Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.

The finite fields are classified by size ; there is exactly one finite field up to isomorphism of size p < sup > k </ sup > for each prime p and positive integer k. Each finite field of size q is the splitting field of the polynomial x < sup > q </ sup > − x, and thus the fixed field of the Frobenius endomorphism which takes x to x < sup > q </ sup >.

In FIM, the ionization takes place close to the tip, where the field is strongest.

However, in physics, it is common to treat an extended object as a " particle " or " field " with its own unique ( e. g. center of mass ) position at any given time, so that the world line of a particle or light beam is the path that this particle or beam takes in the spacetime and represents the history of the particle or beam.

Research in the field typically takes a behavioral approach, assuming that individuals are boundedly rational and act on local information.

This polynomial resembles the divisor in a polynomial long division, which takes the message as the dividend and in which the quotient is discarded and the remainder becomes the result, with the important distinction that the polynomial coefficients are calculated according to the carry-less arithmetic of a finite field.

When determining if the wave is clockwise or counter-clockwise circularly polarized, one again takes the point of view of the source, and while looking away from the source and in the same direction of the wave ’ s propagation, one observes the direction of the field ’ s temporal rotation.

When determining if the wave is clockwise or counter-clockwise circularly polarized, one again takes the point of view of the receiver and, while looking toward the source, against the direction of propagation, one observes the direction of the field ’ s temporal rotation.

This field takes as its premise that economics is a strict subfield of ecology.

CPM takes information from the field related to pressures, flows, and temperatures to estimate the hydraulic behavior of the product being transported.

In two-parter " The Best of Both Worlds " Riker takes command of the Enterprise, assuming the rank of captain through a field promotion and orchestrates Picard's rescue.

Charge separation takes place within the generator, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further movement unfavorable.

The study or discipline of topography, while interested in relief, is actually a much broader field of study which takes into account all natural and man made features of terrain.

Britt-Mari Näsström points out the description in Gylfaginning where it is said of Freyja " whenever she rides into battle she takes half of the slain ", and interprets Fólkvangr as " the field of the Warriors ".

In Europe, Australia and Asia, betting to place is different since the number of " payout places " varies depending on the size of the field that takes part in the race.

It takes its name from Captain Martin Becher who fell there in the first Grand National and took shelter in the small brook running along the landing side of the fence while the remainder of the field thundered over.

The marching band and colorguard performance generally takes place on a football field while the colorguard interprets the music that the marching band or drum & bugle corps is playing via the synchronized spinning of flags, sabres, rifles, or through dance.

Within most fields of study, and in science in particular, the elevation of some principle of that field to the status of " law " usually takes place after a very long time during which the principle is used and tested and verified ; though in some fields of study such laws are simply postulated as a foundation and assumed.

This has two main advantages: driving the RF field takes a fraction of the energy ( allowing lighter-weight batteries for portable units ), and faster sampling as the electron-proton coupling can happen even as measurements are being taken.

The child who takes more time to master simple multiplication 1 ) may best learn to multiply through a different approach, 2 ) may excel in a field outside of mathematics, or 3 ) may even be looking at and understanding the multiplication process at a fundamentally deeper level, or perhaps as an entirely different process.

In the presence of the static, uniform external magnetic field, the Hamiltonian for the absorbing center takes the form Ĥ = Ĥ < sub > 0 </ sup > + Ĥ < sub > 1 </ sup > which is parallel to the direction of the propagation of the electric field k. Because the transition occur between the two eigenstates of Ĥ < sub > 0 </ sub >, a and j, the absorption and the CD intensity are determined as follows:

A small business is defined as one which is independently owned and operated and which is not dominant in its field.

So it was that when Mr. Brown and Mr. Sharpe first saw the French tool on exhibition in Paris in 1868, they brought a sample with them to the United States and started Brown & Sharpe in yet another field where it retains its leadership to this day.

Therefore, the congruence of its secants, that is the image of a general plane field of lines, is of order Af and class Af.

Each year from 1941 on, its medical staff had conducted intensive field investigations to determine changes in population structure and vital rates and, as its primary objective, the incidence of major diseases.

L'Institut pour La Recherche Scientifique En Afrique Centrale ( IRSAC ) has sponsored well-designed field investigations and has cooperated closely with the government of Ruanda-Urundi in the development of its official statistics.

It is very important indeed, in the field of extra-sensory perception and its relation to the survival hypothesis, to know whether the statements are actually only those which any intuitive person might venture and an eager sitter attach to himself.

One year the Department collected a file of case histories to document its argument that men in the field were paying the government's entertainment bills out of personal income.

William Smythe, director of field service, told the commissioners that Multnomah, as of Aug. 22, had spent $58,918 out of its budgeted $66,000 in the category, leaving only $7,082 for the rest of the month.

Several photographs and charts of galaxies help the non-scientist keep up with the discussion, and the smooth language indicates the contributors were determined to avoid the jargon that seems to work its way into almost every field.

Henrietta looked down at her bouquet, still lively with its color and scent, and set her feet on their journey's way again, leaving the village street and crossing the first field, Folly dancing ahead of her.

Biological anthropologists are interested in both human variation and in the possibility of human universals ( behaviors, ideas or concepts shared by virtually all human cultures ) They use many different methods of study, but modern population genetics, participant observation and other techniques often take anthropologists " into the field ," which means traveling to a community in its own setting, to do something called " fieldwork.

While accompanying Mallowan on countless archaeological trips ( spending up to 3 – 4 months at a time in Syria and Iraq at excavation sites at Ur, Ninevah, Tell Arpachiyah, Chagar Bazar, Tell Brak, and Nimrud ), Christie not only wrote novels and short stories, but also contributed work to the archaeological sites, more specifically to the archaeological restoration and labeling of ancient exhibits which includes tasks such as cleaning and conserving delicate ivory pieces, reconstructing pottery, developing photos from early excavations which later led to taking photographs of the site and its findings, and taking field notes.

As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

Murphy had opposed the idea that an individual mind with personality as an entity would survive, instead he claimed the mind and all of its memories would merge itself into a larger field of consciousness.

This is because the distance between the Earth and the Sun is not fixed ( it varies between AU and AU ) and, when the Earth is closer to the Sun ( perihelion ), the Sun's gravitational field is stronger and the Earth is moving faster along its orbital path.

Indeed, the International Committee for Weights and Measures ( CIPM ) notes that " its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored.

In the field of computer graphics, an anisotropic surface will change in appearance as it is rotated about its geometric normal, as is the case with velvet.

The electric charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a magnetic field.

So one has to introduce the charge conjugate antiparticle field, with its own creation and annihilation operators satisfying the relations

When the Vikings returned in force in 892 they found a kingdom defended by a standing, mobile field army and a network of garrisoned fortresses that commanded its navigable rivers and Roman roads.

His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory into its foundations.

His theory of schemes has become established as the best universal foundation for this major field, because of its great expressive power as well as technical depth.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.