting to $ 2. 783 billion — approved by the federal government in the aftermath of the 9 / 11 attacks and resultant destruction of much of lower Manhattan's economic and structural base.

However, if the above estimates for its diameter are coupled with Pluto's density of 2. 0 g / cm < sup > 3 </ sup >, the resultant estimated mass range is about 1 kg.

The resultant images are lacking in detail, but indicate a rough sphere with some kind of concave depression 1 – 2 km in diameter.

A common formation of motorcycles is five in front of the hearse: two motorcycles in tandem (# 1 and # 2, left and right, from the perspective of the hearse ), two motorcycles directly in front of the hearse, in tandem (# 5 and # 6, left and right, as noted ), and a solo rider in the resultant # 4 position, and the missing motorcycle ( in the # 3 position ) representing the fallen.

The resultant album, Louie and Clark Expedition 2 was released in January 2008.

The storm weakened to a Category 3 hurricane by 2 pm, which was initially attributed to inner core processes, but increasing westerly winds aloft, and the resultant vertical wind shear, was later determined to be the cause.

In only his second appearance for Southampton, away to Middlesbrough on 11 September 1999, he was sent off for handling the ball in the goalmouth in the 77th minute, with Paul Gascoigne scoring the resultant penalty as Middlesbrough went on to win 3 – 2.

No. 2 Recruit Depot came into being in January 1940, and the resultant expansion of temporary accommodation resulted in a " tin city " on the fringes of the base.

The resultant increase in water temperature is regulated to less than 1 ° C in summer months, and to 2 ° C the rest of the year.

Air, pure oxygen, or a number of other oxidizers can then oxidise the resultant CuCl back to CuCl < sub > 2 </ sub >, allowing the cycle to repeat.

If the introduced surface had an ionic or polar nature, there would be water molecules standing upright on 1 ( along the axis of an orbital for ionic bond ) or 2 ( along a resultant polarity axis ) of the 4 sp3 orbitals.

He continued his impressive goal scoring record against St. Mirren in the Scottish Cup, scoring in the quarter-finals in a 2 – 2 draw at Tynecastle, as well as in a 2 – 0 victory at St. Mirren Park in the resultant replay.