By a typical application of the transfer principle, every hyperreal x satisfies the inequality

By application of a voltage during the presence of this gas, gas ions in the vicinity of the tip undergo ionisation, with greater numbers of ions generated immediately above atoms occupying edge or planar sites.

The first theory about software was proposed by Alan Turing in his 1935 essay Computable numbers with an application to the Entscheidungsproblem ( decision problem ).

* Alan Turing, " On computable numbers, with an application to the Entscheidungsproblem ", Proceedings of the London Mathematical Society, Series 2, 42 ( 1937 ), pp 230 – 265.

One way to find that analytic continuation is to use Euler's integral for positive arguments and extend the domain to negative numbers by repeated application of the recurrence formula,

It is very probable, too, that the application of our therapy to numbers will compel us to alloy the pure gold of analysis plentifully with the copper of direct suggestion.

It may include the program counter, stack pointer, and other numbers that are not easily accessible to the application programmer.

In the original article (" On computable numbers, with an application to the Entscheidungsproblem ", see also references below ), Turing imagines not a mechanism, but a person whom he calls the " computer ", who executes these deterministic mechanical rules slavishly ( or as Turing puts it, " in a desultory manner ").

Its first four Masters were educated at St John's, and it took until around 1575 for the two colleges ' application numbers to draw even, a position in which they have remained since the Civil War.

UDP provides application multiplexing ( via port numbers ) and integrity verification ( via checksum ) of the header and payload.

* using a client application to join with large numbers of other terminal users in collaborative workgroups.

For example, large numbers of employees discussing key issues in an intranet forum application could lead to new ideas in management, productivity, quality, and other corporate issues.

These port numbers are found in Request for Comments ( RFC ) 1700 and reference the upper-layer protocol, program, or application.

The limits of the application of reductionism become especially evident at levels of organization with higher amounts of complexity, including culture, neural networks, ecosystems, and other systems formed from assemblies of large numbers of interacting components.

* how an application should make system calls to the operating system and, if the ABI specifies direct system calls rather than procedure calls to system call stubs, the system call numbers

This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers.

Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65, 000.

A common application of proof by mathematical induction is to prove that a property known to hold for one number holds for all natural numbers:

This is an example of odd numbers playing a role in an advanced mathematical theorem where the method of application of the simple hypothesis of " odd order " is far from obvious.

This involves statistical multiplexing of data from different application processes, i. e. forming data packets, and adding source and destination port numbers in the header of each transport-layer data packet.

A third application of the compactness theorem is the construction of nonstandard models of the real numbers, that is, consistent extensions of the theory of the real numbers that contain " infinitesimal " numbers.

When an IVR system answers multiple phone numbers the use of DNIS ensures that the correct application and language is executed.

All the results of arithmetical algebra which are deduced by the application of its rules, and which are general in form though particular in value, are results likewise of symbolical algebra where they are general in value as well as in form ; thus the product of and which is when and are whole numbers and therefore general in form though particular in value, will be their product likewise when and are general in value as well as in form ; the series for determined by the principles of arithmetical algebra when is any whole number, if it be exhibited in a general form, without reference to a final term, may be shown upon the same principle to the equivalent series for when is general both in form and value.

The reasons for extracting this particular roleplaying application from the previous discussion of training are twofold.

The appellate court will typically be deferential to the lower court's findings of fact ( such as whether a defendant committed a particular act ), unless clearly erroneous, and so will focus on the court's application of the law to those facts ( such as whether the act found by the court to have occurred fits a legal definition at issue ).

Thus, the license depends on how a particular application that uses Berkeley DB is distributed to the public.

However, this method of designing custom CPUs for a particular application has largely given way to the development of mass-produced processors that are made for many purposes.

Sometimes the problem is not that a statute is unconstitutional, but the application of it is, on a particular occasion, and a court may decide that while there are ways it could be applied that are constitutional, that instance was not allowed or legitimate.

Its purpose is to unburden the application software programmer from the often complex details of the particular computer being used, including such accessories as communications devices, printers, device readers, displays and keyboards, and also to partition the computer's resources such as memory and processor time in a safe and stable manner.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

But it is not the traditional notions Catullus rejects, but rather their particular application to the vita activa of politics and war.

A typical application is furnished by the Arzelà – Ascoli theorem and in particular the Peano existence theorem, in which one is able to conclude the existence of a function with some required properties as a limiting case of some more elementary construction.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

As all alloys do not have the same chemical constituents, the tempering procedure varies according to the material's chemical composition, thermal history and / or a tool's particular service application.

These databases attempt to bring the database world and the application-programming world closer together, in particular by ensuring that the database uses the same type system as the application program.

The client may also request repeat data for a particular application.

A pattern would not tell the designer how many windows to put in the room ; instead, it would propose a set of values to guide the designer toward a decision that is best for their particular application.

The filter response can also be completely characterized in the frequency domain by its transfer function, which is the Fourier transform of the impulse response h. Typical filter design goals are to realize a particular frequency response, that is, the magnitude of the transfer function ; the importance of the phase of the transfer function varies according to the application, inasmuch as the shape of a waveform can be distorted to a greater or lesser extent in the process of achieving a desired ( amplitude ) response in the frequency domain.

Different opinions arise only from the application of these preconceptions to particular cases, and it is then that the darkness of ignorance, which blindly maintains the correctness of its own opinion, must be dispelled.

Depending on the particular formalism adopted for the calculus, it may be seen as a simple application of a " functional substitution " rule of inference, as in Gödel's paper, or it may be proved by considering the formal proof of, replacing in it all occurrences of Q by some other formula with the same free variables, and noting that all logical axioms in the formal proof remain logical axioms after the substitution, and all rules of inference still apply in the same way.

Careful analysis should be done to ensure that the programmer uses the most efficient code for the particular application.

Men rightly observe that a conjugal act imposed on one's partner without regard to his or her condition or personal and reasonable wishes in the matter, is no true act of love, and therefore offends the moral order in its particular application to the intimate relationship of husband and wife.

Depending on the clock frequency, the number of memory wait states, as well as on the characteristics of the particular application program, the average performance for the Intel 8088 ranged from approximately 0. 33 – 1 million instructions per second.

Now in the Web era ( and with wikis in particular ), the application again is strongly centrally controlled, with only technical functionality distributed to the PC.

As an allegorist who could read into the ancient documents the particular philosophical idiosyncrasies of his day, Anatoli deserves a place beside other allegoric and philosophical commentators, from Philo down ; indeed, he may be regarded as a pioneer in the application of the Maimonistic manner to purposes of popular instruction.

In the United States, the LDS Church has applied for a trademark on " Mormon " as applied to religious services ; however, the United States Patent and Trademark Office rejected the application, stating that the term " Mormon " was too generic, and is popularly understood as referring to a particular kind of church, similar to " Presbyterian " or " Methodist ", rather than a service mark.

Mutants strains may also be produced that have practical application or allow the molecular basis of particular cell function to be investigated.

Hypermedia can be considered one particular multimedia application.