Their first published proof replaced the cobordism theory of the first proof with K-theory, and they used this to give proofs of various generalizations in the papers.

Their own proofs of all the steps are rather long according to their admission.

Their bodies writhe and they raise and lash their tails which makes it difficult for the predator to avoid contact with their poison-producing granular glands.

Their beliefs and behavior are difficult to decipher from physical materials, and their languages remain unknown as they had no known writing system.

Their converging styles make it difficult to exactly understand the influences each had on the other, although it is clear enough to say that Aelbert started representing large scale forms ( something he had not done previously ) and placing animals as the focus of his paintings ( something that was specific to him ).

Their overwhelming popularity was due to inexpensive construction and price, although their tone and performance were limited by narrow soundboards, simple actions and string spacing that made proper hammer alignment difficult.

Their relationship was difficult, but eventually they did reach a certain understanding.

Their partly nocturnal and far-ranging behaviour, their low densities, and the fact they inhabit densely vegetated habitats and remote areas makes the censusing and monitoring of clouded leopards extremely difficult.

Their hearing and vision are better than that of a human being and they are difficult to sneak up on because of this.

Their destruction by chemical, thermal, and biochemical processes is extremely difficult, and presents the risk of generating extremely toxic dibenzodioxins and dibenzofurans through partial oxidation.

Their economic value is difficult to measure, but there are anecdotal reports of cities that have achieved substantial economic benefits by " branding " themselves by adopting new slogans.

Their ears are rather difficult to see, and their genus name, “ Aotus ,” means “ earless ” because of this.

Their effects on radio signals also give information, especially useful for daytime meteors which are otherwise very difficult to observe.

Their king was a personal friend of Tostig, and Tostig's unpopularity made it difficult to raise local levies to combat them.

Their camp sites are difficult to find as they are many feet below the present surface.

Their exact relation is difficult to determine from the sparse evidence of runic inscriptions, and they remained mutually intelligible to some degree during the Migration Period, so that some individual varieties are difficult to classify.

Their exact relation is difficult to determine from the sparse evidence of runic inscriptions, and they remained mutually intelligible throughout the Migration Period, so that some individual varieties are difficult to classify.

Their total command of the air and the sabotage of roads and bridges by the Resistance made bringing armoured reinforcements to Normandy slow and difficult, but without them there was no hope of an effective counter-offensive.

Their size, shape and texture make them difficult to expel from the windpipe.

Their war service and veterans ' associations had broadened their horizons, making it difficult for them to return to the humble and circumscribed positions set aside for Africans by the colonial authorities.

Their work proved difficult because of the composition of the soil, which made identifying the strata of the site and its chronology difficult.

Their research involved non-uniform magnetic fields, which were difficult to manipulate and hard to measure accurately.

Their main effort was the development of radio-controlled missiles and glide bombs for use against shipping, a target that is otherwise both difficult and dangerous to attack.

Their books found no less willing readers outside than inside the South, even while memories of the war were still sharp.

Their level of comfort while in the grave depends wholly on their level of Iman or faith in the one God, or Allah, equivalent in Arabic.

Their report reveals that the lagoon water, while not tasting very good, was drinkable, though " muddy and dirty ".

Their second son, John Sheldon Doud Eisenhower, was born on August 3, 1922, while they were in Panama ; John served in the United States Army, retired as a brigadier general, became an author and served as U. S. Ambassador to Belgium from 1969 to 1971.

Their reception of this element varied: Tim Soete of GameSpot felt that it was " morally questionable ", while the Game Revolution reviewer noted that it was " done in a tongue-in-cheek manner ," and he was " not personally offended ".

Their findings also suggest that while the schemas of both novices and experts are activated by the same features of a problem statement, the experts ’ schemas contain more procedural knowledge which aid in determining which principle to apply, and novices ’ schemas contain mostly declarative knowledge which do not aid in determining methods for solution.

Their daughters were declared legitimate and custody was awarded to Louis, while Eleanor's lands were restored to her.

Their literary character is not quite clear ; while most of them are adapted for public delivery, not a few bear the character of ecclesiastical pronouncements.

Their fore flippers are used primarily for steering, while their hind flippers are bound to the pelvis in such a way that they cannot bring them under their body to walk on them.

Their fare, while generally standard, is less regulated.

Their father died while they were young.

Their stealthy approach march, camouflage and noise discipline at Isandhlwana, while not perfect, put them within excellent striking distance of their opponents, where they were able to exploit weaknesses in the camp layout.

Their daughter, Louisa, was born in 1811 but died in 1812 while the family was in Russia.

Their feature film for Paramount Pictures, Easy Come, Easy Go, was canceled when Berry, as well as the film's director and other crew members, were seriously injured in a railroad accident while shooting the movie in Chatsworth, California in August 1965.

Their individual uniforms showed other changes as well ; at home, the blue piping was removed and the block lettered " BREWERS " was changed to a script version similar to the script that spelled their road uniforms, while those outfits had their piping changed from blue-yellow-blue to blue-white yellow.

Their small entourage fought the attackers, but were all killed, while Mary and her mother were imprisoned in the Bishop of Zagreb's castle of Gomnec.

Their own memories are not reliable or complete and they misunderstand each other as they stumble through philosophical arguments while not realizing the implications to themselves.

Their first logo depicts a friar swinging a bat with Padres written at the top while standing in a sun-like figure with San Diego Padres on the exterior of it.

Their major victory at the Battle of Isandlwana is well known, but they also forced back a British column at the Battle of Hlobane mountain, deploying fast-moving regiments over a wide area in the rugged ravines and gullies while the British were quickly on the move.

Their daughter, Barbara Joyce (" Bobbi Jo "), was born on January 28, 1948, while Williams was fishing in Florida.

Their outer edges ( as shown in the illustration ) are attached to muscle in the larynx while their inner edges, or margins are free ( the hole ).

Their light weight makes them easier to lift, while the thinner carbon steel heats quickly.

Their main downfall would be Sony's stubborn resistance to supporting the ubiquitous MP3 codec in their early players and many users found it frustrating to convert their MP3 music collection to ATRAC3 for use on the Network Walkman, while Apple's iPod supported MP3 out of the box and came with the iTunes software.

Their Sunday entertainment features included the first color comic strip pages, and some theorize that the term yellow journalism originated there, while as noted above, the New York Press left the term it invented undefined.

Their films have never left the television airwaves since first appearing in 1958, and they continue to delight old fans while attracting a new legion of fervent admirers.