Any problem that had to be solved by random, brute-force search, could now have a quadratic speedup.

Any n × n real symmetric matrix A determines a quadratic form q < sub > A </ sub > in n variables by the formula

Any smooth function of one variable approximates a quadratic function when examined near enough to its minimum point ; and therefore the force — which is the derivative of energy with respect to displacement — will approximate a linear function.

Any prime number p gives rise to an ideal pO < sub > K </ sub > in the ring of integers O < sub > K </ sub > of a quadratic field K.

Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

Any single-variable quadratic polynomial may be written as

Any quadratic polynomial with two variables may be written as

Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S.

Any càdlàg finite variation process X has quadratic variation equal to the sum of the squares of the jumps of X.

Any polynomial may be decomposed into the product of a constant by a product of irreducible polynomials.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any polynomial can be easily expressed as a power series around any center c, albeit one with most coefficients equal to zero.

* Any polynomial ( real or complex ) is an analytic function.

Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of x < sup > 0 </ sup >.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

Any polynomial in D with function coefficients is also a differential operator.

Any monic polynomial is the characteristic polynomial of some matrix.

Any general polynomial of degree n

Any holomorphic modular form for the modular group can be written as a polynomial in and.

Any polynomial, and more generally any rational function p ( x )/ q ( x ) where p and q are polynomials, transforms the Riemann sphere by mapping it to itself.

Any animal could when travelin' fast, be sent heels over head by the simple process of overtakin' the brute, seizin' its tail, and givin' the latter a pull to one side.

" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any commutative ring R is an algebra over itself, or any subring of R.

Any season ticket holder could put themselves forward for election, with a certain number of nominations, and votes were cast by all season ticket holders over the age of 18.

Any and all profits made from book deals or any movies about Lindh's experience will be automatically handed over to the federal government.

Any one-dimensional Lie algebra over a field is abelian, by the antisymmetry of the Lie bracket.

Any list of these would have to include the Night of the Living Houses ( said to be the first comic strip to enter the collection of the Louvre ) wherein Nemo and a friend are chased down a city street by a gang of tenement houses on legs ; the Walking Bed, in which Nemo and Flip ride over the rooftops on the increasingly long limbs of Nemo's bed ( see illustration ); and the Befuddle Hall sequence, wherein Nemo and his friends attempt to find their way out of a funhouse environment of a Beaux-Arts interior turned topsy-turvy.

Any Hohenstaufen in Sicily was bound to have claims over the cities of Lombardy, and as a check to Manfred, Urban IV introduced Charles of Anjou into the equation to place the crown of the Two Sicilies in the hands of a monarch amenable to papal control.

Any component of target velocity perpendicular to the line of sight cannot be determined by using the Doppler effect alone, but it can be determined by tracking the target's azimuth over time.

In July 2006, a book, ' Peace at Any Price: How the World Failed Kosovo ', written by two former senior staffers at UNMIK, exposed a catalogue of errors and incompetence in the institution over its seven year history.

# Any relatively high-bandwidth transmission over a short period.

Any Transport over MPLS-Cisco Systems.

Any large body of water upwind will impact lake-effect precipitation to the lee of a downwind lake by adding moisture or pre-existing lake-effect bands, which can re-intensify over the downwind lake.

Any production over 100 g must be notified to the OPCW and a country can have a stockpile of no more than one tonne of these chemicals.

Any person over the age of majority and of sound mind ( having appropriate mental capacity ) can draft his own will with or without the aid of a lawyer.

Any amount over and above that required to maintain the capital at the beginning of the period is profit.

Any number of transputers could be connected together over even longish links ( tens of metres ) to form a single computing " farm ".

Any member of the priesthood who presides over a congregation can, and often is, known as " pastor " or ( if an elder ), " presiding elder ".

Any two adjacent conductors can be considered a capacitor, although the capacitance will be small unless the conductors are close together for long distances or over a large area.

Any police entry of an individual's home always requires a warrant ( for either search or arrest ), absent exigent circumstances, or the free and voluntary consent of a person with reasonably apparent use of or control over the property.

# Any sequence satisfying the recurrence relation can be written uniquely as a linear combination of solutions constructed in part 1 as λ varies over all distinct roots of p ( t ).