An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom.

In statistics, the autocorrelation of a random process describes the correlation between values of the process at different points in time, as a function of the two times or of the time difference.

In probability theory and statistics, the cumulative distribution function ( CDF ), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x.

* Cortical magnification, describes how many neurons in an area of the visual cortex are ' responsible ' for processing a stimulus of a given size, as a function of visual field location

As an example, consider the function h ( t ), which describes the height of a growing flower at time t. This function is continuous.

Let r ( t ) be a vector that describes the position of a point mass as a function of time.

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value.

In the case of particles like electrons, neutrons and atoms, the coherence length is related to the spatial extent of the wave function that describes the particle.

The complexity of any such filter is given by the order N, which describes the order of the rational function describing the frequency response.

It is easy graphically to interpolate the factorial function to non-integer values, but is there a formula that describes the resulting curve?

The Man Page for cURL, an open source tool and programming library, describes the function of cURL as " cURL groks URLs ".

In this model we consider a particle as being a point of mass which describes a trajectory in space which is modeled by a function giving its coordinates in space as a function of time.

This describes the factorial as a recursive function, with a single terminating base case.

Part of the definition shown is optional, and describes the types of this function.

While phonetics concerns the physical production, acoustic transmission and perception of the sounds of speech, phonology describes the way sounds function within a given language or across languages to encode meaning.

In On Spirals, Archimedes describes the Archimedean spiral, a function whose radius depends on the angle.

Both concepts can be united using a cumulative distribution function ( CDF ), which describes the probability that an outcome will be less than or equal to a specified value.

The amount of this deviation is known as its gamma value (), the argument for a power law function, which closely describes this behaviour.

The object of a stimulus – response model is to establish a mathematical function that describes the relation f between the stimulus x and the expected value ( or other measure of location ) of the response Y:

The Fermi distribution function describes the filling of electron levels at a given temperature T.

Planck's law very accurately quantitatively describes the power spectral density of electromagnetic radiation, inside a rigid walled cavity in a body made of material that is completely opaque and poorly reflective, when it has reached thermodynamic equilibrium, as a function of absolute thermodynamic temperature alone.

Today, in the era of the integrated musical when an individual song must contribute to the over-all development of the show, it is understandable that a song, no matter how excellent it may be on its own terms, is cut out because it does not perform the function required of it.

The Twelve Traditions informally guide how individual AA groups function, and the Twelve Concepts for World Service guide how the organization is structured globally.

* RRA — Relief Run Average: A function of how many inherited base runners a relief pitcher allowed to score.

By finding how similar two protein sequences are, we acquire knowledge about their structure and therefore their function.

This allows us to link behavior and brain function to help understand how information is processed.

The total derivative is a linear transformation that captures how the function changes in all directions.

To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude " By the Church – Turing thesis " that the function is Turing computable ( equivalently partial recursive ).

The modern census is essential to international comparisons of any kind of statistics and censuses collect data on many attributes of the population, not just how many people they are, although population estimates remain an important function of the census.

In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument.

They express how sensitive that function is to small changes ( or small errors ) in its arguments.

The comparative study of the various legal systems may show how different legal regulations for the same problem function in practice.

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes.

Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.

For example, the word " house " derives its meaning more as a function of how it differs from " shed ", " mansion ", " hotel ", " building ", etc.

Writing a device driver requires an in-depth understanding of how the hardware and the software of a given platform function.

" R. M. Hare also criticised ethical naturalism because of its fallacious definition of the terms ' good ' or ' right ' explaining how value-terms being part of our prescriptive moral language are not reducible to descriptive terms: " Value-terms have a special function in language, that of commending ; and so they plainly cannot be defined in terms of other words which themselves do not perform this function "

An understanding of how biodiversity affects ecological function is an important focus area in ecological studies.

Even today, many brass pedagogues take a rigid approach to teaching how a brass player's embouchure should function.

The amino acids in a protein determine how it folds into a three-dimensional shape ; this structure is, in turn, responsible for the protein's function.

To a much less full extent, the hebephrenic person's belching or flatus has a comparable communicative function ; ;

Axons are distinguished from dendrites by several features, including shape ( dendrites often taper while axons usually maintain a constant radius ), length ( dendrites are restricted to a small region around the cell body while axons can be much longer ), and function ( dendrites usually receive signals while axons usually transmit them ).

Although most legislation is initiated by the executive branch, the Bundestag considers the legislative function its most important responsibility, concentrating much of its energy on assessing and amending the government's legislative program.

In all of these areas, bishops of the United Methodist Church function very much in the historic meaning of the term.

While the complexity, size, construction, and general form of CPUs have changed enormously since 1950, it is notable that the basic design and function has not changed much at all.

Programs containing command software enable hardware engineering and system operations to function much easier together.

This means that death may be consisted of much more than just the brain ’ s inability to function.

According to Hailsham, a former chairman of the British Conservative Party, " Conservatism is not so much a philosophy as an attitude, a constant force, performing a timeless function in the development of a free society, and corresponding to a deep and permanent requirement of human nature itself.

Hexameters also have a primary caesura — a break in sense, much like the function of a comma in prose — at one of several normal positions: After the first syllable in the third foot ( the " masculine " caesura ); after the second syllable in the third foot if the third foot is a dactyl ( the " feminine " caesura ); after the first syllable of the fourth foot ; or after the first syllable of the second foot ( the latter two often occur together in a line, breaking it into three separate units ).

The hi-hat has a similar function to the ride cymbal ; The two are rarely played at once, but one or the other keeps the fine rhythm much of the time, played by the right stick of a right-handed drummer.

However, if there is no " obvious " Euclidean function, then determining whether R is a PID is generally a much easier problem than determining whether it is a Euclidean domain.

Emacs Lisp can also function as a scripting language, much like the Unix Bourne shell, Perl, Python, scsh, or GNU Guile.

These plant communities cover approximately 9. 4 percent of the Earth's surface ( or 30 percent of total land area ), though they once covered much more ( about 50 percent of total land area ), in many different regions and function as habitats for organisms, hydrologic flow modulators, and soil conservers, constituting one of the most important aspects of the biosphere.

These results, however, are very sensitive to the accuracy of the twiddle factors used in the FFT ( i. e. the trigonometric function values ), and it is not unusual for incautious FFT implementations to have much worse accuracy, e. g. if they use inaccurate trigonometric recurrence formulas.

These associations regulate competition and allowed small firms to function in the shadow of much larger companies.

If there is too much thyroid hormone, every function of the body tends to speed up.

( In an ideal " perfect hash function ", no bucket should have more than one record ; but a small number of collisions is virtually inevitable, even if n is much larger than m – see the birthday paradox ).

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

The solution of the Schrödinger equation goes much further than the Bohr model, because it also yields the shape of the electron's wave function (" orbital ") for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds.

While Lippman's journalistic philosophy might be more acceptable to government leaders, Dewey's approach is a better description of how many journalists see their role in society, and, in turn, how much of society expects journalists to function.

He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.

The use of photography, which had rendered much of the representational function of visual art obsolete, strongly affected this aspect of modernism.

This ramping of the speed would be difficult with interlocking involved, as the time needed to set up locks is as much a function of die size as clock rate.