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Page "Graph theory" ¶ 57
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these and applications
One effect of the spirited give-and-take of these discussions was to focus attention on practical applications and the necessity of being armed with the facts: knowledge of the destructive force of even the tiniest `` tactical '' atomic weapon would have a bearing on judgments as to the advisability of its use -- to defend Berlin, for example ; ;
However, electrostatic focus, important for many applications, has not been realized for these devices.
See Amiga software for more information on these applications.
From these studies arose the concept of using aerial applications of herbicides to destroy enemy crops to disrupt their food supply.
For these reasons many CAD applications use the DWG format which can be licensed from AutoDesk or non-natively from the Open Design Alliance.
Some classic examples of these types of tasks are multimedia applications ( images, video, and sound ), as well as many types of scientific and engineering tasks.
Because of these problems, various standardized tests, often called " benchmarks " for this purpose such as SPECint – have been developed to attempt to measure the real effective performance in commonly used applications.
Most of these applications exploit the property of certain isotopes of californium to emit neutrons.
The most talked-about applications of these models in recent years have been their use to infer the consequences of increasing greenhouse gases in the atmosphere, primarily carbon dioxide ( see greenhouse gas ).
In these applications, an important goal is often the recovery of information encoded ( or modulated ) onto the AC signal.
For these non-traditional applications, hundreds of weaves or patterns have been invented.
Yet, due to easier physical implementation of classical controller designs as compared to systems designed using modern control theory, these controllers are preferred in most industrial applications.
In practical applications these three elements are typically contained in one unit.
However, also available general-purpose DBMSs can often be used for such purpose, if they provide basic user-interfaces for straightforward database applications ( limited query and data display ; no real programming needed ), while still enjoying the database qualities and protections that these DBMSs can provide.
A key enabling factor for these applications is the fact that the DFT can be computed efficiently in practice using a fast Fourier transform ( FFT ) algorithm.
Different applications will emphasize different design requirements, leading to different choices among these ( and other ) optimizations, or requiring a filter of a higher order.
Due to the specialized nature of the exposure and the higher degree of control afforded by the film lab equipment, these intermediate and release stocks are specially designed solely for these applications and are generally not feasible for camera shooting.
GIS applications are tools that allow users to create interactive queries ( user-created searches ), analyze spatial information, edit data in maps, and present the results of all these operations.
Most graphics applications will read and display GIF images with any of these table sizes ; but some do not support all sizes when creating images.
For these applications, more expensive stainless steel is preferred.
Parts of hydrology concern developing methods for directly measuring these flows or amounts of water, while others concern modelling these processes either for scientific knowledge or for making prediction in practical applications.
In these applications, the set of all inputs is some sort of metric space, and the hashing function can be interpreted as a partition of that space into a grid of cells.

these and graphs
The red lines in these three graphs correspond to the simulated images above, and the green lines were computed by applying the corresponding parameters to the squared Bessel function given above.
However, these other algorithms can also find minimum spanning forests of disconnected graphs, while Prim's algorithm requires the graph to be connected.
Three of these graphs are shown below, and they clearly show why Medicare ( as currently formulated ) is on the path to fiscal insolvency: No matter what the wage level, marital status, or retirement date, a man or woman can expect to receive benefits that will cost the system far more than the taxes he or she paid into the system.
The graphs of these polynomials ( up to n = 5 ) are shown below:
However, putting all of these conditions together, it remains open whether 3-connected 3-regular bipartite planar graphs must always contain a Hamiltonian cycle, in which case the problem restricted to those graphs could not be NP-complete ; see Barnette's conjecture.
Examples of discrete structures are ( finite ) graphs, permutations, trees, and so on ; each of these has an associated generating function which counts how many structures there are of a certain size.
The definition of a scene graph is fuzzy because programmers who implement scene graphs in applications and, in particular, the games industry take the basic principles and adapt these to suit particular applications.
In these scene graphs, the composite design pattern is often employed to create the hierarchical representation of group nodes and leaf nodes.
Despite the name, these graphs are not necessarily trees, because of the possibility of marriages between distant relatives, but the time ordering of births ( a parent's birthday is always prior to their child's birthday ) causes these graphs to be acyclic.
A naive breadth-first search of these graphs would quickly consume all the memory of any modern computer.
The properties of these random graphs are different from the properties found in scale-free networks, and therefore a model for this growth process is needed.
There are numerous instances of characters listed under section headers which are merely artificial extractions of portions of those characters, and some of these portions are not even actual graphs with an independent existence ( e. g., 亅 jué or juě in 了 liǎo ), as explained by Serruys ( 1984 ), who therefore prefers the term ‘ glyph ’ extraction rather than graphic extraction ( p. 657 ).
His key observation was that these axioms provide an abstraction of " independence " that is common to both graphs and matrices.
In these graphs, the vertices may be labeled by bitvectors, in such a way that two vertices are adjacent if and only if the corresponding bitvectors differ in a single position.
Nevertheless, there are algorithms for these problems that run in exponential time or that handle certain more specialized input graphs in polynomial time.
Forms, rubrics, charts and graphs are useful in these situations to objectively document personal traits with the goal of improving performance in current and future projects.
Within the Brain Atlases, these 3-D ISH digital images and graphs reveal, in color, the regions where a given gene is expressed.
Markström's searches found four graphs on 24 vertices in which the only power-of-two cycles have 16 vertices ; one of these four graphs is planar.

these and are
She said, `` My name is Songau and these girls are Ponkob and Piwen.
This is puzzling to an outsider conscious of the classic tradition of liberalism, because it is clear that these Democrats who are left-of-center are at opposite poles from the liberal Jefferson, who held that the best government was the least government.
And the great majority of these people are of Anglo-Saxon or Celtic descent.
A national consensus of near unanimity exists that these governmental efforts are desirable as well as necessary.
I have just asked these questions in the Pentagon, in the White House, in offices of key scientists across the country and aboard the submarines that prowl for months underwater, with neat rows of green launch tubes which contain Polaris missiles and which are affectionately known as `` Sherwood Forest ''.
Only one rule prevailed in my conversations with these men: The more highly placed they are -- that is, the more they know -- the more concerned they have become.
For these centers, too, are on the gold circuit.
What these fragments are and how they activate the go order may not be revealed.
Often, too, the social institutions are housed in these pavilions and palaces and bridges, for these great structures are not simply `` historical monuments '' ; ;
But more important, and the thing which the casual traveler and the blind sojourner often do not see, is that these places and activities are often the settings in which Persians exercise their extraordinary aesthetic sensibilities.
Water, air, fruit, poetry, music, the human form -- these things are important to Persians, and they experience them with an intense and discriminating awareness.
The line of an eyebrow, the color of the skin, a ghazal from Hafiz, the purity of spring water, the long afternoon among the boughs which crowd the upper story of a pavilion -- these things are noticed, judged, and valued.
Where are the writers to treat these changes??
Lucretius has remarked: `` The reason why all Mortals are so gripped by fear is that they see all sorts of things happening in the earth and sky with no discernable cause, and these they attribute to the will of God ''.
We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.
And Zen Buddhism, though it is extremely difficult to understand how these internal contradictions are reconciled, helps them in their struggle to achieve personal salvation through sexual release.
Whatever pole of this contrast one emphasizes and whatever the tension between these two approaches to understanding the artistic imagination, it will be readily seen that they are not mutually exclusive, that they belong together.
Underlying these conceptions of mimesis are certain presuppositions concerning the nature of primary human experience which require some exposition before the main argument can proceed.
Later abstractive and rational processes may indicate errors of judgment in these apprehensions of value, but the apprehensions themselves are the primary stuff of experience.
Of these there are surely few that would be more rewarding discoveries than Verner Von Heidenstam, the Swedish poet and novelist who received the award in 1916 and whose centennial was celebrated two years ago.
Somewhat uneven in interest for an average reader, eight or ten of these are among the finest of their kind in literature.

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