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.

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.

* However, a larger 35ml measure is increasingly used ( and in particular is standard in Northern Ireland ), which contains 1. 4 units of alcohol.

Each tip of the " Y " of an antibody contains a paratope ( a structure analogous to a lock ) that is specific for one particular epitope ( similarly analogous to a key ) on an antigen, allowing these two structures to bind together with precision.

The second, larger inventory is the Regional Inventory ( RI ), which is broken down by county and contains both those pubs listed in the NI and other pubs that are not eligible for the NI, due to reasons such as having been overly modified, but are still considered historically important, or have particular architectural value.

* Conjugate prior, in Bayesian statistics, a family of probability distributions that contains a prior and the posterior distributions for a particular likelihood function ( particularly for one-parameter exponential families )

In particular, the spatial power spectrum ( how much difference is observed versus how far apart the regions are on the sky ) contains small anisotropies, or irregularities, which vary with the size of the region examined.

* ( Note: this book contains very useful, information dense chapters on primate evolution in general, and human evolution in particular, including fossil history ).

In particular, the C-terminus often contains serine ( Ser ) or threonine ( Thr ) residues that, when phosphorylated, increase the affinity of the intracellular surface for the binding of scaffolding proteins called β-arrestins ( β-arr ).

As with Doom, Heretic contains different cheat codes that variously give the player invulnerability, all weapons, kill everything on a particular level.

Then is a totally ordered subset of A, hence there exists a maximal totally ordered subset containing, in particular A contains a maximal totally ordered subset.

In the early 18th century, Nicolas Malebranche wrote " An organized body contains an infinity of parts that mutually depend upon one another in relation to particular ends, all of which must be actually formed in order to work as a whole ," arguing in favor of preformation, rather than epigenesis, of the individual ; and a similar argument about the origins of the individual was made by other 18th century students of natural history.

In common law systems that rely on testimony by witnesses, a leading question or suggestive interrogation is a question that suggests the particular answer or contains the information the examiner is looking to have confirmed.

* The librarian can use the catalogue to find out whether the library owns an item with a particular title or author, or that contains a short story, chapter, song, or poem with a particular title, or to compile a list of books by a particular author or on a particular subject.

In particular, the Babylonian text Dialogue of Pessimism contains similarities to the agonistic thought of the sophists, the Heraclitean doctrine of contrasts, and the dialectic and dialogs of Plato, as well as a precursor to the maieutic method of Socrates.

The Ekottara Āgama in particular contains variant teachings of basic doctrines such as the Noble Eightfold Path, which are different from those found in the Pali Canon.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

In the theory of formal languages in computability theory, a pumping lemma or pumping argument states that, for a particular language to be a member of a language class, any sufficiently long string in the language contains a section, or sections, that can be removed, or repeated any number of times, with the resulting string remaining in that language.

In data structures, a data structure is said to have sequential access if one can only visit the values it contains in one particular order.

In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior.

The yearbook contains scholarly articles and reviews, dealing with Inklings members in particular, but also with fantasy literature and mythopoeia in general.

In Harmelin, Justice Scalia, joined by Chief Justice Rehnquist, said " the Eighth Amendment contains no proportionality guarantee ," and that " what was ' cruel and unusual ' under the Eighth Amendment was to be determined without reference to the particular offense.

The zodiac of a given planet is the band that contains the path of that particular body ; e. g., the " zodiac of the Moon " is the band of five degrees above and below the ecliptic.