Any quadratic polynomial over the complex numbers ( polynomials of the form where,, and ∈ ) can be factored into an expression with the form using the quadratic formula.

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 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 abilities I may have were achieved in their present shape from experience in sharing in the growth and control of my business, coupled with raising my family.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any example of grand or exquisite diction may have been created by the poet who compiled numerous lays into the two works we possess or may be due to one of his completely unknown fellow-craftsmen.

Any flat-bed press capable of pressing a specimen 22 inches square may be used as an alternative.

Any place called Altenberg may have given rise to Altenberg as a family name, such as:

Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.

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 number of players may be replaced by substitutes during the course of the game.

Any of these may be sources of essential amino acids.

Any of these reactions may be used in LPCVD, but the silane reaction is also done in APCVD.

Any player may block another player's passage, so long as he does not hold or trip the player he intends to block.

Any large, smoothbore, muzzle-loading gun — used before the advent of breech-loading, rifled guns — may be referred to as a cannon, though once standardized names were assigned to different sized cannons, the term specifically referred to a gun designed to fire a shot, as opposed to a demi-cannon-, culverin-, or demi-culverin-.

Any string of characters may or may not be a well-formed name for a file or a link depending upon the context of application.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any suggestion I may have made to you will be without force when I say the word ' cancelled.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

* Any scalar or other field may have a dipole moment.

Any elected or appointed board, committee, town officer or ten voters, may place an article on the warrant.

Any form of energy may be transformed into another form.

Any consistent set of units may be used, although SI units are preferred.

Any voluntary muscle in the body may be affected, although the tremor is most commonly seen in the hands and arms and slightly less commonly in the neck ( causing the patient's head to shake ), tongue, and legs.

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

Any minister and the cabinet as a whole however must have continuing trust of the parliament and may be voted out, resign or be replaced.