A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position ( 3 ) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another, and also since ordered `` up '' and `` down '' implies a larger unit cell, for which no evidence exists.

The assumption of unit-treatment addivity implies that, for every treatment, the th treatment have exactly the same effect on every experiment unit.

For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

He shows how a satisfying argument for the validity of experience can be based neither on demonstration ( since " it implies no contradiction that the course of nature may change ") nor experience ( since that would be a circular argument ).

Scholars have often believed that Ammianus ' work was intended for public recitation for two reasons: the overwhelming presence of accentual clausulae, which implies that it was intended to be read aloud ; and epistle 1063 of Libanius to a Marcellinus of Rome which refers to public recitations.

As ought implies can, Kant argued, it must be possible for the summum bonum to be achieved.

Those who hold for the importance of episcopal apostolic succession appeal to the New Testament, which, they say, implies a personal apostolic succession ( from Paul to Timothy and Titus, for example ).

He implies that what he did was in order to provide for his sick wife, who later died.

" Love and Theft is, as the title implies, a kind of homage ," writes Kot, " never more so than on ' High Water ( for Charley Patton ),' in which Dylan draws a sweeping portrait of the South's racial history, with the unsung blues singer as a symbol of the region's cultural richness and ingrained social cruelties.

In byte-oriented systems ( i. e. most modern computers ), the term uncompressed BCD usually implies a full byte for each digit ( often including a sign ), whereas packed BCD typically encodes two decimal digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9.

The fact that Bede never mentioned a special title for the kings in his list implies that he was unaware of one.

In the narrative, just prior to this test, when Joseph had first met all of his brothers ( but not identified himself to them ), he had held a feast for them ; the narrative heavily implies that Benjamin was Joseph's favorite brother, since he is overcome with tears when he first meets Benjamin in particular, and he gives Benjamin five times as much food as he apportions to the others.

A low interest rate implies that firms can loan money to invest in their capital stock and pay less interest for it.

As the name implies, comic strips can be humorous ( for example, " gag-a-day " strips such as Blondie, Bringing Up Father, Marmaduke and Pearls Before Swine ).

* monomorphism ( or monic ) if implies for all morphisms.

* epimorphism ( or epic ) if implies for all morphisms.

As that history implies, CCL was written for the Macintosh, but Clozure CL now runs on Mac OS X, FreeBSD, Linux, Solaris and Windows.

The chain rule for total derivatives implies a chain rule for partial derivatives.

This implies that for each natural number n, the set of sequences f in Cantor space such that f ( n )

Regarding his attitude towards the Holy See, although with Celtic warmth and flow of words he could defend mere custom, there is nothing in his strongest expressions which implies that he for a moment doubted Rome's supreme authority.

The results for higher moments follow from Hölder's inequality, which implies that higher moments ( or halves of moments ) diverge if lower ones do.

For instance, together with the spectral radius formula, it implies that the C *- norm is uniquely determined by the algebraic structure:

For instance, The Visitation implies the importance of collaboration of black communities by depicting intimacy between two black women who are holding hands together.

The instance method should return a object containing all the information necessary to reconstitute objects of this class and all referenced objects up to a maximum depth given as an integer parameter ( a value of-1 implies that depth checking should be disabled ).

The formulation "... that willing suspension of disbelief for the moment which constitutes poetic faith ," of necessity implies that there are different sorts of suspension of disbelief and specifies that poetic faith is one instance of a larger class.

For instance, Bell's theorem implies that quantum mechanics cannot satisfy both local realism and counterfactual definiteness.

Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).

One vase, for instance, depicts him as sinking down into the earth, upright, and buried at the waist ; this legend is described in the Metamorphoses as well, and implies that Caeneus is falling directly into Tartarus.

which implies, for instance,

The name " Hitmen ," which implies a hired criminal, was one of the icons of the XFL's short life and the butt of many jokes about the league ( quips of teams such as the fictional " Kansas City Shoplifters " coined by Saturday Night Live, for instance ).

* The previous property implies for instance that R < sup > ω </ sup > is not σ-compact: if it were σ-compact, it would necessarily be locally compact since R < sup > ω </ sup > is a topological group that is also a Baire space.

The internal consistency of Titor's story has been questioned: for instance, in some posts he claims that money is widely used and people still have credit cards, despite his statement that centralized banking no longer exists ( this is either an inconsistency or implies the rise of private currencies ).

The term implies a container meant for portability rather than just storage, for instance with hinged lids, clasps or locks, reinforced corners, and handles.

Taking these as a system of linear equations, or by factoring, one can solve for α and β over Q ( γ ) ( one gets, for instance, α =), which implies that this choice of γ is indeed a primitive element in this example.

Together this implies that a class in Smalltalk is an object and that therefore a class needs to be an instance of a class ( called metaclass ).

Zuckermann proposes that " revival linguistics changes the field of historical linguistics by, for instance, weakening the family tree model, which implies that a language has only one parent.

* The Hadwiger conjecture in combinatorial geometry concerns the minimum number of smaller copies of a convex body needed to cover the body, or equivalently the minimum number of light sources needed to illuminate the surface of the body ; for instance, in three dimensions, it is known that any convex body can be illuminated by 16 light sources, but Hadwiger's conjecture implies that only eight light sources are always sufficient.

For instance, if God is Pure Actuality, that is, free from all static potency, it follows that, since change implies a transition from an antecedent potential condition to a subsequent condition in which the potentiality is realized, God is immutable.

This implies for instance the generation of the quadratic differentials on such curves by the differentials of the first kind ; and this has consequences for the local Torelli theorem.

For instance, the word hotel bears the same meaning as in English ( i. e. a normal tourist hotel ), whereas telo implies that the establishment is actually a love hotel.

Many ( St. Thomas, for instance ) have also thought that aseity implies divine simplicity: that God has no parts of any kind ( whether spatial, temporal, or abstract ), since complexes depend on their individual parts, with none of which they are identical.

This implies, for instance, that they should be able to have an attorney to defend them, and that this attorney should have access to the prosecution files.

Becker made contributions to modal logic ( the logic of necessity and possibility ) and Becker ’ s postulate, the claim that modal status is necessary ( for instance that the possibility of P implies the necessity of the possibility of P, and also the iteration of necessity ) is named for him.

For instance, in first-order abstract syntax ( FOAS ) trees, as commonly used in compilers, the tree structure implies the subexpression relation, meaning that no parentheses are required to disambiguate programs ( as they are in the concrete syntax ).

The procedure is based on Herbrand's theorem, which implies that an unsatisfiable formula has an unsatisfiable ground instance, and on the fact that a formula is valid if and only if its negation is unsatisfiable.