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Page "Homomorphism" ¶ 32
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Some Related Sentences

For and example
For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.
For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.
For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;
For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:
For example: 1.
For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.
For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.
For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.
For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;
For example, a 12-to-one engine would power a supersonic VTOL fighter.
For example: Af.
For example: Af.
For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.
For example: Af.
For example, let's consider a standard 283 cubic inch Chevy Aj.
For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.
For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.
For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.
For example, the Friday after Thanksgiving can be substituted for Washington's birthday.
For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.
For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.
For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.

For and functions
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 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.

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