In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

In Ancient Greek, the dative has the functions of the Proto-Indo-European locative and instrumental as well as those of the original dative.

In the wake of Achaemenid expansion shrines were constructed throughout the empire and particularly influenced the role of Mithra, Aredvi Sura Anahita, Verethregna and Tishtrya, all of which, in addition to their original ( proto -) Indo-Iranian functions, now also received Perso-Babylonian functions.

Common modifications include value changes in capacitors or resistors, adding true-bypass so that the effect's circuitry is no longer in the signal path, substituting higher-quality components, replacing the unit's original operational amplifiers ( op-amps ), or adding functions to the device such as allowing additional control of some factor or adding an additional output jack.

Richard Stallman chose Lisp as the extension language for his rewrite of Emacs ( the original used TECO as its extension language ) because of its powerful features, including the ability to treat functions as data.

Good hash functions, in the original sense of the term, are usually required to satisfy certain properties listed below.

The new structure would be located to the east of the original building, and tasked with two functions: offer a large space for public appreciation of various popular collections ; and house office space as well as archives for scholarship and research.

When placed on the external address bus, it replicates the original functions of B and C. Port A has input capture, output compare, pulse accumulator, and other timer functions ; port D has serial I / O, and port E has an analog to digital converter ( ADC ).

QuakeC does not contain any string handling functions or file handling functions, which were simply not needed by the original game.

Historical remark: In its original form by F. Riesz ( 1909 ) the theorem states that every continuous linear functional A over the space C ( 1 ) of continuous functions in the interval can be represented in the form

Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.

A different generalization of Weierstrass ' original theorem is Mergelyan's theorem, which generalizes it to functions defined on certain subsets of the complex plane.

The original services of an inn are now also available at other establishments, such as hotels, lodges, and motels, which focus more on lodging customers than on other services, although they usually also provide meals ; pubs, which are primarily alcohol-serving establishments ; and restaurants and taverns, which serve food and drink.

The following year, Alpine County was created and the redrawing of the county borders placed the inn at the convergence of Alpine, El Dorado, and Amador counties ( the borders were later changed so the inn is no longer in El Dorado County, but the original signpost marking the intersection of the three is still in the building ).

Maplehurst was recently restored to its original condition and is currently known as the Keefer Mansion, a 10 room inn noted for its fine dining.

It was built from a derelict farmhouse and barn ( see early history 1793, West House farm was occupied by an original landowner together with Whitehouse farm which is now converted to private housing in Westmoor ) – this in the style of an old Northumberland inn.

The original Angel was rebuilt in 1819 and became a coaching inn, the first staging post outside the City of London.

Screenshot of the original Avernum, showing a party about to enter an inn.

As Burnard said, the current building dates from 1845, but the original inn on the southern side of the packhorse track was probably built in the middle of the 18th century, certainly well before the turnpike road was created in 1792.

One of Rathcoole's best known pubs is An Poitin Stil, which is built on the site of an original inn house dating back to 1649.

At the centre of the original village, about 200 m from Kneller Hall is the White Hart, an inn dating back at least to the mid-17th Century and possibly much earlier.

The link here is the publican " George Martin " who first of all ran the inn called the " George and Dragon " to the West of the River Greta, he then moved to the original " Morritt's Arms " built on the East bank of the River Greta as a coaching inn by the Morritt family of Rokeby, in approx 1756, and he renamed it " The George " as recorded by Dickens ( maybe having left his " dragon " behind at the present Morritt Arms!

The station was opened by the original London & Croydon Railway ( L & CR ) on 5 June 1839, as Dartmouth Arms ( after the name of the local inn ).

By the late 18th century, the building had reverted to its original use as a coaching inn serving travellers that came from Ballachulish to Loch Lomond via Tyndrum.

Rather, together with a story about a figurehead adorning the Inn's stairwell, said to be based on an 18th-century original from the Pandora, this claim can confidently be refuted and relegated to the realm of creative copy-writing to advertise the inn, which according to cadastral records was called ' The Passage House ' until 1851, following the death of Alexander Luben, tenant and Restronguet Passage boatman from 1823 until his death in 1848.

The Wetherspoons outlet the Gilpin's Bell public house opposite the site of the original inn and the 1950s council housing Gilpin House in Upper Fore Street.

The Bell Inn also claims to be listed in the Domesday Book, but the current building does not date back to this period, and there is evidence that the original inn was situated several hundred metres away.

By Ward's own account, the spell originated during a session in Gygax's original Greyhawk campaign during which the players were stranded in a dungeon ; Ward's character owned a magical item which would have rescued the party, but had left it in an inn before setting out.

: In this visible location, the innkeeper Balthasar Kalkofen built his original inn, popular with boatmen and wagon drivers, in 1697.

Built in 1585 as a tollgate inn on the Finchley boundary, the Spaniards formed the entrance to the Bishop of London's estate-an original boundary stone from 1755 can still be seen in the front garden.

The Green Man was a former coaching inn on the original A3 route from Guildford to London ; a public house had been on the site for more than 400 years.

In 1833 the original inn burned down and was rebuilt, surviving until the lease on the house came up in 1857.

In a real sense they are admittedly conservative, but their conservatism incorporates a traditionalized embodiment of the original `` radicalism '' of 1776.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

In the period since the end of World War 2, -- a period coinciding with merchandising demands for the colorful, the unusual, and the original in signs and displays -- plastics have come on so strong that today they are the acknowledged leaders in the field.

abstracts and other compilations on rare occasions when original papers are not available.

The basic mystery of dreams, which embraces all the others and challenges us from even the most common typical dream, is in the fact that they are original, visual continuities.

But these are dreamed in original action, in some particular continuity which we don't remember having seen in real life.

Now the original absent sitter must decide whether the statements are meaningful to him.

Though Aristotle wrote many elegant treatises and dialogues ( Cicero described his literary style as " a river of gold "), it is thought that the majority of his writings are now lost and only about one-third of the original works have survived.

Conversely, the vowel marks of the Tigrinya abugida and the Amharic abugida ( ironically, the original source of the term " abugida ") have been so completely assimilated into their consonants that the modifications are no longer systematic and have to be learned as a syllabary rather than as a segmental script.

Euclid's original proof adds a third: the two lengths are not prime to one another.

" Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice.

The adaptions are notable for changing the plots and characters of the original books ( e. g., incorporating lesbian affairs, changing killer identities, renaming or removing significant characters, and even using stories from other books in which Miss Marple did not originally feature ).

* 1896 – In Athens, the opening of the first modern Olympic Games is celebrated, 1, 500 years after the original games are banned by Roman Emperor Theodosius I.

The fossils of Ardipithecus have not yet been studied by researchers beyond the original ( 2009 ) group of describers, and the paleobiology and relationships of these creatures are the subject of controversy.

Therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin although they have not received baptism, so still bear original sin.

A set of reverse rounds are applied to transform ciphertext back into the original plaintext using the same encryption key.

The decision-making participants are the Consultative Parties and, in addition to the 12 original signatories, include 16 countries that have demonstrated their interest in Antarctica by carrying out substantial scientific activity there.

Many of these designs are still under patent, and other types are best known by their original trademarked names.

After his death, the king was buried in the church which he had built ; his original tomb has been lost, while his alleged remains are preserved in the shrine where he was reburied after being declared a saint ; his saintliness, however, was never very widely acknowledged outside the bishopric of Liège where he may still be venerated by tradition.

There are also several extant original writings by Alexander.

Unlike his translation of the Pastoral Care, Alfred here deals very freely with his original and though the late Dr. G. Schepss showed that many of the additions to the text are to be traced not to Alfred himself, but to the glosses and commentaries which he used, still there is much in the work which is solely Alfred's and highly characteristic of his style.

The hybrids are quite distinct in that the many shades of pink also have stripes, veining, darkened edges, white centers and light yellow centers also setting them apart from the original light pink.