A precising definition extends the descriptive dictionary definition ( lexical definition ) of a term for a specific purpose by including additional criteria that narrow down the set of things meeting the definition.

Alfred Marshall provides a still widely-cited definition in his textbook Principles of Economics ( 1890 ) that extends analysis beyond wealth and from the societal to the microeconomic level:

In summary, the thermodynamic definition of entropy provides the experimental definition of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature.

It extends from the Arctic in the north to the Southern Ocean ( or, depending on definition, to Antarctica ) in the south, bounded by Asia and Australia in the west, and the Americas in the east.

A popular alternative definition of chronic pain, involving no arbitrarily fixed durations is " pain that extends beyond the expected period of healing.

where, by definition, the left hand side is ζ ( s ) and the infinite product on the right hand side extends over all prime numbers p ( such expressions are called Euler products ):

The NATO definition extends to " all crew-portable direct fire weapons of a calibre less than 50 mm and will include a secondary capability to defeat light armour and helicopters.

Thus it broadens the range of sign systems and sign relations, and extends the definition of language in what amounts to its widest analogical or metaphorical sense.

The radical of a module extends the definition of the Jacobson radical to include modules.

The Open Group is most famous as the certifying body for the UNIX trademark, and its publication of the Single UNIX Specification technical standard, which extends the POSIX standards and is the official definition of a UNIX system.

The first definition is for a planar curve that extends primarily in length and width, but not in height.

The phrase " whole-house weatherization " extends the traditional definition of weatherization to include installation of modern, energy-saving heating and cooling equipment, or repair of old, inefficient equipment ( furnaces, boilers, water heaters, programmable thermostats, air conditioners, and so on ).

A popular alternative definition of chronic pain, involving no arbitrarily fixed durations is " pain that extends beyond the expected period of healing.

This also extends to areas such as animal welfare, where some emergency organisations cover this element through the ' property ' definition, where animals owned by a person are threatened ( although this does not cover wild animals ).

However the definition also extends to products that have been produced using an industrial process.

The definition extends to any object X in n-dimensional space: its centroid is the intersection of all hyperplanes that divide X into two parts of equal moment.

By choosing a = 0, this formula gives both an integral and a series representation for a function that interpolates the harmonic numbers and extends a definition to the complex plane.

After the Oklahoma City bombing of 19 April 1995, by Timothy McVeigh, an American, the CI definition reasonably extends to included domestically-originated terrorism.

For Harsin a " rumor bomb " extends the definition of rumor into a political communication concept with the following features:

Now the Stone Harbor bird sanctuary, 31 acres of magic attraction for exotic herons, is threatened, but the battlefront extends far beyond our state.

Place the template ( Fig. 2 ) on the fabric so that the sides of the 10 inch square cut out of the template are parallel to the warp and filling for woven fabrics, or the wales and courses for knitted fabrics, and so that the same amount of fabric extends beyond the edges of the template on all sides.

Terriberry extends Chan's formulae to calculating the third and fourth central moments, needed for example when estimating skewness and kurtosis:

further extends these results to arbitrary-order central moments, for the incremental and the pairwise cases.

It extends, chiefly as a single street, for several miles along a narrow strip

The modern city not only encloses the entire harbor but takes up the better part of the Gulf of Ajaccio and in suburban form extends for some miles up the valley of the Gravona River.

and for p > 2 it extends these basic operations in a way that happens to be expressible in Knuth's up-arrow notation as

The user can adjust how far the blade extends from the handle, so that, for example, the knife can be used to cut the tape sealing a package without damaging the contents of the package.

He prays to God, recalling the sins of Israel and God's promise of restoration to the Land, and asks Artaxerxes for leave to return to Jerusalem and rebuild its walls ; the king is receptive and extends his aid to this mission.

North and northeast of Lake Chad, the basin extends for more than 800 kilometers, passing through regions characterized by great rolling dunes separated by very deep depressions.

The School of International and Public Affairs traditionally extends invitations to many heads of state and heads of government who come to New York City for the opening of the fall session of the United Nations General Assembly.

Landfill extends into portions of the lake providing space for Navy Pier, Northerly Island, the Museum Campus, and large portions of the McCormick Place Convention Center.

Cloud computing for call centres extends cloud computing to Software as a service, or hosted, on-demand call centres by providing application programming interfaces ( APIs ) on the call centre cloud computing platform that allow call centre functionality to be integrated with cloud-based Customer relationship management, such as Salesforce. com or Oracle CRM and leads management and other applications.

The F-corona ( F for Fraunhofer ) is created by sunlight bouncing off dust particles, and is observable because its light contains the Fraunhofer absorption lines that are seen in raw sunlight ; the F-corona extends to very high elongation angles from the Sun, where it is called the zodiacal light.

When focus is set to the hyperfocal distance, the DOF extends from half the hyperfocal distance to infinity, and the DOF is the largest possible for a given f-number.

When a DHCP server receives an IP lease request from a client, it reserves an IP address for the client and extends an IP lease offer by sending a DHCPOFFER message to the client.

As a result of the dam's construction, the Nile actually begins its flow into Egypt as Lake Nasser, which extends southwards from the dam for 320 km to the border and for an additional 158 km within Sudan.

Protocol 12 extends this prohibition to cover discrimination in any legal right, even when that legal right is not protected under the Convention, so long as it is provided for in national law.

The electromagnetic spectrum extends from below the low frequencies used for modern radio communication to gamma radiation at the short-wavelength ( high-frequency ) end, thereby covering wavelengths from thousands of kilometers down to a fraction of the size of an atom.

Metzger and Aland list the probable date for this manuscript as c. 125 but the difficulty of estimating the date of a literary text based solely on paleographic evidence must allow potentially for a range that extends from before 100 to well into the second half of the 2nd century.

Since quarks make up the baryons and the mesons, and the strong interaction takes place between baryons and mesons, one could say that the color force is the source of the strong interaction, or that the strong interaction is like a residual color force that extends beyond the baryons, for example when protons and neutrons are bound together in a nucleus.

One might expect that by the Hahn-Banach theorem for bounded linear functionals, every bounded linear functional on C < sub > c </ sub >( X ) extends in exactly one way to a bounded linear functional on C < sub > 0 </ sub >( X ), the latter being the closure of C < sub > c </ sub >( X ) in the supremum norm, and that for this reason the first statement implies the second.

An immense plain extends to the south ; in every direction the view is bounded by hills and mountains.

Most of the county is covered by the rugged Kettle River Range, which extends from the Canadian border at the north, all the way to its southernmost perimeter bounded by the Columbia River and Lake Roosevelt.

With the Winchmore Hill conservation area as a focal point, Winchmore Hill is a ward of Enfield borough, bounded on the east by Green Lanes ( the A105 road ), Barrowell Green, Firs Lane and Fords Grove, and on the west by Grovelands Park ; in the south it extends to part of Aldermans Hill, and in the north to Vicars Moor Lane and Houndsden Road.

Sycamore Hills is bounded on the south by Midland Boulevard ( with the exception of the extreme southwest corner, which extends one block further south to Lackland Road ).

The city is bounded to the north by Hobble Creek and extends southward to the Ensign-Bickford plant in Spanish Fork.

The Savannah River drainage basin extends into the southeastern side of the Appalachian Mountains just inside North Carolina, bounded by the Eastern Continental Divide.

It is bounded roughly by Alaskan Way S. on the west, beyond which are the docks of Elliott Bay ; by S. King Street on the south, beyond which is SoDo ; by 5th Avenue S. on the east, beyond which is the International District ; and it extends between one and two blocks north of Yesler Way, beyond which is the rest of Downtown.

Gauchos were generally nomadic, and lived in the Pampas, the plain that extends north from Patagonia, bounded on the west by the Andes and extending on the east to Uruguay and the Brazilian state of Rio Grande do Sul.

The Hohe Rhön ( or Hochrhön ) extends into all 3 states and is bounded by the Vordere Rhön in the northeast, the Grabfeld in the southeast, the Spessart in the southwest and the Kuppenrhön in the northwest.

The northwestern extension, bounded by a dramatic escarpment known as " The Rim ", extends much further into New Mexico, to near the Sacramento Mountains.

The town is bounded on the north by Babahurin Hill and extends towards the northwest which meets the town of Pola.

It is easy to check that the linear form induced by σ is continuous in the sup-norm iff σ is bounded, and the result follows since a linear form on the dense subspace of simple functions extends to an element of B ( Σ )* iff it is continuous in the sup-norm.

) The Stinespring factorization theorem extends the above result to arbitrary separable Hilbert spaces H and G. There, S is replaced by a trace class operator and by a sequence of bounded operators.

The range is bounded by the Trans-Canada Highway on the west side while the northern section of the range extends into Banff National Park to the southern shores of Lake Minnewanka.

Observe that an infinite cone is not bounded by its base and extends to infinity.

Below the extension, is a narrow peninsula, bounded by Matagorda Bay to the south, which extends west to mouth of Lavaca Bay.

The Prospect Heights Historic District covers an area roughly bounded by Flatbush Avenue, Sterling Place, Washington Avenue, and St. Marks Avenue, though a section of the historic district extends as far north as Pacific Street.

In fact this map extends in a canonical way to all bounded complex-valued Borel functions on X.

The incident occurred in the vicinity of two former military bases-RAF Bentwaters, which is just to the north of the forest, and RAF Woodbridge which extends into the forest from the west and is bounded by the forest on its northern and eastern edges.

Contarini also wrote, " The empire of Uzun-Hassan is very extensive, and is bounded by Turkey and Caramania, belonging to the Sultan, and which latter country extends to Aleppo.