On the other hand, if an algorithm finds the optimal value of optimization problem in polynomial time, then the decision problem can be solved in polynomial time by comparing the value of the solution output by this algorithm with the value of k.

The method of comparing hardness by seeing which minerals can scratch others, however, is of great antiquity, having first been mentioned by Theophrastus in his treatise On Stones, c. 300 BC, followed by Pliny the Elder in his Naturalis Historia, c. 77 AD.

On the other hand, comparing with the action on spinors, γ on ordinary vectors acts as the square of its action on spinors.

" On the other hand, Roosevelt's successor, Harry S. Truman, appears to have taken an instant dislike to Patton, at one point comparing him to George Armstrong Custer.

On a very slippery surface such as sheet ice or gravel, it is possible to lock multiple wheels at once, and this can defeat ABS ( which relies on comparing all four wheels, and detecting individual wheels skidding ).

On his return to France he published a severe criticism of Napoleon, comparing him to Nero and predicting the emergence of a new Tacitus.

On December 21, Republican protestors rallied in front of the Washington State Supreme Court Building dressed in orange and holding signs saying " Welcome to Ukraine ", comparing the inclusion of the discovered ballots to the election fraud in the recent Ukrainian presidential election.

By comparing skeletons of apes to man T. H. Huxley ( 1825 – 1895 ) backed up Charles Darwin's theory of evolution, first expressed in On the Origin of Species ( 1859 ), and developed the " Pithecometra principle " which stated that man and ape were descended from a common ancestor.

On a discrete grid, the non-maximum suppression stage can be implemented by estimating the gradient direction using first-order derivatives, then rounding off the gradient direction to multiples of 45 degrees, and finally comparing the values of the gradient magnitude in the estimated gradient direction.

On science education in schools he said of all the many crises in education and science, perhaps the most serious is the disappearing species of the good teacher of physics, mathematics and to a lesser extent the other sciences and that if it is allowed to go much further, there will be no recovery for generations, comparing it to China's Cultural Revolution which he said produced a lost generation.

On 7 January 1727 Mist's Weekly Journal satirised the matter, making several allusions to political change, and comparing the affair to the events of 1641 when Parliament began its revolution against King Charles I of England.

On 19 March 2012, Ashton was criticized by several newspapers for comparing the shooting of Jewish children in Toulouse with the situation in Gaza.

The 1938 Zur Welteismeteorologie (" On World Ice Meteorology ") by Dr. E. Dinies, published by the Reichs Office for Weather Service quotes from Hörbiger's Glazial-Kosmogonie and provided tables of data comparing ice and air temperatures for relative humidity values.

* On July 2, the Daytona Beach News-Journal called the charges against Castor " groundless " and a " cheap shot ," comparing ADP's practices to red-baiting.

In April 1928 his article On the Construction of Tables by Interpolation described the use of punched card equipment for interpolating tables of data, comparing this with the less efficient and more error-prone methods using mechanical devices such as the pinwheel calculators under the Brunsviga brand name.

His paraphrases of Aristotle's Posterior Analytics, Physics and On the Soul are valuable ; but the orations in which he panegyrizes successive emperors, comparing them to Plato's true philosopher, and even to the idea itself, are intended to flatter.

On 19 July 2008, Amorim stirred up controversy by comparing the descriptions used by wealthier countries to characterize the agricultural concessions they were offering during the Doha Round of WTO talks to the work of Nazi propagandist Joseph Goebbels.

On 27 March 1996, Philippe Bouvard, Vincent Perrot and the president of TF1 Patrick Le Lay were fined for having provoked racial hatred by telling a riddle comparing Muslim women to robbers.

On August 19, 2008, he wrote an article comparing John McCain to George W. Bush, concluding that " I fear to the depth of my being that John McCain is just like him.

On November 9, 2009, B ' nai Brith Canada ran a full page ad in the National Post comparing radical Islam with Nazism.

" On another occasion, in thanking James Lovell for a piece of intelligence, Washington wrote: " it is by comparing a variety of information, we are frequently enabled to investigate facts, which were so intricate or hidden, that no single clue could have led to the knowledge of them.

" On February 14, 2006 Tom Tomorrow published a cartoon comparing the reactions to the Muhammad cartoons to the Tom Toles cartoons, alleging a double standard.

On September 24, 2000, after former Jets teammate Keyshawn Johnson claimed that comparing Chrebet to him was like " comparing a flashlight to a star ," Chrebet caught an 18-yard TD pass from Curtis Martin with 52 seconds left to give the Jets a 21-17 victory against Johnson's team at the time ( the Tampa Bay Buccaneers ).

On the narrower ground of poetic form, he felt that in the drama of the future the Greek conception of tragic fate should be joined to the Shakespearean vision of tragic will.

On 16 June 1913, just a few months after the end of the first war, the Bulgarian government ordered an attack on Serbian and Greek positions in Macedonia, without declaring war.

On 15 August 1909 the Military League, a group of Greek officers, took action against the government to reform their country's national government and reorganize the army.

It was especially important for preserving in its libraries manuscripts of Greek and Latin authors throughout a period when instability and disorder caused their mass-destruction in western Europe and north Africa: On the city's fall, thousands of these were brought by refugees to Italy, and played a key part in stimulating the Renaissance, and the transition to the modern world.

On February 4, the last day of his visit, he was shown a text which he recognized as significant — the Codex Sinaiticus — a Greek manuscript of the complete New Testament and parts of the Old Testament dating to the 4th century.

On the other hand, French lait and Spanish leche ( both meaning " milk ") are less obviously cognates of Ancient Greek gálaktos ( genitive singular of gála, " milk "), a relationship more evidently seen through the intermediate Latin lac " milk ", as well as the English word lactic and other terms borrowed from Latin.

In order to reinforce his position that the Greeks were inclined towards plagiarism, he cites numerous instances of such inappropriate appropriation by classical Greek writers, reported second-hand from On Plagiarism, an anonymous 3rd century BC work sometimes ascribed to Aretades.

The etymology from ken – tauros, " piercing bull-stickers " was a Euhemerist suggestion in Palaephatus ' rationalizing text on Greek mythology, On Incredible Tales ( Περὶ ἀπίστων ): mounted archers from a village called Nephele eliminating a herd of bulls that were the scourge of Ixion's kingdom.

On Palm Sunday, in April 2008, a brawl broke out when a Greek monk was ejected from the building by a rival faction.

On Sunday, November 9, 2008, a clash erupted between Armenian and Greek monks during celebrations for the Feast of the Cross.

* Phaenomena, a treatise on spherical astronomy, survives in Greek ; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.

* On the comparative antiquity of the Sinaitic and Vatican manuscripts of the Greek Bible .. ( 1872 )

The first paper from his years of study in Paris appeared in Frankfurt am Main in 1816, under the title of Über das Conjugationssystem der Sanskritsprache in Vergleichung mit jenem der griechischen, lateinischen, persischen und germanischen Sprache ( On the Conjugation System of Sanskrit in comparison with that of Greek, Latin, Persian and Germanic ) ( Windischmann contributed a preface ).

On 24 January 2008, Greece's premier Costas Karamanlis visited Turkey a full 48 years after the last Greek premier and uncle of his Constantine Karamanlis had visited the neighboring country.

This occurs in the context of Irenaeus ' work On the Detection and Overthrow of Knowledge Falsely So Called, ( Greek: elenchos kai anatrope tes pseudonymou gnoseos genitive case, ἔλεγχος καὶ ἀνατροπὴ τῆς ψευδωνύμου γνώσεως ) where the term " knowledge falsely so-called " ( nominative case pseudonymos gnosis ) covers various groups, not just Valentinus, and is a quotation of the apostle Paul's warning against " knowledge falsely so-called " in 1 Timothy 6: 20.

" On the surface this implies that Matthew was written in Hebrew and translated into Greek, but Matthew's Greek " reveals none of the telltale marks of a translation.

On March 25, 1821 ( also the same day as the Greek Orthodox day of the Annunciation of the Theotokos ), the Greeks rebelled and declared their independence, led by Theodore Kolokotronis, but did not achieve it until 1829.

On 5 November, Major Spyros Spyromilios led a revolt in the coastal area of Himarë and expelled the Ottoman garrison without facing significant resistance, while on 20 November Greek troops from western Macedonia entered Korçë.

On the outbreak of hostilities on 18 October, the Greek fleet, placed under the newly promoted Rear Admiral Pavlos Kountouriotis, sailed for the island of Lemnos, occupying it three days later ( although fighting continued on the island until 27 October ) and establishing an anchorage at Moudros Bay.

On the same day, Greek troops of the Epirus Army seized the Ottoman naval base of Preveza.

On 9 November, the wooden Ottoman armed steamer Trabzon was intercepted and sunk by the Greek torpedo boat No. 14 under Lt. Periklis Argyropoulos off Ayvalık.

On, a Greek Farman MF. 7, piloted by Lt. Moutousis and with Ensign Moraitinis as an observer, carried out an aerial reconnaissance of the Ottoman fleet in its anchorage at Nagara, and launched four bombs on the anchored ships.

On the other hand the Illirii, probably the southernmost Illyrian tribe of that time that lived on the border of Albania and Montenegro, were possibly neighboring with the Greek tribes.

On the basis of these photographs, British naturalist Peter Scott announced in 1975 that the scientific name of the monster would henceforth be Nessiteras rhombopteryx ( Greek for " The Ness monster with diamond-shaped fin ").