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field and contains
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).
Semi-conductor materials are often analysable in atom probe, however sample preparation may be more difficult, and interpretation of results may be more complex, particularly if the semi-conductor contains phases which evaporate at differing electric field strengths.
In particular, this field contains all the numbers named in the mathematical constants article, and all algebraic numbers ( and therefore all rational numbers ).
* A tagged union ( also called a variant, variant record, discriminated union, or disjoint union ) contains an additional field indicating its current type, for enhanced type safety.
Since 2012, Essendon's clash guernsey has been predominantly grey, with a red sash fimbriated in black ; the grey field contains, in small print, the names of all Essendon premiership players.
In abstract algebra, a field is a commutative ring which contains a multiplicative inverse for every nonzero element, equivalently a ring whose nonzero elements form an abelian group under multiplication.
In abstract algebra, a finite field or Galois field ( so named in honor of Évariste Galois ) is a field that contains a finite number of elements.
This ring is a field because it contains a multiplicative inverse for each element N other than zero ( an integer that, multiplied by the element modulo p yields 1 ), and it has a finite number of elements ( p ), making it a finite field.
The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties.
The ballpark also contains quirks such as " Tal's Hill ", which is a hill in deep center field on which a flagpole stands, all in fair territory.
Another interesting field is the Volume Space Size which contains the amount of data available on the CD-ROM.
If the packet contains options, this field contains the option type of the next option.
MRI machines make use of the fact that body tissue contains lots of water, and hence protons ( H < sup >+</ sup > ions ), which get aligned in a large magnetic field.
A magnetic field contains energy, and physical systems move toward configurations with lower energy.
At Earth's orbit its typical density is 6 ions / cm < SUP > 3 </ SUP > ( variable, as is the velocity ), and it contains a variable interplanetary magnetic field ( IMF ) of ( typically ) 2 – 5 nT.
However, the ring constructed in this way contains zero divisors and thus cannot be a field.

field and individuals
The structure of our societies and how individuals come to exhibit charitable, philanthropic, and other pro-social, altruistic actions for the common good is a largely researched topic within the field.
# All individuals ( organisms ) exist in a continually changing world of experience ( phenomenal field ) of which they are the center.
The Ph. D. was originally a degree granted by a university to learned individuals who had achieved the approval of their peers and who had demonstrated a long and productive career in the field of philosophy.
Individuals with deeper depressions would be able to discern changes in light over a wider field than those individuals with shallower depressions.
In Strange Defeat he clearly states his view that individuals can change events and he castigates the French government's refusal to trust its own officers in the field of battle, thus leading to the surrender of France to the Nazis.
The Ganzfeld ( German for " whole field ") is a technique used to test individuals for telepathy.
Neurological physical therapy is a field focused on working with individuals who have a neurological disorder or disease.
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field.
In this latter field, R. D. Laing, Thomas Szasz and Michel Foucault were instrumental in moving medicine away from emphasis on " cures " and towards concepts of individuals in balance with their society, both of which are changing, and against which no benchmarks or finished " cures " were very likely to be measurable.
In the late 20th century the appellation of prophet has been used to refer to individuals particularly successful at analysis in the field of economics, such as in the derogatory prophet of greed.
One is awarded every year by Carnegie Mellon University to individuals who have " notably advanced the field of science.
The fundamental assumption of the field is that individuals are influenced by one another's behavior.
Research in the field typically takes a behavioral approach, assuming that individuals are boundedly rational and act on local information.
Industrial sociology, until recently a crucial research area within the field of sociology of work, examines " the direction and implications of trends in technological change, globalization, labour markets, work organization, managerial practices and employment relations to the extent to which these trends are intimately related to changing patterns of inequality in modern societies and to the changing experiences of individuals and families the ways in which workers challenge, resist and make their own contributions to the patterning of work and shaping of work institutions.
Bourdieu and Coleman were fundamentally different at the theoretical level ( as Bourdieu believed the actions of individuals were rarely ever conscious, but more so only a result of their habitus ( see below ) being enacted within a particular field, but this realization by both seems to undeniably connect their understanding of the more latent aspects of social capital.
Many individuals choosing a specialized field of study, such as real estate or accounting, are well-suited for their respective industries through pursuing a Master of Real Estate Development or Master of Science in Accounting degree, for example.
These studies are important to the field because they can lead to better intervention strategies when it comes to counseling individuals with eating disorders.
Individuals in the group collaboratively constructed the new field of psychogeography, which they defined as " the study of the specific effects of the geographical environment ( whether consciously organized or not ) on the emotions and behavior of individuals.
For example, if individuals attend to the right hand corner field of view, movement of the eyes in that direction may have to be actively suppressed.
The AITO Dahl-Nygaard prize is awarded annually to two individuals that have made significant technical contributions to the field of Object-Orientation.
A ganzfeld experiment ( from the German for “ entire field ”) is a technique used in the field of parapsychology to test individuals for extrasensory perception ( ESP ).
Most individuals focus on a particular field such as ecology, evolution, taxonomy, physiology, or molecular biology, and within that field ask questions pertaining to or best answered by examining reptiles and amphibians.
The membership typically comprises distinguished individuals in the relevant field, who may be elected by the other members, or appointed by the government.

field and trained
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 ; ;
In these days of serious shortage of properly trained teachers qualified to teach physically handicapped and mentally handicapped children, the establishment of such an institute will be a major contribution to the field.
Reflecting Archaeoastronomy's development as an interdisciplinary subject, research in the field is conducted by investigators trained in a wide range of disciplines.
This is closely related to the increase in the size of armies throughout the early modern period ; heavily armored cavalrymen were expensive to raise and maintain and it took years to replace a skilled horseman or a trained horse, while arquebusiers and later musketeers could be trained and kept in the field at much lower cost, and were much easier to replace.
Retired judges or private lawyers often become arbitrators or mediators ; however, trained and qualified non-legal dispute resolution specialists form a growing body within the field of ADR.
The hop plant is a vigorous, climbing, herbaceous perennial, usually trained to grow up strings in a field called a hopfield, hop garden, or hop yard when grown commercially.
Infantry were recruited and trained in a wide variety of manners in different regions of Europe all through the Middle Ages, and probably always formed the most numerous part of a medieval field army.
In counter insurgency type campaigns, select and specially trained units of police armed and equipped as light infantry have been designated as police field forces who perform paramilitary type patrols and ambushes whilst retaining their police powers in areas that were highly dangerous.
On Janeway's orders, he trained as a field medic and assisted The Doctor until the Doctor recruited Kes as his primary assistant.
Medical professionals specializing in the field of urology are called urologists and are trained to diagnose, treat, and manage patients with urological disorders.
In a professional or military organization, this does not eliminate the need for skilled and trained communicators to coordinate the per-unit authorized frequency lists and node addresses-it merely allows the deployment of relatively unskilled technicians as " field communicators " and end-users of the existing coordinated architecture.
Larrey manned ambulances with trained crews of drivers, corpsmen and litter-bearers and had them bring the wounded to centralized field hospitals, effectively creating a forerunner of the modern MASH units.
The field was mostly neglected by traditional astronomers though until the 1960s, with most scientists who practiced infrared astronomy having actually been trained physicists.
The synthesis included evidence from biologists, trained in genetics, who studied populations in the field and in the laboratory.
The U. S. Army built an air field in the town in 1942 to train new pilots ; at one time the largest air navigation school in the world, Hondo Army Air Field trained over 14, 000 navigators for service during World War II before closing in 1946.
Lanfranc was trained in the liberal arts, at that time a field in which northern Italy was famous ( there is little or no evidence to support the myth that his education included much in the way of Civil Law, and none that links him with Irnerius of Bologna as a pioneer in the renaissance of its study ).
This is usually performed by civilian specialists trained in the field, often with prior military service in explosive ordnance disposal.
The Praetorian Guard, long strangers to active military operations, were marched into the Campus Martius, regularly drilled, and trained in the construction of fortifications and field works.
The divisions were also specially trained in anti-airborne operations ; during their formation both divisions had undergone month-long anti airborne exercises whilst waiting for their heavy equipment, and had also spent the last 15 months studying the best reactions to a parachute attack in classroom and field exercises.
Fisticuffs in particular are dangerous not only to the participants but to all players on or off the field, and referees are generally trained to respond immediately and aggressively to stop the fight, and to eject and ban instigators of these fights.
According to the Swedish Armed Forces field manual, a trained fire and maneuver team is as effective as four individual soldiers of same quality.
During his youth he trained as a field biologist with The School for Field Studies in Kenya in 1985 and Alaska in 1986.
During the Cold War, NATO forces routinely trained to fight through extensive works called " Soviet-style trench systems ", named after the Warsaw Pact's complex systems of field fortifications, an extension of Soviet field entrenching practices for which they were famous in their Great Patriotic War.

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