Additional philosophical considerations, advanced notably by Aristotle, supported further the circularity principle.

Finally, for 1950 only, runners would be credited with a stolen base if they were " well advanced " toward the base they were attempting to steal ", and the pitcher is charged with a balk, with the further exception of a player attempting to steal, who would otherwise have been forced to advance on the balk by a runner behind them.

The prospect for tranquility was further advanced in 1931 when Ferrera and his insurgents were killed, while leading one last unsuccessful effort to overthrow the government, after government troops discovered their hiding place in Chamelecon.

The transformation of an inflationary development into the hyperinflation has to be identified as a very complex phenomenon, which could be a further advanced research avenue of the complexity economics in conjunction with research areas like mass hysteria, bandwagon effect, social brain and mirror neurons.

With no further threat by the Serbs and the subsequent Byzantine civil wars, the Ottomans captured Constantinople in 1453 and advanced southwards into Greece, capturing Athens in 1458.

Queen Elizabeth had not advanced him further on account of his opposition to the alienation of ecclesiastical revenues.

# To arrange concerts and entertainments with a Cornish-Celtic flavour through which these aims can be further advanced.

Modular arithmetic was further advanced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.

None of the telecommunications forms are as prevalent or as advanced as those in modern Western countries, but the system includes some of the most sophisticated technology in the world and constitutes a foundation for further development of a modern network.

None of the telecommunications forms were as prevalent or as advanced as those in modern Western countries, but the system included some of the most sophisticated technology in the world and constituted a foundation for further development of a modern network.

After 1997, China's telecommunications services were enhanced further with the acquisition of Hong Kong's highly advanced systems.

He advanced still further under Pope Benedict XIII, who made him prefect of the judicial tribunal known as the Segnatura di Giustizia.

Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study of mathematics.

Once a planet's finite resources are exhausted no further species on that planet can develop advanced technology.

The dual pipe system, the advanced architecture, and the apparent layout of the Akrotiri find resemble Plato's description of the legendary lost city of Atlantis, further indicating the Minoans as the culture which primarily inspired the Atlantis legend.

Two running plays further advanced the ball to the 7-yard line.

Free trade advanced further in the late 20th century and early 2000s:

Later transmission methods such as SONET and fiber optic transmission further advanced digital transmission.

Trajan's army advanced further into Dacian territory and forced King Decebalus to submit to him a year later.

In more advanced treatments, one further distinguishes pseudovector fields and pseudoscalar fields, which are identical to vector fields and scalar fields except that they change sign under an orientation-reversing map: for example, the curl of a vector field is a pseudovector field, and if one reflects a vector field, the curl points in the opposite direction.

A further quirk of the system was that while players advanced in levels and hit points, superpowers did not, lending a different feel to characters at low, middle and high power levels.

It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther ; and then more time still to reach this third point, while the tortoise moves ahead.

He then advanced a few miles further until he neared Stark's position.

The " cognitive map hypothesis " has been further advanced by recent discoveries of head direction cells, grid cells, and border cells in several parts of the rodent brain that are strongly connected to the hippocampus.

He then had little more to publish on the subject ; but the emergence of Hilbert modular forms in the dissertation of a student means his name is further attached to a major area.

Might be further upgraded with modular armor " Kaktus " and UTD-32 engine.

Most traditional designs are however single-piece and the possibilities inherent in the modular origami idea were not explored further until the 1960s when the technique was re-invented by Robert Neale in the USA and later by Mitsonobu Sonobe in Japan.

Since then, the concept has been generalized, and the connections with quadratic number fields, the modular group, and other areas of mathematics have been further elucidated.

In later developments, the case n = 1 was first discussed by Kurt Heegner, using modular forms and modular equations to show that no further such field could exist.

In quantum computing, modular exponentiation appears as the bottleneck of Shor's algorithm, where it must be computed by a circuit consisting of reversible gates, which can be further broken down into quantum gates appropriate for a specific physical device.

Land Warrior's software system was powered by a variant of the Linux operating system and has a modular, open architecture for further improvement.

In the same paper, Dedekind observed further that any lattice of ideals of a commutative ring satisfies the following stronger form of the modular identity, which is also self-dual:

A further design issue is additionally a decision between holistic and atomistic, or ( more concrete ) modular structure.

Director, Ben Jones reported that being of a modular construction, which allows for quick and easy erection and future development if crowd numbers dictate, the stadium could be built in 12 to 14 weeks and any further development would be completed in very short time.

:( Provides further examples of Picard – Fuchs equations satisfied by modular functions of genus 0, including non-triangular ones, and introduces Inhomogeneous Picard – Fuchs equations as special solutions to isomonodromic deformation equations of Painlevé type.

The advantages of this approach in comparison to beam formwork or modular formwork is a further reduction of labor time and cost.

In a further refinement of these techniques, statistical predictions can be coupled to an algorithm called arithmetic coding.

** RISC — arithmetic instructions use registers only, so explicit 2-operand load / store instructions are needed: load a, reg1 ; load b, reg2 ; add reg1 + reg2 -> reg3 ; store reg3, c ; unlike 2-operand or 1-operand, this leaves all three values a, b, and c in registers available for further reuse.

To achieve two goals-faster arithmetic results, and keeping the arithmetic mill busy at all times-every triangle is further subdivided into groups of about 16 pixels.

Gentzen ( 1934 ) further introduced the idea of the sequent calculus, a calculus advanced in a similar spirit that better expressed the duality of the logical connectives, and went on to make fundamental advances in the formalisation of intuitionistic logic, and provide the first combinatorial proof of the consistency of Peano arithmetic.

Gentzen further demonstrated the power and flexibility of this technique a few years later, applying a cut-elimination argument to give a ( transfinite ) proof of the consistency of Peano arithmetic, in surprising response to Gödel's incompleteness theorems.

Reducing a general matrix to a Hessenberg matrix and then reducing further to a triangular matrix, instead of directly reducing a general matrix to a triangular matrix, often economizes the arithmetic involved in the QR algorithm for eigenvalue problems.

They further say that such arithmetic as is sped up by application of the sūtras can be performed on a computer or calculator anyway, making their knowledge rather irrelevant in the modern world.

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM – GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list ; and further, that the two means are equal if and only if every number in the list is the same.

The address space was further limited by the use of another 2 bits of the address to indicate the indexing mode for all logical and arithmetic ( i. e. non branch ) instructions.

In practical implementations, it would be usual to use an entropy code such as arithmetic code to further improve the performance of the dominant pass.

Therefore, if a counterexample to the Erdős – Straus conjecture exists, the smallest n forming a counterexample would have to be a prime number, and it can be further restricted to one of six arithmetic progressions modulo 840.