If the initial value of a polynomial ( and of its finite differences ) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences.

* A space X is completely regular if and only if it has the initial topology induced by C ( X ) or C *( X ).

Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

An initial morphism from X to U is an initial object in the category of morphisms from X to U. In other words, it consists of a pair ( A, φ ) where A is an object of D and φ: X → U ( A ) is a morphism in C, such that the following initial property is satisfied:

An initial morphism from X to U

Given a functor U and an object X as above, there may or may not exist an initial morphism from X to U. If, however, an initial morphism ( A, φ ) does exist then it is essentially unique.

* ( A, φ ) is an initial morphism from X to U

* ( A, φ ) is an initial object of the comma category ( X ↓ U )

Suppose ( A < sub > 1 </ sub >, φ < sub > 1 </ sub >) is an initial morphism from X < sub > 1 </ sub > to U and ( A < sub > 2 </ sub >, φ < sub > 2 </ sub >) is an initial morphism from X < sub > 2 </ sub > to U. By the initial property, given any morphism h: X < sub > 1 </ sub > → X < sub > 2 </ sub > there exists a unique morphism g: A < sub > 1 </ sub > → A < sub > 2 </ sub > such that the following diagram commutes:

Their sum is X, the total number of successes, which in this experiment has the value Af.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

On the other hand, Mac OS X has since version 10. 6 shown hard drive size using decimal prefixes ( thus matching the drive makers ' packaging ).

EFI booting has been supported in only Microsoft Windows versions supporting GPT, the Linux kernel 2. 6. 1 and later, and Mac OS X on Intel-based Macs.

In the United States, the Food and Drug Administration has categorized benzodiazepines into either category D or X meaning potential for harm in the unborn has been demonstrated.

it has 2 < sup > n </ sup > distinct terms corresponding to all the subsets of S, each subset giving the product of the corresponding variables X < sub > s </ sub >.

A result of this has been an increase in the maximum speed on the railway line on the Pan-European Corridor X, from the Slovenian border via Zagreb, Novska, Vinkovci to the Serbian border.

Formally, a topological space X is called compact if each of its open covers has a finite subcover.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

# X has a sub-base such that every cover of the space by members of the sub-base has a finite subcover ( Alexander's sub-base theorem )

# Every net on X has a convergent subnet ( see the article on nets for a proof ).

# Every filter on X has a convergent refinement.

# Every infinite subset of X has a complete accumulation point.

Whereas we say X is an H-set of Z if every cover of X with open sets of Z has a finite subfamily whose Z closure contains X.

That is is the Lie derivative of f in the direction X, and one has df ( X )= X ( f ).

Traditionalist Roman Catholic groups, congregations and clergymen, however, continue to support missionizing Jews according to traditional patterns, sometimes with success ( e. g., the Society of St. Pius X which has notable Jewish converts among its faithful, many of whom have become traditionalist priests ).

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

AFP is still in use in Mac OS X, even though most other AppleTalk protocols have been deprecated.

The Catholic Encyclopaedia make the point that the oath and the penalties were so severe that it stopped the efforts of the Gallicanizing party among the English Catholics, who had been ready to offer forms of submission similar to the old oath of Allegiance, which was condemned anew about this time by Pope Innocent X.

Positive feedback loops, such as the simple X activates Y and Y activates X motif, essentially links output signals to their input signals and have been noted to be an important regulatory motif in cellular signal transduction because positive feedback loops can create switches with an all-or-nothing decision.

The work having been begun by Pius X, it was sometimes called the " Pio-Benedictine Code " but more often the 1917 Code.

The founder, having heard that it was probable that Pope Gregory X, then holding a council at Lyon, would suppress all such new orders as had been founded since the Lateran Council, having commanded that such institutions should not be further multiplied, went to Lyon.

While a young researcher working for the Lowell Observatory in Flagstaff, Arizona, Tombaugh was given the job to perform a systematic search for a trans-Neptunian planet ( also called Planet X ), which had been predicted by Percival Lowell and William Pickering.

Many Unix, GNU, BSD and Linux programs and packages have been ported to Cygwin, including the X Window System, K Desktop Environment 3, GNOME, Apache, and TeX.

In the following, we use Earley's dot notation: given a production X → αβ, the notation X → α • β represents a condition in which α has already been parsed and β is expected.

In contrast, the Holy See has not questioned the validity of the consecrations that the late Archbishop Marcel Lefebvre performed in 1988 for the service of the relatively numerous followers of the Traditionalist Catholic Society of St. Pius X that he had founded, and of the bishops who, under pressure from the Chinese Catholic Patriotic Association, " have been ordained without the Pontifical mandate and who have not asked for, or have not yet obtained, the necessary legitimation ", and who consequently, Pope Benedict XVI has declared, " are to be considered illegitimate, but validly ordained ".

In Canto X Circle 6 (" Where the heretics lie ") of Dante's Inferno, Epicurus and his followers are criticized for supporting a materialistic ideal when they are mentioned to have been condemned to the Circle of Heresy.

This portion was printed in 1514, but publication was delayed until 1522 by waiting for the Old Testament portion, and the sanction of Pope Leo X. Erasmus had been working for years on two projects: a collation of Greek texts and a fresh Latin New Testament.

Originally developed on IRIX, Freeciv has been ported to many different operating systems: it is distributed with many Linux distributions, offers installers for Microsoft Windows, and has been known to run on Mac OS X, Solaris, Ultrix, QNX, OS / 2, Cygwin, AmigaOS, RISC OS, Maemo, ZETA, SkyOS and various BSDs.

In fact, Idol had been a member of the punk band Generation X from 1976 – 1981, which was named after Deverson and Hamblett's 1965 sociology book Generation X — a copy of which was owned by Idol's mother.

In American cinema, directors Kevin Smith, Richard Linklater and Todd Solondz have been called Generation X filmmakers.

:* The numbers in the X and Y registers are then loaded into the ALU and the calculation is carried out following instructions from the permanent memory.

In the case of haemophilia, it is sex-linked thus only carried on the X chromosome.

X. 25 can be carried over the B or D channels of a BRI line, and over the B channels of a PRI line.

Thirty-nine local authorities in the UK either imposed an outright ban, or imposed an X ( 18 years ) certificate ( effectively preventing the film from being shown, as the distributors said the film could not be shown unless it was unedited and carried the original AA ( 14 ) certificate ).

" Apollo X " would have replaced the LEM carried on the top of the S-IVB stage with a small space station slightly larger than the CSM's service area, containing supplies and experiments for missions between 15 and 45 days ' duration.

By 2002, while Linux's popularity, and hence the installed base of X, surged, X. Org was all but inactive ; active development was largely carried out by XFree86.

Scaled Composites ' SpaceShipOne was a reusable suborbital spaceplane that carried pilots Mike Melvill and Brian Binnie on consecutive flights in 2004 to win the Ansari X Prize.

At fertilization the gametes fuse to form a cell, usually with 46 chromosomes, and either XX female or XY male, depending on whether the sperm carried an X or a Y chromosome.

NeXTSTEP's user interface was refined and consistent, and introduced the idea of the Dock ( carried through OpenStep and into OS X ) and the Shelf.

Later revisions allowed multiple addresses in addition to X. 121 addresses to be carried on the same DTE-DCE interface: Telex addressing ( F. 69 ), PSTN addressing ( E. 163 ), ISDN addressing ( E. 164 ), Internet Protocol addresses ( IANA ICP ), and local IEEE 802. 2 MAC addresses.

Secretariat's genetic legacy may be linked in part to the likelihood that he carried the " x-factor ", a trait linked to a large heart, carried only on the X chromosome, and thus, a trait Secretariat could only pass on via his daughters.

Scaled Composites SpaceShipOne was a reusable suborbital spaceplane that carried pilots Mike Melvill and Brian Binnie on consecutive flights in 2004 to win the Ansari X Prize.

ArkanoiD emphasized all the communications were carried over X. 25 network and the Internet was not involved.

The following on-going series had issues released during Vertigo's anniversary year and those issues carried the " Vertigo X " branding:

In the meantime, Michael, afraid of a new Latin invasion, proposed to Pope Clement IV to reunite the Greek and the Latin Churches ; and negotiations ensued which were carried on during the reign of five popes, Clement IV, Gregory X, John XXI, Nicolaus III, and Martin IV.

An LLC sublayer was a key component in early packet switching networks such as X. 25 networks with the LAPB data link layer protocol, where flow control and error management were carried out in a node-to-node fashion, meaning that if an error was detected in a frame, the frame was retransmitted from one switch to next instead.

There is also the simultaneous approximation of the walls of the pharynx to the posterior free border of the soft palate, which is carried out by the palatopharyngeus ( pharyngeal plexus — IX, X ) and the upper part of the superior constrictor ( pharyngeal plexus — IX, X ).

He carried a musket on the populist side in the July Revolution of 1830, and was one of the members of the National Guard who followed Charles X to Rambouillet.

Racer X carried on for a short time with guitarist ( and fellow GIT alum ) Chris Arvin and vocalist Oni Logan ( later of George Lynch's Lynch Mob ) when singer Jeff Martin departed to play drums in Jake E. Lee's Badlands, in which he replaced Eric Singer who left to join Alice Cooper.

In classical anatomy, most sensory information from the face is carried by the fifth nerve, but sensation from certain parts of the mouth, certain parts of the ear and certain parts of the meninges is carried by " general somatic afferent " fibers in cranial nerves VII ( the facial nerve ), IX ( the glossopharyngeal nerve ) and X ( the vagus nerve ).