This turns the seminormed space into a pseudometric space ( notice this is weaker than a metric ) and allows the definition of notions such as continuity and convergence.

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity.

In the general context of a G-valued series, a distinction is made between absolute and unconditional convergence, and the assertion that a real or complex series which is not absolutely convergent is necessarily conditionally convergent ( meaning not unconditionally convergent ) is then a theorem, not a definition.

Ten years after, in, Lamberto Cesari changed the continuity requirement in Tonelli's definition to a less restrictive integrability requirement, obtaining for the first time the class of functions of bounded variation of several variables in its full generality: as Jordan did before him, he applied the concept to resolve of a problem concerning the convergence of Fourier series, but for functions of two variables.

The definition of the network layers is based on the OSI model ; although only the lower layers are defined in the standard, interaction with upper layers is intended, possibly using a IEEE 802. 2 logical link control sublayer accessing the MAC through a convergence sublayer.

It is argued that the speed of convergence of the trapezoidal rule reflects and can be used as a definition of classes of smoothness of the functions.

Hence the definition above, which arose when it became clear that neither convergence everywhere nor convergence almost everywhere give a satisfactory answer.

In the second, he contrasts the deductivist and heuristic approaches and provides heuristic analysis of some ' proof generated ' concepts, including uniform convergence, bounded variation, and the Caratheodory definition of a measurable set.

In a more general definition of weakly simple polygons, they are the limits of sequences of simple polygons of the same combinatorial type, with the convergence under the Hausdorff metric.

This definition is formal in that it does not always have a positive radius of convergence.

This definition demonstrates that convergence of filters can be viewed as a fundamental topological notion.

As for filters, this definition shows that convergence of nets can be viewed as a fundamental topological notion.

Substituting this into the definition of the derivative via a difference quotient and taking limits means that the higher order terms – and higher – become negligible, and yields the formula interpreted as

Extension blocks ( blocks that " extend " the 87a definition via a mechanism already defined in the 87a spec ) consist of the sentinel, an additional byte specifying the type of extension, and a linked list of sub-blocks with the extension data.

The definition in general is somewhat technical, but in the case of real matrix groups, it can be formulated via the exponential map, or the matrix exponent.

While the definition via velocities of curves is quite straightforward given the above intuition, it is also the most cumbersome to work with.

Kolmogrov's definition of a random string was that it is random if has no description shorter than itself via a universal Turing machine.

One immediate application is the definition of the basic concepts of analysis such as derivative and integral in a direct fashion, without passing via logical complications of multiple quantifiers.

The vehicles are self-contained and provide wired and wireless services including voice and radio interoperability, voice over IP, network based video surveillance and secured high definition video conferencing for leaders and first responders in crisis areas with up to 5 Mbit / s of bandwidth via a 1. 8-meter satellite antenna.

The performance was also sold in high definition via Blu-ray Disc.

This follows immediately from the Galois connection between ideals of and closed subsets of and the observation that, by the definition of, each prime ideal of corresponds to a generic point of the closed subset associated to via the Galois connection.

Starkly so, Reform Judaism rejected the traditional definition of a Jew via matrilineal descent, effectively severing the united peoplehood that had linked Reform and non-Reform movements.

Complex data creation in most SQL ORDBMSs is based on preliminary schema definition via the user-defined type ( UDT ).

Previously, network programming from the United States was received on cable via affiliates from Spokane, Washington, but local viewers now have more choice, given the advances with cable or satellite television that are now being offered as digital or HD ( high definition ) service.

This version has enhanced graphics for high definition displays as well as online leaderboards and support for multiplayer via split screen and Xbox Live.

Thus, similar to the definition of other fundamental quantities ( like time and mass ), space is defined via measurement.

Every vertex in a polygon is assigned a texture coordinate ( which in the 2d case is also known as a UV coordinate ) either via explicit assignment or by procedural definition.

The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, however, it is now taken to be the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system.

When part definition is defined mathematically via a solid model, the assertion that one cannot interrogate the model — the direct analog of " scaling the drawing "— becomes ridiculous ; because when part definition is defined this way, it is not possible for a drawing or model to be " not to scale ".

Also, upscaling and up-converting DVD units are available that connect to televisions via a high definition interface and increase the overall picture quality.

It broadcasts a high definition digital signal on UHF channel 47 ( virtual channel 11. 1 via PSIP ) from a transmitter atop the Willis Tower.

It broadcasts a high definition digital signal on UHF channel 19 ( virtual channel 9. 1 via PSIP ) from a transmitter atop the Willis Tower.

Thus one can question whether power source is truly a key distinguishing concept ; but for economics purposes, the NBER's definition made sense, because most of the commercial value of the existence of machine tools comes about via those that are powered by electricity, hydraulics, and so on.

The HDD200 decoder interfaces with the 4DTV receiver via the Multi-Media Access Port ( MMAP ), allowing access to several high definition channels available on the 4DTV system.

* Limits of nets of Riemann sums, in the definition of the Riemann integral.

Unlike these standards, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis.

" Mr. Vito Tanzi, Director of the IMF's Fiscal Affairs Department, gave definition that the transformation to a market economy is not complete until functioning fiscal institutions and reasonable and affordable expenditure programs, including basic social safety nets for the unemployed, the sick, and the elderly, are in place.

If the algebra in question is not first-countable, one must substitute nets for the sequences used in the definition.

My definition of this much abused adjective is that a reconstructed rebel is one who is glad that the North won the War.

At this point a working definition of idea is in order, although our first definition will have to be qualified somewhat as we proceed.

A tragedy, by his definition, is an imitation of an action that is serious, of a certain magnitude, and complete in itself.

Now good definition is one thing that all of us can acquire with occasional high-set, high-rep, light-weight workouts.

But contest definition -- that dramatic muscular separation of every muscle group that seems as though it must have been carved by a sculptor's chisel -- is something quite different.

It is the one exercise that drastically influences the definition of the thighs at the hipline -- that mark of the champion that sets him apart from all other bodybuilders ; ;

But for purely definition purposes -- used in conjunction with your regular Squatting, Leg Curling, Leg Extensor programs -- a heavy weight is not needed.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

Though there is obviously great need for continued experimentation with various types of short-term intervention to further efforts in developing an operational definition of prevention at the secondary -- or perhaps, in some instances, primary -- level, the place of short-term intervention has already been documented by a number of investigators in a wide variety of settings.

Finally, when the accelerometer output is zero, the entire system remains stationary, and the platform is, by definition, leveled.

When her brother Winslow became a student at Brown University in 1874, she wrote him about a course in history he was taking under Professor Diman: `` What is Prof. Diman's definition of civilization, and take the world through, is its progress ever onward, or does it retrograde at times??

One definition of paternalism is `` The principle or practice, on the part of a government, of managing the affairs of a country in the manner of a father dealing with his children ''.

If Bultmann's own definition of myth is strictly adhered to ( and it is interesting that this is almost never done by those who make such pronouncements ), the evidence is overwhelming that he does not at all exaggerate the extent to which the mythological concepts of traditional theology have become incredible and irrelevant.

Anarchism is generally defined as the political philosophy which holds the state to be undesirable, unnecessary, and harmful ,< ref name =" definition ">

The majority of the clocks are caesium clocks ; the definition of the SI second is written in terms of caesium.