The main problem is to prove a signalizer functor theorem for nonsolvable signalizer functors.

By this theorem, once a star's chemical composition and its position on the main sequence is known, so too is the star's mass and radius.

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

This is because of the following main theorem on the iterations of a rational function:

The verification covers code, design, and implementation, and the main theorem states that the C code correctly implements the formal specification of the kernel.

The same work contained the celebrated formula known as Taylor's theorem, the importance of which remained unrecognised until 1772, when J. L. Lagrange realized its powers and termed it " le principal fondement du calcul différentiel " (" the main foundation of differential calculus ").

The crucial Takagi existence theorem was known by 1920 and all the main results by about 1930.

The main extra idea needed is an argument closely related to the theorem of Hadamard and de la Vallée Poussin, used by Deligne to show that various L-series do not have zeros with real part 1.

This is known as the main theorem of elimination theory.

Its main theorem due to Serre states:

Some of his major results, Zariski's main theorem and the Zariski theorem on holomorphic functions, were amongst the results generalized and included in the programme of Alexander Grothendieck that ultimately unified algebraic geometry.

* Zariski's main theorem

One of the first major results was the main theorem on the symmetric functions that described the invariants of the symmetric group S < sub > n </ sub > acting on the polynomial ring R …, x < sub > n </ sub > by permutations of the variables.

After completing a doctorate under the supervision of Alexander Grothendieck, he worked with him at the Institut des Hautes Études Scientifiques ( IHÉS ) near Paris, initially on the generalization within scheme theory of Zariski's main theorem.

The motivation here is that the p-torsion in the ideal class group of had already been identified by Kummer as the main obstruction to the direct proof of Fermat's last theorem.

Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's Euler systems, described in and, and later proved other generalizations of the main conjecture for imaginary quadratic fileds.

That theorem has its main interest in the case that the power series has radius of convergence exactly 1: if the radius of convergence is greater than one, the convergence of the power series is uniform for r in so that the sum is automatically continuous and it follows directly that the limit as r tends up to 1 is simply the sum of the a < sub > n </ sub >.

Combining this with the p-parity theorem by and the announced proof of the main conjecture of Iwasawa theory for GL ( 2 ) by, they conclude that a positive proportion of elliptic curves over Q have analytic rank zero, and hence, by, satisfy the Birch and Swinnerton-Dyer conjecture.

In subsequent papers in 1846 and 1847 he published his main theorem, the unique factorization into ( actual and ideal ) primes.

Under the assumption that pseudorandom functions exist with " exponential hardness " as specified in their main theorem, Razborov and Rudich show that these proofs cannot separate certain complexity classes.

: Our main theorem in Section 4 gives evidence that no proof strategy along these lines can ever succeed.

However, the main ideas can be understood using the finite-dimensional spectral theorem.

We will see that for compact operators, the proof of the main theorem uses essentially the same idea from the finite dimensional argument.

He rummaged, found composers and arrangers, collaborated on the main design and outline of harmonization with musicians, ballad singers, and musicologists.

The main question raised by the incident is how much longer will UN bury its head in the sand on the Congo problem instead of facing the bitter fact that it has no solution in present terms??

The central storage is near a main artery quite easy to reach with large transports on a short crescent swing, with fewer trucks in the residential streets.

At this point the drains are readjusted so that the suds box drain will discharge directly into the waste line and the main tub drain is set at the 2-1/2 mark on the drain gauge.

the way in which the transformation of state depends on the operating variables for the main types of reactors is discussed in the next chapter.

Because of this diversionary attack the main group that had been pinned down on the hill was able to surge forward again.

At present the doctor's main concern was in seeing to it that Japanese salvage firms were not permitted to operate on the hulks of warships sunk too close inshore, because the work involved setting off nerve-shattering blasts at all hours.

But the rest of it, the main part, wasn't based on logic at all.

This music is characterized by a large technical research and focuses mainly on twelve long Noubate " series ", its main instruments are the mandolin, violin, lute, guitar, zither, flute and piano.

The main vocalisation is the male's loud advertisement call which seeks to both encourage a female to approach and discourage other males from intruding on its territory.

Some frogs and toads are toxic, the main poison glands being at the side of the neck and under the warts on the back.

Setting circles are angular measurement scales that can be placed on the two main rotation axes of some telescopes.

In a metafictional touch, the husband is a writer working on a manuscript called " A Clockwork Orange ," and Alex contemptuously reads out a paragraph that states the novel's main theme before shredding the manuscript.

The main isotopes of argon found on Earth are ( 99. 6 %), ( 0. 34 %), and ( 0. 06 %).

We left the main road and wound into the leafy fastnesses of the hills, till we reached a little hamlet and an isolated white villa high on the hillside.

The parish's main Gaelic football pitch and two secondary schools are on the mainland at Poll Raithní.

Ancient Pueblo culture has been divided into three main areas or branches, based on geographical location:

In 2010, the main macro deficiencies of the Armenian economy — namely, unsustainable growth drivers, a narrow and resource-dominated export base, and overdependence on private transfers — were still prevalent.

It has two main features on which its distinction as a major contribution to Avicennan studies may be said to rest: the first is its clarity and readability ; the second is the comparative approach adopted by the author [...].

While there are ancient relations between the Indian Vedas and the Iranian Avesta, the two main families of the Indo-Iranian philosophical traditions were characterized by fundamental differences in their implications for the human being's position in society and their view on the role of man in the universe.

The main treaty was opened for signature on December 1, 1959, and officially entered into force on June 23, 1961.

Classical Arminianism, which sees Arminius as the main contributor, and Wesleyan Arminianism, which sees John Wesley as the main contributor, are the two main outlooks on how the system is realistic in detail.