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Page "Characteristic class" ¶ 17
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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 Chern
For complex vector bundles of dimension greater than one, the Chern classes are not a complete invariant.
For this, we need the following fact: the first Chern class of a trivial bundle is zero, i. e.,
For a line bundle L, the Chern character ch is defined by
For example, if the manifold has dimension 6, there are three linearly independent Chern numbers, given by c < sub > 1 </ sub > ³, c < sub > 1 </ sub > c < sub > 2 </ sub >, and c < sub > 3 </ sub >.
For example, in G = U ( N ) Chern – Simons theory at level k the normalized correlation function is, up to a phase, equal to
For example, if one considers a Chern – Simons theory with gauge group G on a manifold with boundary then all of the 3-dimensional propagating degrees of freedom may be gauged away, leaving a 2-dimensional conformal field theory known as a G Wess – Zumino – Witten model on the boundary.
For hypersurfaces, the result had been shown first by Allendoerfer and Weil in 1940 which is cited in this paper of Chern.
For example, Chern v. Bank of America held that a loan officer ’ s statement over the phone about interest rates was “ advertising .” Conversely, Bank of the West v. Superior Court implied that advertising might require “ widespread promotional activities directed to the public-at-large ” and that mere “ personal solicitations are not advertising .”
For these surfaces with second Chern class can be any integer from 3 to 11.

For and class
For instance, in giving school grades or in making recommendations for the award of a college scholarship, does he consciously or unconsciously favor students of one or another social class??
For example, the class of all sets would be a proper class.
For example, the ( discounted ) annual season ticket from London to Brighton ( standard 2nd class ) as of January 2010 costs £ 3, 280 for, while an annual DB ( German ) 100 BahnCard, which allows one year's travel on the entire German rail network, costs almost exactly the same ( 3800 Euros ).
For example the entries in the Sales Journal are taken and a debit entry is made in each customer's account ( showing that the customer now owes us money ) and a credit entry might be made in the account for " Sale of class 2 widgets " ( showing that this activity has generated revenue for us ).
For the class, see Bacilli.
For example, an " X " is used to indicate a variable group amongst a class of compounds ( though usually a halogen ), while " R " is used for a radical, meaning a compound structure such as a hydrocarbon chain.
For example, most law students in the United States are required to take a class in Constitutional Law during their first year, and several law journals are devoted to the discussion of constitutional issues.
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 example, a 1978 environmental law treatise reprinted the entire text of Rule 23 and mentioned " class actions " 14 times in its index.
For example, thousands of shareholders of a public company may have losses too small to justify separate lawsuits, but a class action can be brought efficiently on behalf of all shareholders.
For example, a court might certify a case for class treatment where a number of individual bond-holders sue to determine whether they may convert their bonds to common stock.
For example, in the United States, class lawsuits sometimes bind all class members with a low settlement.
For example, settlement of class actions follows a predictable path of negotiation with class counsel and representatives, court scrutiny, and notice.
For example, a " Banana " class would represent the properties and functionality of bananas in general.
For about a decade, every student taking the 6. 004 class at MIT was part of a team — each team had one semester to design and build a simple 8 bit CPU out of 7400 series integrated circuits.
For instance, you might wish to add spell checking to all s, which in most languages would require access to the source code of the string class — and such basic classes are rarely given out in source form.
For these reasons, it is often considered a party of the centre-left and its base consists largely of the working class.
For the upper class of the 17th, 18th and 19th centuries, diplomatic immunity was an easy concept to understand.
For example, under standard organizational and casing conventions, might be the name of a file that defines a class called X.
* For those who prefer low distortion figures, the use of tubes with class A ( generating little odd-harmonic distortion, as mentioned above ) together with symmetrical circuits ( such as push – pull output stages, or balanced low-level stages ) results in the cancellation of most of the even distortion harmonics, hence the removal of most of the distortion.
For instance, some argue that modern representative democracy is a realization of political egalitarianism, while in reality, most political power still resides in the hands of a ruling class, rather than in the hands of the people.
For path-connected spaces, therefore, we can write π < sub > 1 </ sub >( X ) instead of π < sub > 1 </ sub >( X, x < sub > 0 </ sub >) without ambiguity whenever we care about the isomorphism class only.

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