That makes them useful for classifying different parts of the magnetic field of the magnetosphere, each associated with a distinct type of circuit.

The Chebotarev density theorem reduces the problem of classifying Galois extensions of a number field to that of describing the splitting of primes in extensions.

The magnetic charges of a gauge field theory can be understood to be the group generators of the cohomology group for the fiber bundle M. The cohomology arises from the idea of classifying all possible gauge field strengths, which are manifestly exact forms, modulo all possible gauge transformations, given that the field strength F must be a closed form:.

The Hasse – Minkowski theorem reduces the problem of classifying quadratic forms over a number field K up to equivalence to the set of analogous but much simpler questions over local fields.

Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin – Wedderburn theorem classifying semi-simple rings.

Oncology is a field of medicine with a long history of classifying tumor stages and subtypes based on anatomic and pathologic findings.

The field, then, is ripe for new Southerners to step to the fore and write of this twentieth-century phenomenon, the Southern Yankeefication: the new urban economy, the city-dweller, the pains of transition, the labor problems ; ;

Both the extent to which this is true and the limits of the field of perceptual skill involved should be acknowledged.

`` It would be a disgrace, and, as I have already said to the people of Tennessee, if Hearst is nominated, we may as well pen a dispatch, and send it back from the field of battle: ' All is lost, including our honor ' ''.

Some historians have found his point of view not to their taste, others have complained that he makes the Tory tradition appear `` contemptible rather than intelligible '', while a sympathetic critic has remarked that the `` intricate interplay of social dynamics and political activity of which, at times, politicians are the ignorant marionettes is not a field for the exercise of his talents ''.

One's daily work becomes sacred, since it is performed in the field of influence of the moral law, dealing as it does with people as well as with matter and energy.

To obey the moral law is just ordinary common sense, applied to a neglected field.

Such is the field for exercising our reverence.

In the field of political values, it is certainly true that students are not radical, not rebels against their parents or their peers.

Although because of the important achievements of nineteenth century scholars in the field of textual criticism the advance is not so striking as it was in the case of archaeology and place-names, the editorial principles laid down by Stevenson in his great edition of Asser and in his Crawford Charters were a distinct improvement upon those of his predecessors and remain unimproved upon today.

For it is their catastrophic concept of the Anglo-Saxon invasions rather than Kemble's gradualist approach which dominates the field.

The national average is more than $4 and that figure is considered by experts in the mental health field to be too low.

This is one of the most constructive suggestions made in this critical field in years, and I certainly hope it sparks some action.

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

The Office of Foreign and Domestic Commerce is also active in the field of international trade, assisting Rhode Island firms in developing and enlarging markets abroad.

We do not favor one field over another: we think that all inquiry, all scholarly and artistic creation, is good -- provided only that it contributes to a sense and understanding of the true ends of life, as all first-rate scholarship and artistic creation does.

Recently added is the Brown & Sharpe turret drilling machine which introduces the company to an entirely new field of tool development.

Under the auspices of the Women's Recreation Association, interclass competition is organized in badminton, basketball, field hockey, golf, tennis, and swimming.

Mossberg's latest contribution to the field is the Model 500 ( from $73.50 ) ; ;

It is usually helpful to make a sketch map in the field, showing the size and location of the features of interest and to take photographs at the site.

Your competition is now proportionately greater -- you are competing not only against manufacturers in the same field but also against a vast array of manufacturers of other appealing consumer products.

New to the field is a duplex type butyrate laminate in which the two sheets of the laminate are of different color.

Owing respectively to Green's theorem and the divergence theorem, such a field is necessarily conserved and free from sources or sinks, having net flux equal to zero through any open domain.

More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.

The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B, which is also known as the " magnetic flux density " or the " magnetic induction ".

The units for magnetic flux Φ, which is the integral of magnetic field over an area, are the weber ( Wb ) in the SI and the maxwell ( Mx ) in the cgs system.

The conversion factor is 10 < sup > 8 </ sup >, since flux is the integral of field over an area, area having the units of the square of distance, thus 10 < sup > 4 </ sup > ( magnetic field conversion factor ) times the square of 10 < sup > 2 </ sup > ( linear distance conversion factor, i. e., centimetres per meter ).

Magnetic flux from the surroundings ( such as other wires ) may diminish or enhance the field the Hall probe intends to detect, rendering the results inaccurate.

* Active gravitational mass is a measure of the strength of an object ’ s gravitational flux ( gravitational flux is equal to the surface integral of gravitational field over an enclosing surface ).

Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path ; Carl Friedrich Gauss ; Jean-Baptiste Biot and Félix Savart, both of which in 1820 came up with the Biot-Savart Law giving an equation for the magnetic field from a current-carrying wire ; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity.

Equivalent technical statements are that the sum total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

In a geomagnetic storm, a surge in the flux of charged particles temporarily alters Earth's magnetic field, which induces electric fields in Earth's atmosphere, thus causing surges in our electrical power grid s. Artist's rendition ; sizes are not to scale.

Ptolemy, in his treatise Optics, held an extramission-intromission theory of vision: the rays ( or flux ) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field.

Oliver Heaviside FRS ( ( 18 May 1850 – 3 February 1925 ) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations ( later found to be equivalent to Laplace transforms ), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.

He held an extramission-intromission theory of vision: the rays ( or flux ) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field.

In Type II superconductors, raising the applied field past a critical value H < sub > c1 </ sub > leads to a mixed state ( also known as the vortex state ) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large.

A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field through the secondary winding.

If the turns of the coil are oriented perpendicularly to the magnetic field lines, the flux is the product of the magnetic flux density B and the area A through which it cuts.

The combined effect of the leakage flux and the electric field around the windings is what transfers energy from the primary to the secondary.

: Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known as magnetostriction.

The vector field B is the magnetic flux density and the vector A is the magnetic vector potential.