Axiom 2: Any property entailed by — i. e., strictly implied by — a positive property is positive

Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.

Any positive divisor of is a product of prime divisors of raised to some power.

Any invertible matrix can be uniquely represented according to the polar decomposition as the product of a unitary matrix and a hermitian matrix with positive eigenvalues.

Any gas discharge lamp has a positive ( anode ) and a negative electrode.

for some p between 1 and n. Any two such expressions of q ( at the same point m of M ) will have the same number p of positive signs.

Any system where there is positive feedback together with a gain greater than one will result in a runaway situation.

* Any positive multiple of the repunit R < sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b.

Any fluctuations in food supply ( either positive, for example, due to technology improvements, or negative, due to droughts and pest invasions ) tend to translate directly into population fluctuations.

The theory, Any press is good press, has been coined to describe situations where bad behaviour by people involved with an organization or brand has actually resulted in positive results, due to the fame and press coverage accrued by such events.

Any positive immunological effect is thought to be the result of melatonin acting on high affinity receptors ( MT1 and MT2 ) expressed in immunocompetent cells.

Any positive test result should be confirmed by a lab using the western blot.

Any hope towards positive relations with Russia ended in the late 18th and early 19th centuries when tensions with the Cossacks escalated and Russia began trying to conquer the Caucasus, starting with Georgia.

On 8 July 2011 on BBC Radio 4's Any Questions, at the height of the furore surrounding the alleged illegal and corrupt activities of News of the World journalists, Parris eulogised the newspaper and gave an enthusiastic appreciation of what he considered the virtues and positive achievements of Rupert Murdoch.

* Any open manifold admits a ( non-complete ) Riemannian metric of positive ( or negative ) curvature.

Any positive rational number can be written as the sum of unit fractions, in multiple ways.

Any positive integer n has 2 < sup > n − 1 </ sup > distinct compositions.

Any element y ∈ Y := Ran ( S − I ) has a distance larger than or equal to 1 from u ( otherwise y < sub > i </ sub > = x < sub > i + 1 </ sub >-x < sub > i </ sub > would be positive and bounded away from zero, whence x < sub > i </ sub > could not be bounded ).

Any skew semistandard tableau of shape / with positive integer entries gives rise to a sequence of partitions ( or Young diagrams ), by starting with, and taking for the partition places further in the sequence the one whose diagram is obtained from that of by adding all the boxes that contain a value ≤ in ; this partition eventually becomes equal to.

Any voltage is a difference in electric potential between two points-for example, the separation of positive and negative electric charges on opposite sides of a resistive barrier.

Any open flame or electric sparks, including lit tobacco products like cigarettes, cigars or pipes, in the area also present a danger of ignition of any hydrogen gas emanating from a battery ( this is the reason, when recharging the battery in place in the vehicle or jump starting, that the negative cable of the recharger or attached to the other vehicle's jumping battery negative post is always attached away from the battery to ground on the engine or frame, and is always attached to complete the circuit only after the positive cable has been attached to the battery's positive terminal ( and is removed in the reverse order, i. e., negative cable first from the frame or engine, breaking the circuit, then positive cable from the battery )-in this fashion, any sparks which may occur will occur at the more distant location of the negative cable attachment point, away from the battery and potentially explosive gases, and no sparks will occur, as the circuit is no longer complete, when the positive cable is attached or detached from the battery ).

* Any number constructible out of the integers with roots, addition, and multiplication is therefore an algebraic integer ; but not all algebraic integers are so constructible: in a naïve sense, most roots of irreducible quintics are not.

Any integer power of an nth root of unity is also an nth root of unity:

Any non integer flash setting will make the mark appear to move forward or backward, e. g. a slight increase of the flash frequency will make the point appear to move backward.

Any chain represents an integer, according to the four rules below.

Any eigenvalue of has ordinary eigenvectors associated to it, for if is the smallest integer such that for a generalized eigenvector, then is an ordinary eigenvector.

Any integer has finitely many distinct compositions.

Any right-angled triangle whose sidelengths are a Pythagorean triple is a Heronian triangle, as the side lengths of such a triangle are integers, and its area is also an integer, being half of the product of the two shorter sides of the triangle, one of which must be even.

Any integer can be written as a fraction with the number one as denominator.

Any solar calendar must use intercalation ( leap years ) to make up for the fact that a year is not equivalent to an integer number of days.

* In mathematics, it is often important to find factors of an integer number N. Any number N has four obvious factors: ± 1 and ± N.

Any other case of this type of pentation produces an undefined result, since integer tetration does not take on the value − 1.

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.