For the interpretation of these significant investigations, it should be remembered that reciprocal relations exist in the hypothalamus with respect to autonomic and somatic functions which are closely associated with the emotions.

For many years he had provided music and entertainment for functions throughout the Northwest.

For the Greeks, Apollo was all the Gods in one and through the centuries he acquired different functions which could originate from different gods.

For liturgical functions other than the Mass the bishop typically wears the cope.

For example, one cannot define all the trigonometric functions in a Banach algebra without identity.

For non-integer α, the functions J < sub > α </ sub >( x ) and J < sub >− α </ sub >( x ) are linearly independent, and are therefore the two solutions of the differential equation.

For the spherical Bessel functions the orthogonality relation is:

For instance, NASA has extremely rigorous software testing procedures for many operating systems and communication functions.

For a certain class of Green functions coming from solutions of integral equations, Schmidt had shown that a property analogous to the Arzelà – Ascoli theorem held in the sense of mean convergence — or convergence in what would later be dubbed a Hilbert space.

For those priests over 80 who became cardinal-deacons and were not ordained to the episcopacy, this is the highest position they can normally attain in the Church hierarchy ( though all cardinals rank above bishops in rank and order of precedence, those cardinals who are not bishops do not have the right to perform the functions reserved solely to bishops, such as ordination ).

For some distributed parameter systems the vectors may be infinite-dimensional ( typically functions ).

For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in ROM, and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require hardware floating-point.

For example: clairsentience is one of the six human special functions mentioned or recorded in Buddhism.

For the same reason, filter functions whose critical response is at lower frequencies ( compared to the sampling frequency 1 / T ) require a higher order, more computationally intensive FIR filter.

For polynomials of degree four and smaller there are explicit formulae for the roots ( the formulae are elementary functions ).

For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using Bessel functions of the first kind, as a function of the sideband number and the modulation index.

For instance, by assigning to every open set U the associative algebra of real-valued continuous functions on U, one obtains a presheaf of algebras on X.

For periodic functions, both the Fourier transform and the DTFT comprise only a discrete set of frequency components ( Fourier series ), and the transforms diverge at those frequencies.

Direction of causal flow is upward. For a multivariate function, functional decomposition generally refers to a process of identifying a set of functions such that

For crimes that are not committed in the exercise of his functions, the President of the Republic answers before the common courts, once his term of office has ended.

For example, operation-preserving functions exist between the set of real numbers with addition and the set of positive real numbers with multiplication.

For most types of hashing functions the choice of the function depends strongly on the nature of the input data, and their probability distribution in the intended application.

For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin, which is, like sin, conventionally denoted in roman type and not in italics ( note that software libraries of mathematical functions often use the name < tt > asin </ tt >):

For example, scientists developing a new viral drug to treat an infection with a pathogenic virus ( e. g. HIV-1 ) may find that a candidate drug functions to prevent viral replication in an in vitro setting ( typically cell culture ).

For this purpose the Internet Protocol defines an addressing system that has two functions: identifying hosts and providing a logical location service.

For many film-goers, De Palma's gangster films, most notably Scarface and Carlito's Way, pushed the envelope of violence and depravity, and yet greatly vary from one another in both style and content and also illustrate De Palma's evolution as a film-maker.

For example, if in a search task the reaction times vary proportionally with the number of elements, then it is evident that this cognitive process of searching involves serial instead of parallel processing.

For pregnant women, guidelines vary: screening women with age or other risk factors is recommended by the U. S. Preventive Services Task Force ( USPSTF ) ( which recommends screening women under 25 ) and the American Academy of Family Physicians ( which recommends screening women aged 25 or younger ).

For instance, the soma of a neuron can vary from 4 to 100 micrometers in diameter.

For example, teaching on predestination may vary in terms of three considerations.

For instance, the number of cities having a certain population size is found to vary as a power of the size of the population, and hence follows a power law.

For example, a human voice can be sent as a radio wave or microwave by making the wave vary to correspond variations in the voice.

For an efficient way to partition sampling resources among groups that vary in their means, their variances, and their costs, see " optimum allocation ".

For example, the lot size for a residence in Chicago is usually deep, while the width can vary from wide for a row house to wide for a large stand – alone house.

For some ingredients, e. g. flour, this quantity can vary considerably.

For most types of deer in modern English usage, the male is called a " buck " and the female is termed a " doe ", but the terms vary with dialect, and especially according to the size of the species.

For a propagating electromagnetic wave, such as a surface wave propagating along the surface of the Earth, these parameters vary with frequency and direction.

For instance 1 ampere of current consists of about electrons per second ; even though this number will randomly vary by several billion in any given second, such a fluctuation is minuscule compared to the current itself.

For a waveguide or transmission line containing more than one type of dielectric medium ( such as microstrip ), the wave impedance will in general vary over the cross-section of the line.

For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used.

For this reason, the quality of the video produced by decoding the results of different encoders that use the same video codec standard can vary dramatically from one encoder implementation to another.

For regular variables, the period of variation and its amplitude can be very well established ; for many variable stars, though, these quantities may vary slowly over time, or even from one period to the next.

For example, the fern Ceratopteris thalictrioides has spores of only one kind, which vary continuously in size.

For discussion of why the thermal energy storage abilities of pure substances vary, see factors that affect specific heat capacity.

For example, at the peak age of 15, the dark-adapted pupil can vary from 4 mm to 9 mm with different individuals.

For tournaments, the fee might be 10 % of the buy-in, but can vary widely.

For bottled spirits over 100 ml containing no solids, actual alcohol content is allowed to vary within 0. 15 % of ABV stated on the label.

For any given organization, measures of effectiveness vary, depending upon its mission, environmental context, nature of work, the product or service it produces, and customer demands.

For solids, on the other hand, diffusion of atoms to the surface might not be sufficient and the surface tension can vary with an increase in surface area.

For example, the levels of ionizing radiation and radio interference can vary by factors of hundreds to thousands ; and the shape and location of the magnetopause and bow shock wave upstream of it can change by several Earth radii, exposing geosynchronous satellites to the direct solar wind.