They sounded rather like The Band, with Schwarz's guitar work influenced greatly by Robbie Robertson's.

Later, as parliamentary white opposition to apartheid grew, the Progressive Party merged with Harry Schwarz's Reform Party and became the Progressive Reform Party.

In fact, Akaike was so impressed with Schwarz's Bayesian formalism that he developed his own Bayesian formalism, now often referred to as the ABIC for " a Bayesian Information Criterion " or more casually " Akaike's Bayesian Information Criterion ".

It was demonstrated by Hermann Schwarz that already for the cylinder, different choices of approximating flat surfaces can lead to different limiting values of the area ( Known as Schwarz's paradox.

Under Schwarz's leadership, the orchestra became particularly known for performing works of twentieth century composers, especially of neglected American composers.

A common German folk-tale is of the German priest / monk named Berthold Schwarz who independently invented gunpowder, thus earning it the German name Schwarzpulver or in English Schwarz's powder.

A good stepping stone leads to many others, so some of the most powerful results in mathematics are known as lemmata, such as Bézout's lemma, Urysohn's lemma, Dehn's lemma, Euclid's lemma, Farkas ' lemma, Fatou's lemma, Gauss's lemma, Nakayama's lemma, Poincaré's lemma, Riesz's lemma, Schwarz's lemma, Itō's lemma and Zorn's lemma.

However, Schwarz's design was " radically different from Zeppelin's " and in December 1897, Zeppelin admitted the Schwarz design could not be developed.

Sean Dooley speculates on the indirect benefits Zeppelin gained from Carl Berg and Schwarz's work.

Scheibler later bought out Schwarz's share and thus became sole owner of a large business.

Schwarz's brick, turreted castle-style house, built in 1890, now serves as the enclave's community center.

Schwarz's tenure was marked by artistic consolidation, but also financial troubles.

Schwarz's five-year contract was not renewed when it expired.

In September 2008, the orchestra announced the conclusion of Schwarz's music directorship after the 2010 – 2011 season, at which time Schwarz is scheduled to become the orchestra's conductor laureate.

The Band borrowed Brinsley Schwarz's instruments to rehearse.

On other days they often appeared at other venues, such as The Marquee, which is where Dave Robinson, Brinsley Schwarz's manager, had seen them and introduced them to the band.

In February 2004, investment firm D. E. Shaw & Co., L. P., acquired the FAO Schwarz stores in New York and Las Vegas, as well as FAO Schwarz's catalog and internet business.

It also notes that F. Schwarz's pamphlet, J. von Müller und seine Schweizergeschichte ( Bâle, 1884 ), traces the genesis of the Swiss History.

Schwarz's breakaway would see the demise of the United Party and realign opposition politics in South Africa.

* Schwarz's lemma, a result which in turn has many generalisations and applications in complex analysis.

Schwarz's direct success in making converts exceeded that of any other Protestant missionary in India, in addition to which he succeeded in winning the esteem of Muslims and Hindus.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If Af is the null space of Af, then Theorem 12 says that Af.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

* Theorem If X is a normed space, then X ′ is a Banach space.

many small primes p, and then reconstructing B < sub > n </ sub > via the Chinese Remainder Theorem.

Kleene's Church – Turing Thesis: A few years later ( 1952 ) Kleene would overtly name, defend, and express the two " theses " and then " identify " them ( show equivalence ) by use of his Theorem XXX:

Image: Thales ' Theorem Simple. svg | Thales ' theorem: if AC is a diameter, then the angle at B is a right angle.

Theorem 1. 8: For all elements in a group, then.

Unicity: Suppose satisfies, then by Theorem 1. 8,.

In a ring all of whose ideals are principal ( a principal ideal domain or PID ), this ideal will be identical with the set of multiples of some ring element d ; then this d is a greatest common divisor of a and b. But the ideal ( a, b ) can be useful even when there is no greatest common divisor of a and b. ( Indeed, Ernst Kummer used this ideal as a replacement for a gcd in his treatment of Fermat's Last Theorem, although he envisioned it as the set of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.

Theorem 1: If a property is positive, then it is consistent, i. e., possibly exemplified.

Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.

It was then simplified in 1947, when Leon Henkin observed in his Ph. D. thesis that the hard part of the proof can be presented as the Model Existence Theorem ( published in 1949 ).

To see the equivalence, note first that if Theorem 1 holds, and φ is not satisfiable in any structure, then ¬ φ is valid in all structures and therefore provable, thus φ is refutable and Theorem 2 holds.

If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬ φ is not satisfiable in any structure and therefore refutable ; then ¬¬ φ is provable and then so is φ, thus Theorem 1 holds.

In the General Possibility Theorem, Kenneth Arrow argues that if a legislative consensus can be reached through a simple majority, then minimum conditions must be satisfied, and these conditions must provide a superior ranking to any subset of alternative votes ( Arrow 1963 ).

~ p ∨ p. Since p → p is true ( this is Theorem 2. 08, which is proved separately ), then ~ p ∨ p must be true.

If n is not a prime power, then every Sylow subgroup is proper, and, by Sylow's Third Theorem, we know that the number of Sylow p-subgroups of a group of order n is equal to 1 modulo p and divides n. Since 1 is the only such number, the Sylow p-subgroup is unique, and therefore it is normal.

He began research under the supervision of Ernest William Barnes, who suggested that he attempt to prove the Riemann hypothesis: Littlewood showed that if the Riemann hypothesis is true then the Prime Number Theorem follows and obtained the error term.

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

The Concurrency Representation Theorem in the Actor model provides a fairly general way to represent concurrent systems that are closed in the sense that they do not receive communications from outside.

The two problems are mathematical duals, and hence the Duality Theorem provides a method of proving the relationships described above.

Actor model theory provides the means to characterize all the possible computations of a closed Actor system using the Representation Theorem 2007 as follows: