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In general, the surrounding graph must be systematically recolored to turn the ring's coloring into a good one, as was done in the case above where there were 4 neighbors ; for a general configuration with a larger ring, this requires more complex techniques.
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general and surrounding
Meanwhile he has been thinking about the facts surrounding the problem, facts which he knows can never be complete, and the general background, much of which has already been lost to history.
Estonia's international realignment toward the West has been accompanied by a general deterioration in relations with Russia, most recently demonstrated by the controversy surrounding relocation of the Bronze Soldier WWII memorial in Tallinn.
In general, for frost to form the deposition surface must be colder than the surrounding air.
The International Organization for Standardization's ISO 9001: 2008 series describes standards for a QMS addressing the principles and processes surrounding the design, development and delivery of a general product or service.
In general, Reform Judaism maintains that Judaism and Jewish traditions should be modernized and compatible with participation in the surrounding culture.
This included inviting additional lay Catholic and non-Catholic observers, reducing the number of proposed schemata to seventeen ( which were made more general, in keeping with the pastoral nature of the council ) and later eliminating the requirement of secrecy surrounding general sessions.
Six hospitals of various specializations provide medical service for Toruń itself, its surrounding area and to the region in general.
* The Baltic region, an ambiguous term referring to the general area surrounding the Baltic Sea
When the supernova remnant slows to the speed of the random velocities in the surrounding medium, after roughly 30, 000 years, it will merge into the general turbulent flow, contributing its remaining kinetic energy to the turbulence.
A general formal framework that can be used to represent the essential elements of the social situation surrounding a norm is the repeated game of game theory.
As a general rule, lower altitudes tend to have higher temperatures where the sun heats the ground and that heat is then radiated upward, but as the air begins to rise it is trapped by ( 1 ) the surrounding elevation and ( 2 ) the weight of the air ( essentially the atmospheric pressure ) above it.
# Informed consent in the U. S. can be overridden in emergency medical situations pursuant to 21CFR50. 24, which was first brought to the general public's attention via the controversy surrounding the study of Polyheme.
Prentice's efforts to piece together Uncle Rory's fragmentary notes and the minimal clues surrounding his disappearance mirror his efforts to make sense of the world, love, and life in general.
The Franciscus Ziekenhuis Roosendaal is a general hospital for the residents of Roosendaal and surrounding areas.
At the same time the surrounding countryside adapted to market needs and shared in the general increase of wealth.
The city and surrounding area is served by the Medical Center of South Arkansas, MCSA, accredited by the Joint Commission on the Accreditation of Healthcare Organizations, is a general acute-care hospital licensed by the Arkansas Department of Health.
The Hughson Chronicle, a legal newspaper with a general circulation of approximately 4, 200, covers the City of Hughson and surrounding rural areas.
As a nomadic confedation composed mainly of the Xianbei and Wuhuan, the Donghu were prosperous in the 4th century BC during the later Zhou dynasty, forcing surrounding tribes to pay tribute and constantly harassing the State of Zhao ( 325 BC, during the early years of the reign of Wuling ) and the State of Yan ( in 304 BC Qin Kai, general of King Zhao of Yan, was given as a hostage to the Donghu ).
Oswego Municipal Airport, located approximately outside the central business district, serves the general aviation needs of Oswego and the surrounding area.
The remaining area of the township is a legally separate entity from the surrounding City of Novi and has all the powers granted under Michigan state law to general law townships.
By 1888 Queen City offered a considerable business district — five general stores, two grocers, two hardware stores, two hotels, jewelry store, lumber yard, photography gallery, music store, and barber shop were just some of the businesses serving the community and surrounding farms.
Non-conforming postal codes lead to a general misconception of the actual boundaries of this, and surrounding, areas.
general and graph
It is impossible for the graph of a function to intersect a vertical asymptote ( or a vertical line in general ) in more than one point.
Thus all the sets comprise a general directed graph ( ownership defines a direction ), or network construct.
The Delaunay triangulation of a discrete point set P in general position corresponds to the dual graph of the Voronoi tessellation for P. Special cases include the existence of three points on a line and four points on circle.
The unification of two argument graphs is defined as the most general graph ( or the computation thereof ) that is consistent with ( i. e. contains all of the information in ) the inputs, if such a graph exists ; efficient unification algorithms are known.
( N. B., while hierarchies are commonly studied using graph theory, the general terminology used is different, and words such as " direct " may have different general meanings )
The final step in the graph requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity.
The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory.
Cayley's formula is the special case of complete graphs in a more general problem of counting spanning trees in an undirected graph, which is addressed by the matrix tree theorem.
In general, for a puzzle with n disks, there are 3 < sup > n </ sup > nodes in the graph ; every node has three edges to other nodes, except the three corner nodes, which have two: it is always possible to move the smallest disk to the one of the two other pegs ; and it is possible to move one disk between those two pegs except in the situation where all disks are stacked on one peg.
For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e. g., the closed graph theorem in functional analysis.
The term has been generalized to include measurements in much more general mathematical spaces ; for example, in graph theory, one might consider a geodesic between two vertices / nodes of a graph.
In the more general definition of a cuboid, the only additional requirement is that these six faces each be a quadrilateral, and that the undirected graph formed by the vertices and edges of the polyhedron should be isomorphic to the graph of a cube.
A scene graph is a general data structure commonly used by vector-based graphics editing applications and modern computer games.
Donald Knuth states that the Petersen graph is " a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general.
Although such structures may seem strange at first, they can be readily understood by noting that the equivalent generalization of their Levi graph is no longer bipartite, but is rather just some general directed graph.
Therefore, much of the theory about the clique problem is devoted to identifying special types of graph that admit more efficient algorithms, or to establishing the computational difficulty of the general problem in various models of computation.
For the 2010 / 2011 report, the statistics show that violent crime continues a general downward trend observed over the last few decades as shown in the graph.
general and must
Such a list must naturally be selective, and the treatment of each man is brief, for I am interested only in their general ideas on the moral measure of literature.
But there was one thing that he had to stress, and that was that the contribution to the general church expenses, the dollar money, had been seriously falling behind in this church, and that must be looked after immediately.
Our military forces must be capable of contending successfully with any contingency which may be forced upon us, from limited emergencies to all-out nuclear general war.
For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;
It seems reasonable that if general nuclear war is not to be one cataclysmic act of burning each other's citizens to cinders, we must have a manned strategic force of long-endurance aircraft capable of going into China or Russia to find and destroy their strategic forces which continued to threaten us.
Finally, a balance must be effected among project finance, utilization of agricultural surpluses, and general balance of payments support.
A more realistic analysis must take into account the fact that Brandywine people in the urban-fringe area are, in general, less segregated locally than group members in rural areas.
Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.
Five per cent of the voters in each county must sign petitions requesting that the Republicans be allowed to place names of candidates on the general election ballot, or 2
The secretary's greatest achievement is perhaps the rekindling of NATO realization that East-West friction, wherever it take place around the globe, is in essence the general conflict between two entirely different societies, and must be treated as such without regard to geographical distance or lack of apparent connection.
While each scene has its own character and completeness it must fit into the general sequence to which it belongs.
All colonels must retire at age fifty-nine ; and all four-star generals must retire at age sixty-six, or after 12 years as general.
In general, pelagic species must keep swimming to keep oxygenated water moving through their gills whilst demersal species can actively pump water in through their spiracles and out through their gills.
Although there are often disputes about its organisation and funding, British parties to this day must still voice their general support for the NHS in order to remain electable.
The moral guide must then promote and encourage social behaviors that maximize general benefit.
In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.
In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.
In general topological spaces, however, the different notions of compactness are not equivalent, and the most useful notion of compactness — originally called bicompactness — involves families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.
In general, must be renewed periodically, or may be valid for a specific period of time ( e. g., the lifetime of the product upon which the individual is certified ).
In addition, vicars general and episcopal vicars are to be doctors or at least licensed in canon law or theology ( c. 478. 1 ), and canonical advocates must either have the doctorate or be truly expert in canon law ( c. 1483 ).
Benefits must be defined, risks assessed, and cost quantified in three general areas:
In general the parameter a and the position of the axis and directrix are not given but must be determined from other information.
The subgroup of generated by all commutators is called the derived group or the commutator subgroup of G. Note that one must consider the subgroup generated by the set of commutators because in general the set of commutators is not closed under the group operation.
must be homogeneous and has the general form
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