The same argument proves that no subfield of the real field is algebraically closed ; in particular, the field of rational numbers is not algebraically closed.

The field of chemistry uses analysis in at least three ways: to identify the components of a particular chemical compound ( qualitative analysis ), to identify the proportions of components in a mixture ( quantitative analysis ), and to break down chemical processes and examine chemical reactions between elements of matter.

Field automorphisms are important to the theory of field extensions, in particular Galois extensions.

The < tt > MixColumns </ tt > step can also be viewed as a multiplication by a particular MDS matrix in a finite field.

The term argot is also used to refer to the informal specialized vocabulary from a particular field of study, hobby, job, sport, etc.

Ideas from it have proved influential, and have been developed by others, in particular dessins d ' enfants and a new field emerging as anabelian geometry.

The black letter law refers to the basic standard elements for a particular field of law, which are generally known and free from doubt or dispute.

The International Organization for Standardization, ISO, has a special technical committee for cycles, TC149, that has the following scope: " Standardization in the field of cycles, their components and accessories with particular reference to terminology, testing methods and requirements for performance and safety, and interchangeability.

Graduate programs in BME, like in other scientific fields, are highly varied, and particular programs may emphasize certain aspects within the field.

However, Ogden prescribed that any student should learn an additional 150-word list for everyday work in some particular field, by adding a word list of 100 words particularly useful in a general field ( e. g., science, verse, business, etc.

In particular, they have been found to be exceptionally good field emitters.

At the Master's level and higher, students tend to specialize in a particular field.

Of particular note, programs that were placed within the top 10 % of all size programs in that field based on an average of the R95 and S95 rank order include Aeronautics, Astrophysics, Biochemistry and Molecular Biophysics, Bioengineering, Biology, Chemical Engineering, Chemistry, Electrical Engineering, Environmental Science and Engineering, Geology, Geophysics, Materials Science, Mechanical Engineering, Physics, Planetary Science, and Social Science ( Economics ).

The term is synonymous with wealth ( commonly denoted as a person with fame and fortune ), implied with great popular appeal, prominence in a particular field, and is easily recognized by the general public.

While people may gain celebrity status as a result of a successful career in a particular field ( primarily in the areas pertaining towards sports and entertainment ), in other cases, people become celebrities due to media attention for their extravagant lifestyle or wealth ( as in the case of a socialite ); for their connection to a famous person ( as in the case of a relative of a famous person ); or even for their misdeeds ( as in the case of a well-known criminal ).

Therefore, there exists a contact force density or Cauchy traction field that represents this distribution in a particular configuration of the body at a given time.

It is not a vector field because it depends not only on the position of a particular material point, but also on the local orientation of the surface element as defined by its normal vector.

* Collection ( museum ), objects in a particular field forms the core basis for the museum

The company organization of each camp had a dual-authority supervisory staff: firstly, Department of War personnel or Reserve officers ( until 1 July 1939 ), a " company commander " and junior officer, who were responsible for overall camp operation, logistics, education and training ; and secondly, ten to fourteen technical service civilians, including a camp " superintendent " and " foreman ," employed by either the Departments of Interior or Agriculture, responsible for the particular field work.

In particular, this field contains all the numbers named in the mathematical constants article, and all algebraic numbers ( and therefore all rational numbers ).

A design pattern in architecture and computer science is a formal way of documenting a solution to a design problem in a particular field of expertise.

An organized collection of design patterns that relate to a particular field is called a pattern language.

) is reserved for those who can prove a particular distinction in the field, usually through a body of published work or the submission of a dissertation.

Evidence is plentiful that early and later also he has been indebted to the Gothic romancers, who deal in extravagant horror, to the symbolists writing at the end of the preceding century, and in particular to the stream-of-consciousness novelists, Henry James and James Joyce among them.

In particular, Governor Nelson Rockefeller has expressed as cogently and clearly as anyone the case for a resumption of atmospheric tests.

In addition, petitioner has failed to show any particular need for the report and notes.

By dealing with common landscape in an uncommon way, Roy Mason has found a particular niche in American landscape art.

Hence, thought of as a line in a particular plane **yp, any tangent to Q has a unique image and moreover this image is the same for all planes through L.

The preferential mating of this particular population has been analyzed in a separate study.

Of particular utility in the analysis of the development, persistence, and change of social systems has been the use of the master or comprehensive processes.

The broad conclusions of that pioneering work remain undisturbed, but subsequent research has expanded and somewhat altered their empirical support, has suggested important revisions in the general analytic frame of reference, and has sharpened the meaning of particular analytic concepts in this area.

Yet the truth, according to the New Testament, is that every local church has its existence only by being the embodiment of the whole church in that particular place.

By seeing such varied places, both interesting and beautiful, you will become aware of the many different civilizations Rome has lived through, and in particular, get a feel of Renaissance Rome.

Mr. Nixon, he believes, has no particular political philosophy and mismanaged his own campaign.

`` The white colonnaded, cedar-roofed Southern mansion is directly traceable via the grey and buff stone of grey-skied England to the golden stucco of one particular part of the blue South, the Palladian orbit stretching out from Vicenza: the old mind of Andrea Palladio still smiles from behind many an old rocking chair on a Southern porch, the deep friezes of his architectonic music rise firm above the shallower freeze in the kitchen, his feeling for light and shade brings a glitter from a tall mint julep, his sense of columns framing the warm velvet night has brought together a million couple of mating lips ''.

The term " the United States " has historically been used, sometimes in the plural (" these United States "), and other times in the singular, without any particular grammatical consistency.

Anthropologists ' involvement with the U. S. government, in particular, has caused bitter controversy within the discipline.

At the same time, Angola has promoted the revival of the Community of Portuguese-Speaking Countries ( CPLP ) as a forum for cultural exchange and expanding ties with Portugal ( its former ruler ) and Brazil ( which shares many cultural affinities with Angola ) in particular.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

However, if the excited atom has been previously ionized, in particular if one of its inner shell electrons has been removed, a phenomenon known as the Auger effect may take place where the quantity of energy is transferred to one of the bound electrons causing it to go into the continuum.

It has had particular influence in folk music, and has become an emblematic African American spiritual.

Alain de Lille has often been confounded with other persons named Alain, in particular with another Alanus ( Alain, bishop of Auxerre ), Alan, abbot of Tewkesbury, Alain de Podio, etc.

Often dismissed as an unreliable tradition, it has been studied with attention by modern scholars, in particular Neil Christie, who see in it a possible record of a formal invitation by the Byzantine state to settle in northern Italy as foederati, to help protect the region against the Franks, an arrangement that may have been disowned by Justin II after Narses ' removal.

He predicts that this man will be able to divine the color of this particular shade of blue, despite the fact that he has never experienced it.