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Page "Limit (category theory)" ¶ 99
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For and given
For the moment there was no woman in his life, and it was this vacuum that had given Claire her opportunity.
For readjustment to the U.S., volunteers should be given some separation allowance at the end of their overseas service, based on the length of time served.
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 the industry of this model, the effect of such public pressures in the past has been to hold the price well below the short-run profit-maximizing price ( given the wage rate and the level of GNP ), and even below the entry-limited price ( but not below average cost ).
For some substances, auxiliary properties such as the melting point are given.
For circular fibers in a closely packed hexagonal array, the packing efficiency is given by: Af where Af, and 0.906 is the ratio of the area of a circle to that of the circumscribed hexagon.
For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.
For Mrs. Shaefer -- who had been given a clean bill of health by her own physician at the time she visited Lee -- and her friend were agents for the California Pure Food and Drug Inspection Bureau.
On the clock given him was the inscription, `` For Outstanding Contribution to Billiken Basketball, 1960-61 ''.
For nearly a year, they have been receiving counseling, separately and together, in an effort to understand and overcome the antagonisms which had given rise to the possibility of divorce.
A Sonata For Violin And Piano, called `` Bella Bella '', by Robert Fleming, was given its first United States performance.
For this reason the examples given below are grouped by voltage level.
" For some people, a program is only an algorithm if it stops eventually ; for others, a program is only an algorithm if it stops before a given number of calculation steps.
Algorithm versus function computable by an algorithm: For a given function multiple algorithms may exist.
For Altaicists, the version of Altaic they favor is given at the end of the entry, if other than the prevailing one of Turkic – Mongolic – Tungusic – Korean – Japanese.
For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).
For example, one can say for a given transition that it corresponds to the excitation of an electron from an occupied orbital to a given unoccupied orbital.
For an ideal gas the internal energy is given by
For example, given two image elements A and B, the most common compositing operation is to combine the images such that A appears in the foreground and B appears in the background.
For example, if for a given problem size a parallelized implementation of an algorithm can run 12 % of the algorithm's operations arbitrarily quickly ( while the remaining 88 % of the operations are not parallelizable ), Amdahl's law states that the maximum speedup of the parallelized version is times as fast as the non-parallelized implementation.
For example, some see the World Bank and the IMF as corrupt bureaucracies which have given repeated loans to dictators who never do any reforms.
For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.
For cross-referencing, they are given with list indices from Andreini ( 1-22 ), Williams ( 1-2, 9-19 ), Johnson ( 11-19, 21-25, 31-34, 41-49, 51-52, 61-65 ), and Grünbaum ( 1-28 ).
For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For and diagram
For example, if 95 % of the program can be parallelized, the theoretical maximum speedup using parallel computing would be 20 × as shown in the diagram, no matter how many processors are used.
For example, here is a cell diagram of a Daniell cell:
Diagram: For categories C and J, a diagram of type J in C is a covariant functor.
For example: some early medieval manuscripts of Macrobius include maps of the Earth, including the antipodes, zonal maps showing the Ptolemaic climates derived from the concept of a spherical Earth and a diagram showing the Earth ( labeled as globus terrae, the sphere of the Earth ) at the center of the hierarchically ordered planetary spheres.
For phaneritic felsic rocks, the QAPF diagram should be used, and a name given according to the granite nomenclature.
For example, in the upper left of the four hemes shown, oxygen binds at the left of the iron atom shown in the upper left of diagram.
For each of these possibilities there is a Feynman diagram describing it.
For example, 8k2 in a circuit diagram indicates a resistor value of 8. 2 kΩ.
For functional FMEA, failure modes are identified for each function in a system or equipment item, usually with the help of a functional block diagram.
For the three horizontal orientations on the right side of the diagram, the hand is held outward, with the fingers pointing away from the signer, and presumably toward the viewer.
For water, however, this is not true because the melting point of ordinary ice decreases as a function of pressure, as shown by the dotted green line in the phase diagram.
For those high-pressure forms of ice which can exist in equilibrium with liquid, the diagram shows that melting points increase with ice.
For quality control in manufacturing in the 1960s, Kaoru Ishikawa developed a cause and effect diagram, known as an Ishikawa diagram or fishbone diagram.
For example the lower path in the diagram involves inductive, conductive and capacitive modes.
For the diagram on the right, we have:
For the diagram on the right, the LOPs are found as before:
For example, in the diagram above, White can win the game even if Black moves first.
For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit.
For example, programs ( or program phrases ) might be represented by partial functions, or by Actor event diagram scenarios, or by games between the environment and the system: these are all general examples of domains.
For example, the water phase diagram has a triple point corresponding to the single temperature and pressure at which solid, liquid, and gaseous water can coexist in a stable equilibrium.
For instance, in a two-set Venn diagram, one circle may represent the group of all wooden objects, while another circle may represent the set of all tables.
For example, if one set represents dairy products and another cheeses, the Venn diagram contains a zone for cheeses that are not dairy products.

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