# Function

## Meanings and phrases

n.

- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function); mathematical function; single-valued function; map; mapping
- what something is used for; purpose; role; use
- the actions and activities assigned to or required or expected of a person or group; office; part; role
- a vaguely specified social event; affair; occasion; social occasion; social function
- a relation such that one thing is dependent on another
- a formal or official social gathering or ceremony
- a set sequence of steps, part of larger computer program; routine; subroutine; subprogram; procedure

v.

- perform as expected when applied; work; operate; go; run
- serve a purpose, role, or function; serve
- perform duties attached to a particular office or place or function; officiate

n.

- an organic process that takes place in the body; bodily process; body process; activity

n.

- (electronics) graph showing how a particular characteristic of a device varies with other parameters; characteristic curve

n.

- function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the angle; trigonometric function

n.

- an operation that controls the recording or processing or transmission of interpretation of data; control operation

n.

- the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx; derivative; differential coefficient; differential; first derivative

n.

- (mathematics) the set of values of the independent variable for which a function is defined; domain

n.

- a function in which an independent variable appears as an exponent; exponential

- It grows quickly, faster than an exponential function in fact.
- The exponential function extends to an entire function on the complex plane.
- This complex exponential function is sometimes denoted ("cosine plus i sine").

n.

- a call that passes control to a subroutine; after the subroutine is executed control returns to the next instruction in main program

n.

- a word that is uninflected and serves a grammatical function but has little identifiable meaning; closed-class word

n.

- a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x

n.

- (physiology) the principle that specific functions have relatively circumscribed locations in some particular part or organ of the body; localization of function; localization principle; localisation principle; localization; localisation

n.

- (physiology) the principle that specific functions have relatively circumscribed locations in some particular part or organ of the body; localisation of function; localization principle; localisation principle; localization; localisation

n.

- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function); function; single-valued function; map; mapping

n.

- a function of a topological space that gives, for any two points in the space, a value equal to the distance between them; metric

n.

- (mathematics) the set of values of the dependent variable for which a function is defined; image; range

n.

- formal expression containing variables; becomes a sentence when variables are replaced by constants

n.

- (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function); function; mathematical function; map; mapping

n.

- a vaguely specified social event; affair; occasion; social occasion; function

- Whilst the house system was kept by name only, the main social function of the house system was lost.
- Sport emancipation led to its emergence and consolidation, which was followed by a new social function.
- The social function of the room is for the poorest people of the city, or students from the nearby university to meet.

n.

- a function that takes the value 1 if a specified function of the arguments exceeds a given threshold and 0 otherwise

n.

- function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the angle; circular function

E.g.

- This feature is known as wave function collapse.
- The observer collapses the wave function into their own reality.
- So the wave function is said to supply a non-separable representation.

E.g.

- The fort's primary function during this time was as a munitions depot.
- Though called a castle, Balmoral's primary function is that of a country house.
- Its primary function is to operate and maintain the Kariba Dam on the Zambezi River.

E.g.

- The main function of this temple was Soorasamgaram.
- Modular Battalions main function was internal operations.
- This was her main function at Eleusis, and became panhellenic.

E.g.

- The probability distribution function "P"(δ).
- It also determines the probability distribution function of the energy.
- And the corresponding distribution function estimator formula_17 is formula_18.

E.g.

- Assume "K" to be a symmetric kernel density function with unit variance.
- A common model is the exponential failure distribution, which is based on the exponential density function.
- The probability density function (pdf) for the noncentral "F"-distribution is when formula_9 and zero otherwise.

E.g.

- The controller, C, has the transfer function C(s).
- That is, the transfer function's spectral radius is 1.
- This typical 4000 Hz notch is due to the transfer function of the ear.

E.g.

- Demyelinating Schwann cells causes abnormal axon structure and function.
- He finds clear similarities in character, structure and function of these texts.
- BDNF is a protein that regulates the structure and function of neuronal synapses.

E.g.

- Furthermore, the dashboard instruments did not function.
- These do not function in the same way as African time lines."
- Other cells of the body do not function as agents of heredity.

E.g.

- The GKW operator is related to the Riemann zeta function.
- Here, is the Riemann zeta function, and is the imaginary unit.
- The Ihara zeta function is an example of a Ruelle zeta function.

E.g.

- Differently named, but same function Modern UN System
- Some alternative definitions lead to the same function.
- The same function may have several different algorithms".

E.g.

- There exists a vast variety of different hash function designs.
- It is based on earlier hash function designs PANAMA and RadioGatún.
- The content of this padding is always specified by the hash function used.

E.g.

- It also continued to function as an episcopal see.
- The hospital continued to function until February 1945.
- She sold the factories in 1812, and they continued to function until 1912.

E.g.

- The probability density function (pdf) for the noncentral "F"-distribution is when formula_9 and zero otherwise.
- This function is fitted to the distribution of detection ranges represented as a probability density function (PDF).
- The probability density function (PDF) for a particle in one dimension is found by solving the one-dimensional diffusion equation.

E.g.

- This is the number of evaluations required to minimize the objective function.
- That is, the objective is to obtain a good player, but without an objective function.
- A search algorithm takes an objective function as input and evaluates candidate solutions one-by-one.

E.g.

- Every continuous function is sequentially continuous.
- Thus, any uniformly continuous function is continuous.
- Any Hölder continuous function is uniformly continuous.

E.g.

- The Cauchy distribution has no moment generating function.
- It follows that the ordinary generating function of the Fibonacci sequence, i.e.
- One of them is: The exponential generating functions are The (ordinary) generating function is an asymptotic series.

E.g.

- Lateral differences in normal man and lateralization of brain function.
- Though specific mechanisms regarding brain function remain to be fully described—e.g.
- This allows for the discovery of causal mechanisms of brain function, and they have e.g.

E.g.

- This can be done by deconstructing the utility function.
- A utility function, such as U=U(X1,X2,X3,X4...Xn), can be constructed, in which the household's utility is a function of various goods and services (Xs).
- Also in economics, a cardinal or ordinal utility function gives the degree of satisfaction of a consumer obtained by consuming quantities and of two goods.

E.g.

- The Palace did not perform its original function.
- Then the estimate of original function F can be written as formula_19.
- In the basement the utility areas of the building retain their original function.

E.g.

- The municipality ceased to function in 1948.
- The mint of Abydos ceased to function in the mid-3rd century AD.
- It opened in 1973, and ceased to function as an independent body on 1 January 2009.

E.g.

- Stone machicolations performed a similar function.
- The hi-hat has a similar function to the ride cymbal.
- BNEP performs a similar function to SNAP in Wireless LAN.

E.g.

- Extend the domain of the partition function by setting "p"(0) = 1.
- For atoms the partition function values can be found in the NIST Atomic Spectra Database.
- In 2011, together with Ken Ono, he developed a finite algebraic formula for the values of the partition function.

E.g.

- Another important function is to debate the major issues of the city.
- The most important function of cementing is to achieve zonal isolation.
- An important function of enzymes is in the digestive systems of animals.

E.g.

- C1orf112 has a domain of unknown function DUF4487.
- DUF4647, a domain of unknown function, is present from amino acid 1-454.
- The domain of unknown function, DUF4641 covers almost the entire protein.

E.g.

- The dose must be adjusted in those with poor kidney function.
- Dosing must be adjusted for altered kidney function and for haemofiltration.
- The clearance by the kidneys is lower, as kidney function has not fully developed.

E.g.

- Here formula_54 is the cumulative distribution function of the standard normal distribution.
- The cumulative distribution function is where formula_16 is the complementary error function.
- The cumulative distribution function is "F"("x";"a","b") = ("x"−"a")/("b"−"a") when "x"∈["a","b"].

E.g.

- Most computer devices require programs to function properly.
- either – WordStar does not function properly on these operating systems.
- The brain requires the use of many neurosteroids to develop and function properly.

E.g.

- A good solution to this is the gamma function.
- See Particular values of the gamma function for calculated values.
- On the other hand, the gamma function is most difficult to avoid."

E.g.

- The contact rate itself may be a function of time.
- A flow that is not a function of time is called steady flow.
- A hydrometer is used to measure the density of the suspension as a function of time.

E.g.

- Yet, other studies show a decrease in cognitive function even at much lower levels.
- Larger doses of amphetamine may impair cognitive function and induce rapid muscle breakdown.
- Past studies have suggested that BPO pantomimes may allow aphasics to avoid an impaired cognitive function.

E.g.

- Very commonly, cancer is associated with a loss of function of INK4a, ARF, Rb, or p53.
- A loss of function mutation in this gene has been associated with developmental encephalopathy.
- These experiments generally involve loss of function, gain of function, tracking and expression.

E.g.

- A "nested" function is a function defined within another function.
- A function defined on an interval of the integers is usually called a sequence.
- Let be a real valued function defined in an open neighborhood of a real number .

E.g.

- The bombe was an electromechanical device whose function was to discover some of the daily settings of the Enigma machines on the various German military networks.
- As common with Amiga games at the time, "Franko" utilizes an eight-directional joystick and a single fire button whose function changes depending on the direction held.
- Unlike CBs, gems do not contain small nuclear ribonucleoproteins (snRNPs), but do contain a protein called survival of motor neuron (SMN) whose function relates to snRNP biogenesis.

E.g.

- Continued use of enemas may weaken the colon's normal function, causing or worsening constipation and colitis.
- By the following day, the company had not succeeded in reestablishing the normal function of their computer systems.
- In children, the outcome of distal radius fracture is usually very good with healing and return to normal function expected.

E.g.

- where is the ordinary one-dimensional Dirac delta function.
- Here is the Dirac delta function.
- The delta function has only radial dependence, so the Laplace operator (a.k.a.

E.g.

- Schizophrenic patients having the risk allele (T\T) show more deficiencies in executive function tasks.
- It exercises the executive function and the regulatory regulation according to the Constitution and the laws"".
- Frontal Assessment Battery The Frontal Assessment Battery (FAB), is a short screening test to evaluate executive function (EF).

E.g.

- Sets must also be designed to function within the space provided.
- Affiliations in Bijelo Polje and Budva function within the Faculty.
- Consequently, Serreta began to function within this new institution.

E.g.

- In case of linear function, "at no point is there an attempt to show that the equation's graph really is a line.
- Linear phase Linear phase is a property of a filter, where the phase response of the filter is a linear function of frequency.
- The simplest case, apart from the trivial case of a constant function, is when is a linear function of , meaning that the graph of is a line.

E.g.

- These are the characteristic function and the imputation concept.
- It is the summation function of the characteristic function of the prime numbers.
- In 1821, William Hamilton began his analysis of Hamilton's characteristic function.

E.g.

- However, the biological function is not known.
- Its exact function is not yet fully known (as of May 2005).
- This means that the function is not going to return any value.

E.g.

- They are larger than vesicles and their specific function varies.
- The number of these stacks varies with the specific function of the cell.
- It was believed that each region of the brain had a set and specific function.

E.g.

- Estetrol has relatively minimal effects on liver function.
- Alcohol may be metabolised more slowly if liver function is impaired.
- B) Cirrhotic patients altered baseline liver function tests (Childs B & C).

E.g.

- The missile train was able to function autonomously for up to 28 days.
- This "icebox on wheels" was a limited success in that it was only able to function in cold weather.
- Swimming helped him develop better body balance in terms of being able to function using his stump and his right hand.

E.g.

- A loss function formula_81 is used for measuring the discrepancy between the target output and the computed output .
- Backpropagation computes the gradient in weight space of a feedforward neural network, with respect to a loss function.
- During model training, the input–output pair is fixed, while the weights vary, and the network ends with the loss function.

E.g.

- Side effects are more common and potentially more severe in those with poor immune function.
- More research also supported that DPP-4 inhibition would not cause compromised immune function.
- This is because trauma exposure can disrupt the HPA axis, thus altering peripheral immune function.

E.g.

- Therefore, he also developed a new production function.
- The two functions are summed, yielding the total production function.
- The production function of a firm or a society can be plotted in three-dimensional space.

E.g.

- People with balance and motor function challenges often need specialized equipment to sit or stand safely and securely.
- People with lesions at the L4 to S2 who are complete paraplegics may have motor function issues in their gluts and hamstrings.

E.g.

- There are similarities of form and function between them.
- This takes advantage of the connectedness of the form and function of language.
- Differentiation between species can often be difficult due to the strong similarities in form and function.

E.g.

- (Here ∂"u" is a new function.
- Michelman was charged with organizing the software support for this new function.
- The second statement, codice_5 re-binds the key sequence "C-x 2" to the new function.

E.g.

- They needed dogs that could function without any special guidance or training.
- The player also needs to buy ammo for most weapons, but a small number can function without the need for ammo.
- In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity.

E.g.

- Let "g" be a square integrable holomorphic function on Ω, i.e.
- Intuitively, it states that every non-constant holomorphic function is locally a polynomial.
- Since "Ch" can be defined for any L function as a holomorphic function on Ω since "h" is integrable on ∂Ω.

E.g.

- However, the biological function is not known.
- Most biological substrates lose their biological function when denatured.
- The solid matter may be an abnormal by-product of a biological function, or a foreign body.

E.g.

- It has a function room that can be hired out for events.
- Set in woodland on the Ringland Road, Taverham, is "Roundwood", an indoor bowling centre with bar and function room.
- There is a dedicated function room that is used for social and business events and can accommodate a maximum of 100 people seated.

E.g.

- Kronecker interpreted a field such as abstractly as the rational function field .
- By the Hilbert–Serre theorem, "F" is a rational function with exactly one pole at formula_26 of order formula_27.
- Ihara (and Sunada in the graph-theoretic setting) showed that for regular graphs the zeta function is a rational function.

E.g.

- The likelihood function is: we solve for the estimated parameters that max "L"*.
- The likelihood function for n independent observations in a logit model is where: "Y" = 1 or 0 (choosing e.g.
- EL estimates are calculated by maximizing the empirical likelihood function subject to constraints based on the estimating function and the trivial assumption that the probability weights of the likelihood function sum to 1.

E.g.

- The CCC often uses the c-base station located in Berlin as an event location or as function rooms.
- The restaurant on the ground floor has a riverside dining area and upstairs are function rooms and offices.
- The main hall on the ground floor has a 3,700-seat capacity and 500-seat function rooms on the second floor.

E.g.

- Let be a smooth function such that near the boundary.
- Thus is a smooth function on , vanishing at .
- Let "g" be a smooth function on "N" vanishing at "f"("x").

E.g.

- The terrorist attack on the World Trade Center on September 11, 2001 left many people with impaired lung function.
- The lung research studied lung function "in vivo" and "in vitro" using animal models developed for pulmonary diseases.
- Phase II trials for asthma treatment showed increased lung function for patients, showing increased forced expiratory volume.

E.g.

- The contribution of each diagram to the correlation function must be divided by its symmetry factor.
- To compute a correlation function in the interacting theory, there is a contribution from the terms now.
- The Euclidean correlation function is just the same as the correlation function in statistics or statistical mechanics.

E.g.

- It can be employed on abstract systems which have a cost function "F".
- Therefore, the players maximize the mathematical expectation of the cost function.
- The following simple example illustrates the importance of the cost function in determining the optimal transport plan.