For instance, if we impose some requirements on a distribution f, we can attempt to translate these requirements in terms of the Fourier transform of f. The Paley – Wiener theorem is an example of this.

For many years, Paley worked in public relations for the fashion designer Mainbocher.

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

For the past 40 years Congress has advocated a carefully planned, balanced and competitive railway system.

For a few details of the system the lines are 1-1/4'' '' X-Tru-Coat, a product of Republic Steel Corp., and all lines are welded.

For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.

For a time following the abandonment of the local plant, electric current for Manchester was brought in from the south with an emergency tie-in with the Vermont Marble Company system to the north.

For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.

For the purposes of the treaty system, Antarctica is defined as all of the land and ice shelves south of 60 ° S latitude.

For example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically ( or thermally ) insulated ; an insulated wall approximates an adiabatic boundary.

For tourists, the Acapulco city government has established a system of yellow buses with Acapulco!

For example a two dimensional array with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression: ( in a row major language ) and ( in a column major language ) in the case of a zero-based indexing system.

For example a target acquisition element can send a message with target details which is automatically routed through the tactical and technical fire control elements to deliver firing data to the gun's laying system and the gun automatically laid.

For bridged alkenes, the Bredt's rule states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large enough.

For example, when a user logs into a computer that is part of a Windows domain, Active Directory checks the submitted password and determines whether the user is a system administrator or normal user.

For a system of point particles without any intrinsic angular momentum ( see below ), it turns out to be

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For a Gaussian response system ( or a simple RC roll off ), the rise time is approximated by:

For example, the three-domain system separates Archaea and Bacteria, previously grouped into the single kingdom Monera ( bacteria ).

For example, the DIN 41612 connectors used in the VMEbus system can withstand 50 to 500 insertions and removals ( called mating cycles ), depending on their quality.

For example in the case of anthrax, it is likely that by 24 – 36 hours after an attack, some small percentage of individuals ( those with compromised immune system or who had received a large dose of the organism due to proximity to the release point ) will become ill with classical symptoms and signs ( including a virtually unique chest X-ray finding, often recognized by public health officials if they receive timely reports ).

For example, an IBM PC might have either a monochrome or a color display adapter ( using different display memory addresses and hardware ), but a single, standard, BIOS system call may be invoked to display a character at a specified position on the screen in text mode.

For this reason, activists talk about the issue of ecological debt which implies a sort of predatory economic system.

For most purposes, most jurisdictions, including the U. S. federal system and most states, have merged the two courts.

For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward ( though the equilibrium constant will stay the same ).

For many decades thereafter, historians derided the Parliamentary Republic as a quarrel-prone system that merely distributed spoils and clung to its laissez-faire policy while national problems mounted.

For example, the Canadian province of Quebec, which is French-speaking, has its own system of French-speaking television, movie and music celebrities.

For one thing, there is a natural belt of rock across the river bed ; ;

For the only time in the opera, words are not set according to their natural inflection ; ;

For so long as death was not violent, it was natural and to be welcomed, making a funeral a feast.

For the Aztec the count by 20s was completely natural.

For example, Pyrethrum ( refers to several Old World plants of the genus Chrysanthemum ) is a natural insecticide with minimal environmental impact.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography.

For Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").

For most of human history, pearls were the ultimate precious beads of natural origin because of their rarity, although the pearl-culturing process has now made them far more common.

For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.

For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.

For natural numbers ( taken to include 0 ) n and k, the binomial coefficient can be defined as the coefficient of the monomial X < sup > k </ sup > in the expansion of.

Some sets are infinite ; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by, has infinitely many elements, and we cannot use any normal number to give its size.

For example, Georg Cantor ( who introduced this concept ) demonstrated that the real numbers cannot be put into one-to-one correspondence with the natural numbers ( non-negative integers ), and therefore that the set of real numbers has a greater cardinality than the set of natural numbers.

* For every natural number, the-sphere is compact.

For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant N such that no bit of Ω after the Nth can be proven to be one or zero within that system.

For example, the cofinality of ω² is ω, because the sequence ω · m ( where m ranges over the natural numbers ) tends to ω² ; but, more generally, any countable limit ordinal has cofinality ω.

For this reason, its practice violated the natural laws of medicine, transforming health care practitioners into those who harm rather than heal.

For example, by inoculating in the months of milder climate, one had a better chance of fighting the infection and becoming immune instead of the alternative: natural exposure to the disease during harsher weather, when the body's defenses were already challenged.

For example, philosopher John D. Kenyon writes: Reason might manage to raise a doubt about the truth of a conclusion of natural inductive inference just for a moment in the study, but the forces of nature will soon overcome that artificial skepticism, and the sheer agreeableness of animal faith will protect us from excessive caution and sterile suspension of belief.

For instance, we could define natural number as follows ( after Peano ):

For example, Darwinism may be used to refer to Darwin's proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow.

For example, while burning an area of fairly thick forest and thus turning it into a more open, grassy environment might reduce the viability of a large browser ( an animal that eats leaves and shoots rather than grasses ), the reverse could also be true: removing the browsing animals ( by eating them, or by any other means ) within a few years produces a very thick undergrowth which, when a fire eventually starts through natural causes ( as fires tend to do every few hundred years ), burns with greater than usual ferocity.