The remainder of the cast fulfilled its assignments no more than satisfactorily just as the old production and limited stage direction proved only serviceable.

As discussed above, in ZFC, the axiom of choice is able to provide " nonconstructive proofs " in which the existence of an object is proved although no explicit example is constructed.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

On his arrival at Ephesus a three months ' truce was concluded with Tissaphernes, the satrap of Lydia and Caria, but negotiations conducted during that time proved fruitless, and on its termination Agesilaus raided Phrygia, where he easily won immense booty from the satrap Pharnabazus ; Tissaphernes could offer no assistance, as he had concentrated his troops in Caria.

In Ireland, Shane Butler said that AA “ looks like it couldn ’ t survive as there ’ s no leadership or top-level telling local cumanns what to do, but it has worked and proved itself extremely robust .” Butler attributed this to " AA ’ s ' inverted pyramid ' style of governance has helped it to avoid many of the pitfalls that political and religious institutions have encountered since it was established here in 1946.

* Metamath-a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems ; while the Metamath language is not accompanied with an automated theorem prover, it can be regarded as important because the formal language behind it allows development of such a software ; as of March, 2012, there is no " widely " known such software, so it is not a subject of " automated theorem proving " ( it can become such a subject ), but it is a proof assistant.

These authors proved, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflexion and refraction.

Ashton-Tate's product portfolio proved to be weak, with no provision for evolution into the GUI environment of Windows.

In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis ( in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i. e. no parallel postulate.

Church subsequently modified his methods to include use of Herbrand – Gödel recursion and then proved ( 1936 ) that the Entscheidungsproblem is unsolvable: There is no generalized " effective calculation " ( method, algorithm ) that can determine whether or not a formula in either the recursive-or λ-calculus is " valid " ( more precisely: no method to show that a well formed formula has a " normal form ").

Beria was no easy man to defeat, and his ethnicisation policies ( that a local or republican leaders had to have ethnic origins, and speak the language of the given area ) proved to be a tool to strengthen the MVD's grip on local party organs.

But the search proved fruitless as no manuscripts could be found.

Although Babbage's design was technically feasible, no one had built a mechanical device to such exacting standards before, so the engine proved to be much more expensive than anticipated.

Church proved that there is no computable function which decides for two given λ calculus expressions whether they are equivalent or not.

" However the Times also reflected widespread skepticism as to whether the forward pass could be effectively integrated into the game: " There has been no team that has proved that the forward pass is anything but a doubtful, dangerous play to be used only in the last extremity.

It is not even rigorously proved whether DFTs truly require ( i. e., order or greater ) operations, even for the simple case of power of two sizes, although no algorithms with lower complexity are known.

The rebels dispersed and there was no fighting, as Washington's forceful action proved the new government could protect itself.

After his son Philip married Queen Mary of England, it appeared that France would be completely surrounded by Habsburg domains, but this hope proved unfounded when the marriage produced no children.

During this voyage Alarcón proved to his satisfaction that no open-water passage existed between the Gulf of California and the South Sea.

The struggle against HIV has provided no cure, but improved antiretroviral treatments, and in the late 2000s ( decade ), male circumcision was proved to diminish infection risk.

In as much as patients can throw themselves into the nervous sleep, and manifest all the usual phenomena of Mesmerism, through their own unaided efforts, as I have so repeatedly proved by causing them to maintain a steady fixed gaze at any point, concentrating their whole mental energies on the idea of the object looked at ; or that the same may arise by the patient looking at the point of his own finger, or as the Magi of Persia and Yogi of India have practised for the last 2, 400 years, for religious purposes, throwing themselves into their ecstatic trances by each maintaining a steady fixed gaze at the tip of his own nose ; it is obvious that there is no need for an exoteric influence to produce the phenomena of Mesmerism.

In all the three conditions ( erectile dysfunction, coronary heart disease and cerebrovascular diseases ), despite the epidemiological association with periodontitis, no causative connection has proved yet.

I say, where the insanity is absolute, and is duly proved: For if reason and humanity enforce the plea in these circumstances, it is no less necessary to observe a caution and reserve in applying the law, as shall hinder it from being understood, that there is any privilege in a case of mere weakness of intellect, or a strange and moody humor, or a crazy and capricious or irritable temper.

More than 300 teenagers last Sunday proved there is and as many more are expected to prove it again for Jim Kern and his wife Lynn from 4 to 8 p.m. Sunday at First Presbyterian Church.

This proved conclusively that The Wrangler was a jinx, so he walked on down to Hurrays, an even more glorified gambling den than the Golden Calf.

Authors such as David Schneider, Clifford Geertz, and Marshall Sahlins developed a more fleshed-out concept of culture as a web of meaning or signification, which proved very popular within and beyond the discipline.

It is the belief of Old Babylonian scholars such as Carruccio that Old Babylonians " may have used the abacus for the operations of addition and subtraction ; however, this primitive device proved difficult to use for more complex calculations ".

Hopes that the 2005 Ashes series would be closely fought proved well-founded, as the series was more competitive than anyone had predicted and was still undecided as the closing session of the final Test began.

However, chlorpromazine proved to reduce the effects of psychosis in a more effective and specific manner than lobotomy, even though it was known to be capable of causing severe sedation.

The army reforms were not yet completed by the war of 1809, in which Charles acted as commander in chief, yet even so it proved a far more formidable opponent than the old and was only defeated after a desperate struggle involving Austrian victories and large loss of life on both sides.

Late in 2010, some Congressmen ( after the four-day Bicentennial holiday was proved successful ) asked for a law that would forbid the opening of supermarkets and department stores on Sundays, however retailers claimed that Sunday shopping made about 20 % of their weekly sales, more than other day of the week, thus preventing the law from taking place.

A necessity in a wolf-catching sighthound didn't exist, in addition to the old proved technique of batue with the use of baits, flags and other appeared new, way more effective — from airplanes, from propeller sleighs, with electronic lure whistles.

Despite the numerical advantage of the Persians, the hoplites proved devastatingly effective against the more lightly armed Persian infantry, routing the wings before turning in on the centre of the Persian line.

BC proved more popular there and also spread to other English-speaking countries.

Repco produced a more powerful version of their V8 to maintain competitiveness against Ford's new Cosworth DFV, but it proved very unreliable.

This proved to be very helpful for Croatia's inhabitants who found working in foreign countries more financially rewarding.

Labour shortages proved to be a more frequent problem.

These cautious tactics aroused derision amongst their more conservative French and Russian opponents but proved appropriate to the new nature of warfare.

Similar to the AMD K5, the Cyrix 6x86 was a design far more focused on integer per-clock performance than clock scalability, something that proved to be a strategic mistake.

Two 2008 case studies show that the layout of a system provides a strong correlation to the ease of use for a system and that it proved more beneficial for the design to focus on presenting information in a way that reflected the most important goals and tasks of the user, rather than the structure of the organization.

Realizing that iron was more difficult to pierce with breech-loaded cannon, Armstrong designed rifled muzzle-loading guns, which proved successful ; The Times reported: " even the fondest believers in the invulnerability of our present ironclads were obliged to confess that against such artillery, at such ranges, their plates and sides were almost as penetrable as wooden ships.

In a sense it is more of a research program proposal: part of the research is to find a proper formal statement that is physically reasonable and that can be proved to be true or false ( and that is sufficiently general to be interesting ).

The Enquiry proved little more successful than the Treatise.

This action, known as the Devastaciones de Osorio, proved disastrous ; more than half of the resettled colonists died of starvation or disease, over 100, 000 cattle were abandoned, and many slaves escaped.