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 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 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 single-variable quadratic polynomial may be written as

Any quadratic polynomial with two variables may be written as

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 organism that falters or misperceives the signals or weakens is done.

Any information we have here in Taiwan is at your disposal ''.

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 alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

Any action is understood to create " seeds " in the mind that sprout into the appropriate results ( Pāli vipaka ) when they meet the right conditions.

** Any union of countably many countable sets is itself countable.

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 quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.

" 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 person who is seen as a threat to civil aviation is banned from flying.

* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

* 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 form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.

* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.

Any mutations for the preference opposite to the given characteristic, though tending to promote survival against ecological selection, nevertheless tend not to survive in the gene pool because male offspring that result from matings based on the preference are less sexually attractive to the majority of the females in the population, and thus infrequently chosen as mates.

Any characteristic of a Class III game makes it a Class III game.

Limiting: Any process by which a specified characteristic ( usually amplitude ) of the output of a device is prevented from exceeding a predetermined value.

Note that for orientable compact surfaces without boundary, the Euler characteristic equals, where is the genus of the surface: Any orientable compact surface without boundary is topologically equivalent to a sphere with some handles attached, and counts the number of handles.

Any convex polyhedron's surface has Euler characteristic

Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where ( in units where c = 1 ) E is equal to H at any point in space.

*" Any form of cultural knowledge or social activity characteristic of a social group and / or cultural group that can be recognized by other groups such as Western anthropologists, but not necessarily by the group of origin, as mathematical knowledge or mathematical activity ".

Any definite conclusion to Cynewulf being either Northumbrian or Mercian has been hard to come by, but linguistic evidence suggests that the medial e in the signed Cynewulf would have, during the broad window period of Cynewulf ’ s existence, been characteristic of a Mercian dialect.

Any language, in Bakhtin's view, stratifies into many voices: " social dialects, characteristic group behavior, professional jargons, generic languages, languages of generations and age groups, tendentious languages, languages of the authorities, of various circles and of passing fashions.

:; Cavity back: Any iron whose design characteristic is such that the weight is distributed primarily around the outer edges of the club-head in order to maximize forgiveness on off-center hits.

Any semiconductor diode has an exponential voltage / current characteristic that gives an effective " knee " voltage sometimes used as a voltage reference.

Any protons ejected from the target itself were identified by their characteristic energies.