The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

The Hong Kong Transport Department ( HKTD ) allows and licenses the operation of two types of public light buses – ( 1 ) green minibuses that have route numbers, stop at designated stops ( many routes have hail and ride sections along which passengers can board and exit anywhere unless it's a no-stopping zone ) and which have their fares, service and frequency regulated by the HKTD ; and ( 2 ) red minibuses that may or may not have regular routes, may or may not be numbered, may or may not have fixed stops and whose fares and service levels are not regulated by HKTD.

The X-hat gives control over the tension holding the hats closed, and allows the player to apply similar tension and produce similar tone to pedal operation, but not to vary the tension while playing.

Along with helping IKEA make non-taxable profit, IKEA's complicated corporate structure allows Kamprad to maintain tight control over the operations of Ingka Holding, and thus the operation of most IKEA stores.

However, the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects.

Multitasking allows simultaneous operation of programs that may be able to share data with each other.

This allows more realistic operation in that the modeller can operate independently several locomotives on the same stretch of track.

:::: Using lead as the liquid metal provides excellent radiation shielding, and allows for operation at very high temperatures.

In normal operation, Denise allows between 1 and 5 bitplanes, giving 2 to 32 unique colours.

This allows blitter operation and control to proceed independently of, and concurrently with, the CPU.

In contrast, an untyped language, such as most assembly languages, allows any operation to be performed on any data, which are generally considered to be sequences of bits of various lengths.

This reform was the first of its kind on the African continent actually put into practice, and allows investors to concentrate on their area of expertise ( i. e. network operation or service provision ) across a maximum number of previously separate sectors ( i. e. telecommunications, broadcasting, Internet ).

The Low Altitude Parachute Extraction System ( LAPES ) is a somewhat risky maneuver which allows accurate delivery onto a field when landing is not possible, and the practice was stopped after a fatal crash was caused by one such failed operation.

The system does not require the use of a floor guide, which allows easy operation and an uninterrupted threshold.

In a communications network, a conference operation is an operation that allows a call to be established among three or more stations in such a manner that each of the stations is able to communicate directly with all the other stations.

The Remote Operations Service Element ( ROSE ) is the OSI service interface, specified in ITU-T Recommendation X. 219, ISO / IEC International Standard 9072-1, that ( a ) provides remote operation capabilities, ( b ) allows interaction between entities in a distributed application, and ( c ) upon receiving a remote operations service request, allows the receiving entity to attempt the operation and report the results of the attempt to the requesting entity.

) This feature allows high power operation for extended periods of time.

Telemetry is used in complex systems such as missiles, RPVs, spacecraft, oil rigs and chemical plants since it allows the automatic monitoring, alerting, and record-keeping necessary for efficient and safe operation.

Compared with standard SNES games, the additional microprocessor allows higher clock speeds ; faster access to the random-access memory ( RAM ); greater memory mapping capabilities, data storage, and compression ; new direct memory access ( DMA ) modes, such as bitmap to bit plane transfer ; and built-in CIC lockout for piracy protection and regional marketing control.

A connector specification that allows a slot-based peripheral to have direct connection to a microprocessor using a HyperTransport interface was released by the HyperTransport Consortium.

The 43203 Interface Processor ( IP ) allows a more conventional microprocessor to be interfaced as an Attached Processor ( AP ) to an iAPX 432 system.

In the 80386 microprocessor and later, virtual 8086 mode ( also called virtual real mode, V86-mode or VM86 ) allows the execution of real mode applications that are incapable of running directly in protected mode while the processor is running a protected mode operating system.

In addition to the brushless motor's higher efficiency, certain HVAC systems ( especially those featuring variable-speed and / or load modulation ) use brushless motors because the built-in microprocessor allows for programmability, better control over airflow, and serial communication.

The microprocessor lab allows study of using microprocessors as an industrial control tool.

This level of abstraction allows the guest machine to run on host machines with a different type of microprocessor, but is also very slow.

As an illustration of the principle of simplicity the heliocentric discovery has a peculiar appeal because it allows simplicity to be arithmetized ; ;

Moreover, it allows the present management to reassign vehicles so that mileage will be more uniformly distributed throughout the fleet ; ;

A new radial drill press with a 16 inch capacity has a tilting head that allows drilling to be done at any angle.

For example, the inflected forms of a word can be represented, insofar as regular inflection allows, by a stem and a set of endings to be attached.

Of course, in prudential calculation, in balancing the good directly intended and done against the evil unintended and indirectly done, no greater precision can be forthcoming than the subject allows.

) `` Quoting Mr. Kennan's phrase that anything would be better than a policy which led inevitably to nuclear war, he ( Toynbee ) says that anything is better than a policy which allows for the possibility of nuclear war ''.

One argument given in favor of using the axiom of choice is that it is convenient to use it because it allows one to prove some simplifying propositions that otherwise could not be proved.

It could be suggested that in Murder on the Orient Express Poirot allows the murderers to escape justice as well, after he discovers that twelve different people stabbed the victim – Mr. Ratchett – in his sleep.

The nature of classifiers and their constructions allows the speaker to use them more frequently in narratives ; one study found this to be 17. 7 %.

* The German-designed bow anchor, Bügelanker ( or Wasi ), has a sharp tip for penetrating weed, and features a roll-bar which allows the correct setting attitude to be achieved without the need for extra weight to be inserted into the tip.

Solomonoff used this algorithm, and the code lengths it allows, to define a " universal probability " of a string on which inductive inference of the subsequent digits of the string can be based.

However, there may be several such allophones, or the linguist may prefer greater precision than this allows.

It allows the true brightnesses of objects to be compared without regard to distance.

Moreover, the ansibles Le Guin uses in her stories apparently have a very limited bandwidth which only allows for at most a few hundred characters of text to be communicated in any transaction of a dialog session.

BWF allows metadata to be stored in the file.

It allows additional data to be held in the file header.

The. ra format allows files to be stored in a self-contained fashion on a computer, with all of the audio data contained inside the file itself.

For example, an abstract stack data structure could be defined by three operations:, that inserts some data item onto the structure,, that extracts an item from it ( with the constraint that each pop always returns the most recently pushed item that has not been popped yet ), and, that allows data on top of the structure to be examined without removal.

This information hiding strategy allows the implementation of the module to be changed without disturbing the client programs.

This allows a single antibody to be used by several different parts of the immune system.

The terms anode and cathode should not be applied to a Zener diode, since it allows flow in either direction, depending on the polarity of the applied potential ( i. e. voltage ).

This step allows apoptotic signals to cause cell death, or the process to be stopped, should the cell no longer need to die.