The Singapore dollar is legal tender in Brunei since a Currency Interchangeability Agreement was signed on 1967-06-12.

Despite the emergence of new currencies in Malaysia, Singapore and Brunei, the Interchangeability Agreement which the three countries continued to adhere to as they were originally parts of a currency union meant the Malaysian dollar was also exchangeable at par with the Singapore dollar and Brunei dollar until May 8, 1973, when the Malaysian government pulled out of the agreement.

Interchangeability of parts was finally achieved by combining a number of innovations and improvements in machining operations and machine tools, which were developed primarily for making textile machinery.

Interchangeability of firearms parts at the U. S. armories was found to have been in use for a number of years by the time of the 1853 British Parliamentary Commissions Committee on Small Arms inquiry.

Interchangeability was not complete in the Paterson works, and traditional gunsmithing techniques did not fill the gap entirely there.

Interchangeability of parts was achieved by combining a number of innovations and improvements in machining operations and the invention of several machine tools, such as the slide rest lathe, screw-cutting lathe, turret lathe, milling machine and metal planer.

On 27 June 2007, Singapore and Brunei celebrated the 40th anniversary of the Currency Interchangeability Agreement ( since 12 June 1967 ) with the joint-issue of the commemorative $ 20 notes.

* Interchangeability ( computer science ): The ability that an object can be replaced by another object without affecting code using the object.

The dollar is accepted as " customary tender " in Singapore according to the Currency Interchangeability Agreement, although it is not legal tender there.

Interchangeability relies on parts ' dimensions falling within the tolerance range.

* Interchangeability: the “ closeness of agreement ” between the specific PRT's Resistance vs.

The notes have " 40th Anniversary Currency Interchangeability Agreement " overprinted on obverse.

It replaces the " sheaves of wheat " design, and was minted until 2008.

The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space.

Citing the etymology of her name, 19th century scholar Guðbrandur Vigfússon theorizes that Sif " betokens mother earth with her golden sheaves of grain ; she was the goddess of the sanctity of the family and wedlock ".

The Royall family coat-of-arms was adopted as the school crest, which shows three stacked wheat sheaves beneath the university motto ( Veritas, Latin " truth ").

The White Rose of York was depicted below the branch alluding to the home county of Yorkshire and the sheaves of Sheffield ( Sheaf field ) were shown at either side of the owl's head.

There was perhaps a more direct route available: the abelian category concept had been introduced by Grothendieck in his foundational work on homological algebra, to unify categories of sheaves of abelian groups, and of modules.

It was a possible question to pose, around 1957, about a similar purely category-theoretic characterisation, of categories of sheaves of sets, the case of sheaves of abelian groups having been subsumed by Grothendieck's work ( the Tohoku paper ).

The theory rounded itself out, by establishing that a Grothendieck topos was a category of sheaves, where now the word sheaf had acquired an extended meaning with respect to the idea of Grothendieck topology.

The djed may originally have been a fertility cult related pillar made from reeds or sheaves or a totem from which sheaves of grain were suspended or grain was piled around.

The common theme was gigantism: fishing for leviathans, hunting for or riding oversized animals, and bringing in the impossibly huge sheaves.

In fact it was the need to put ( in particular ) the work of Oka on a clearer basis that led quickly to the consistent use of sheaves for the formulation of the theory ( with major repercussions for algebraic geometry, in particular from Grauert's work ).

Siegel was heard to complain that the new theory of functions of several complex variables had few functions in it — meaning that the special function side of the theory was subordinated to sheaves.

When mowing rye, the villagers let some stalks stand, tie flowers among them, and when finished with their work gather around them and shout three times: “ Fru Gaue, you keep some fodder, this year on the wagon .” In Prignitz, they call her fru Gode and leave a bunch of grain standing in each field which they call “ Fru Gode ’ s portion .” In the district of Hameln, it was custom, if a reaper while binding sheaves passed over one, to jeer and call out: “ Is that for fru Gauen?

Their sign was a white band with the chaplet of sheaves of grain.

) For a proper morphism in the sense of scheme theory, it was shown that this functor sends coherent sheaves to coherent sheaves.

The existence of these derived functors is supplied by homological algebra of the abelian category of sheaves ( and indeed this was a main reason to set up that theory ).

It was clear from the outset that perverse sheaves are fundamental mathematical objects at the crossroads of algebraic geometry, topology, analysis and differential equations.

He was an avid art collector and he left behind over 50, 000 books and sheaves of official correspondence.

In return, de Hilton was to provide an annual contribution of 24 sheaves of oats for every draught ox he owned, to the nearby monastery at Monkwearmouth, and was required to attend the mother church of St Peters for the feasts of the Nativity, Easter, Whitsuntide and Saints Peter and Paul.

Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology.

For sheaf cohomology on an algebraic variety, Grothendieck found six spectral sequences relating the possible hyperhomology groups of two chain complexes of sheaves and the hyperhomology groups of their tensor product .< ref > ( EGA III < sub > 2 </ sub >, Théorème 6. 7. 3.

In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. This is the main step, in numerous areas, from sheaf theory as a description of a geometric problem, to its use as a tool capable of calculating dimensions of important geometric invariants.

" On the Nemíga the sheaves are laid out with heads ; men thresh with flails in hedgerows ; on the barn-floor they spread out life ; they winnow the soul from the body.

For technical purposes, injective sheaves are usually superior to the other classes of sheaves mentioned above: they can do almost anything the other classes can do, and their theory is simpler and more general.

This means that they are some of the simplest sheaves to handle in terms of homological algebra.

The name perverse sheaf is a bit of a misnomer for neither are they sheaves, in the ordinary, stylistic, genealogical or literal senses, nor are they perverse.

The justification is that perverse sheaves have several features in common with sheaves: they form an abelian category, you can take their cohomology, and to construct one, it suffices to construct it locally everywhere.

In the late 19th century, farmers would come to the community to acquire binder twine with which they could bind sheaves of wheat.

War arrows were ordered in the thousands for medieval armies and navies, supplied in sheaves normally of 24 arrows.

The sheaves were replaced by a stylised SWFC logo that had been in use on club merchandise for several years prior to the introduction of the new crest.

This shutter greatly improved efficiency over the typical Leica shutter by using stronger metal blade sheaves that were " fanned " much faster, vertically along the minor axis of the 24 × 36 mm frame.

Divisions of labour between men, women, and animals that are still in place in Indonesian rice cultivation, were carved into relief friezes on the ninth century Prambanan temples in Central Java: a water buffalo attached to a plough ; women planting seedlings and pounding grain ; and a man carrying sheaves of rice on each end of a pole across his shoulders ( pikulan ).

In 1985 the lift span sheaves, the grooved wheels that guide the counterweight cables, were replaced.

Analogous properties were established by Jean-Pierre Serre ( 1957 ) for coherent sheaves in algebraic geometry, when X is an affine scheme.

Consequently a number of merchant ships were converted to pipe-laying by stripping the interiors and building in large cylindrical steel tanks, fitting special hauling gear and suitable sheaves and guides.

These sheaves were then ' shocked ' into conical stooks, resembling small tipis, to allow the grain to dry for several days before being threshed.

* Expanding collet chucks were used to locate the sheaves by gripping the internal bore, during certain operations.

For example, sheaves were applied to transformation groups ; as an inspiration to homology theory in the form of Borel-Moore homology for locally compact spaces ; to representation theory in the Borel-Bott-Weil theorem ; as well as becoming standard in algebraic geometry and complex manifolds.

Bow sheaves, some very large, were characteristic of all cable ships.

The lyrics were written in 1874 by Knowles Shaw, who was inspired by Psalm 126: 6, " He that goeth forth and weepeth, bearing precious seed, shall doubtless come again with rejoicing, bringing his sheaves with him.