Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

The intuitive statement of the four color theorem, i. e. ' that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color ', needs to be interpreted appropriately to be correct.

" Financial economics ", at least formally, also considers investment under " certainty " ( Fisher separation theorem, " theory of investment value ", Modigliani-Miller theorem ) and hence also contributes to corporate finance theory.

" Another version of Hahn – Banach theorem is known as Hahn – Banach separation theorem or the separating hyperplane theorem, and has numerous uses in convex geometry.

Another version of Hahn – Banach theorem is known as the Hahn – Banach separation theorem.

The hyperplane separation theorem proves that in this case, each point not in the convex hull can be separated from the convex hull by a half-space.

The Tietze extension theorem can be used to show that an interval is an injective cogenerator in a category of topological spaces subject to separation axioms.

* Gabbay's separation theorem

** Minkowski separation theorem

By the Sturm separation theorem, the non-vanishing of forces λ to be the lowest eigenvalue.

Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.

You might be looking for Gabbay's separation theorem, the separating axis theorem, or the mutual fund separation theorem.

But contest definition -- that dramatic muscular separation of every muscle group that seems as though it must have been carved by a sculptor's chisel -- is something quite different.

However implausible this is, it is certainly the case that Aristotle's rigid separation of action from production, and his justification of the subservience of slaves and others to the virtue – or arete – of a few justified the ideal of aristocracy.

The theme of exile and separation is embodied in two characters, Rieux and Rambert, both of whom are separated from the women they love.

The angle between those lines can be measured, and is the angular separation between the two stars.

Animism encompasses the beliefs that there is no separation between the spiritual and physical ( or material ) world, and souls or spirits exist, not only in humans, but also in all other animals, plants, rocks, geographic features such as mountains or rivers, or other entities of the natural environment.

Lightning is also caused by a violent separation, this time of clouds by winds to create a bright, fire-like flash.

* δ Apodis is a double star with a separation of 103 arcseconds.

After the separation of the two offices the position of Astronomer Royal has been largely honorary, though he remains available to advise the Sovereign on astronomical and related scientific matters, and the office is of great prestige.

A more radical defense is to deny the separation of physical world and the platonic world, i. e. the mathematical universe hypothesis.

Analytical chemistry is the study of the separation, identification, and quantification of the chemical components of natural and artificial materials.

The separation of components is often performed prior to analysis.

The separation of materials is accomplished using chromatography, electrophoresis or Field Flow Fractionation methods.

Informally, it is the similarity between observations as a function of the time separation between them.

However, it is more correct for a very slender plate when the angle becomes large and flow separation occurs, or if the flow speed is supersonic.

It does however retain its separation from sexual attraction and as such is seen by many as an orientation within an orientation amongst the asexual community.

The last is equal to a projected separation of about 529 Astronomical Units ( AU ) at the estimated distance of Antares, giving a minimum value for the separation of the pair.

Spectroscopic examination of the energy states in the outflow of matter from the companion star suggest that it is about 224 AU behind the primary, giving a combined separation of about 574 AU.

Agarose is used generally as the medium for analytical scale electrophoretic separation in agarose gel electrophoresis and for column-based preparative scale separation as in gel filtration chromatography and affinity chromatography.

The book of Ruth portrays a perfect example of a true belief in the Creator God in that it propagates inclusion of all, even in the ancient world of the Israelites where separation is made obvious between Israelites and non-Israelites.

These regarded issues such as whether the universe is eternal or non-eternal ( or whether it is finite or infinite ), the unity or separation of the body and the self, the complete inexistence of a person after Nirvana and death, and others.

There was a separation between deciphering the messages, and sending out intelligence derived from them.

Everson used the metaphor of a wall of separation between church and state, derived from the correspondence of President Thomas Jefferson.

The Christian right points out that the term " separation of church and state " is derived from a letter written by Thomas Jefferson, not from the Constitution itself.

" She knew the separation of the now common terms Miss and Mrs. had derived from " Mistress ", but one could not suggest that women use the original title with its now louche connotations.

The name is derived from its separation from the Town of Bristol.

More clearly, D ' Souza states, " Today courts wrongly interpret separation of church and state to mean that religion has no place in the public arena, or that morality derived from religion should not be permitted to shape our laws.

It can be partially purified by " dry fractionation " by pressing tallow or other fatty mixtures, leading to separation of the higher melting stearin-rich material from the liquid, which is typically enriched in fats derived from oleic acid.

In recent years, programs derived from yoga, a Hindu religious practice, have been introduced into public schools in the U. S. Advocates for the programs say they help children to relax and concentrate, but critics counter that the programs violate the separation of church and state.

The concept of executive privilege is not mentioned explicitly in the United States Constitution, but the Supreme Court of the United States ruled it to be an element of the separation of powers doctrine, and / or derived from the supremacy of executive branch in its own area of Constitutional activity.

The characteristic impedance of a parallel-wire transmission line like twin lead or ladder line depends on its dimensions ; the diameter of the wires d and their separation D. This is derived below.

If there was any justification for this departure from convention, it lay in the fact that most people previously appointed to the position already held a formal title – such as a British knighthood or peerage, or a military rank – whereas Hollingworth's previous style, " The Most Reverend ", derived from his former position as the Anglican Archbishop of Brisbane and was considered inappropriate for a person holding an official position in a country which maintains a formal separation between church and state.

A blended unconformity is a type of disconformity or nonconformity with no distinct separation plane or contact, sometimes consisting of soils, paleosols, or beds of pebbles derived from the underlying rock.

Upon separation of Financing, Walter Industries, which in 2008 derived most if its revenues from its core natural resources and energy businesses, rebranded itself Walter Energy, reflecting its focus on its these core businesses.

Sol-gel derived materials have diverse applications in optics, electronics, energy, space, ( bio ) sensors, medicine ( e. g. controlled drug release ) and separation ( e. g. chromatography ) technology.

The prohibition of negiah is derived from two verses in Leviticus: " Any man shall not approach ( קרב qarab ) his close relative to uncover nakedness ; I am God " ( 18: 6 ), and: " You shall not approach a woman in her time of unclean separation, to uncover her nakedness " ( 18: 19 ).

Sol-gel derived materials have diverse applications in optics, electronics, energy, space, ( bio ) sensors, medicine ( e. g., controlled drug release ), reactive material and separation ( e. g., chromatography ) technology.

It is debatable whether the state secrets privilege is based upon the President's powers as commander-in-chief and leader of foreign affairs ( as suggested in United States v. Nixon ) or derived from the idea of separation of powers ( as suggested in United States v. Reynolds ).

The name is derived from separation Pharmacia dextran.

Confusion and dissension is caused by Title 10 U. S. Code § 467's separation of " imagery " or " satellite information " from " geospatial information " as imagery is generally considered just one of the forms which geospatial information might take or be derived from.