Problems of this sort are inevitable, since SO ( 3 ) is diffeomorphic to real projective space RP < sup > 3 </ sup >, which is a quotient of S < sup > 3 </ sup > by identifying antipodal points, and charts try to model a manifold using R < sup > 3 </ sup >.

Problems began when King Frederick II of Prussia violated the Pragmatic Sanction and invaded Silesia on 16 December 1740, using the Treaty of Brieg of 1537 under which the Hohenzollerns of Brandenburg were to inherit the Duchy of Brieg as a pretext.

Problems began as soon as lines began to meet and, in much of the north-eastern United States, standard gauge was adopted.

Problems began shortly after launch when one solar panel failed to unfold, leading to a shortage of power for the spacecraft's systems.

Problems began when the Wichita Falls and Northwestern Railroad missed Eschiti by two miles and Kell City ( named after the railroad ’ s promoter ) sprang up along the railroad's route.

Problems with a bridge also began the process of restoring this section.

Problems between the group and producer J-Swift began during the recording of the debut, with infighting and " personality conflicts ".

Problems began when the LCMS began exploratory talks with leaders of the American Lutheran Church ( ALC ).

Problems with drummer Nick Jago began surfacing publicly at the 2003 NME Awards, when Jago remained on stage for nine minutes, completely silent, while accepting an award.

Problems began to surface in 2004 when faculty held a public protest over issues related to remedial courses and governance.

Problems began to come to light when it emerged that some large-scale housing areas had been built with materials and techniques that had not been fully tested, with the result that insulation, sound-proofing and durability were not adequate.

Problems began to arise as the Fringe became too big for students and volunteers to deal with.

Problems began to crop up for David now.

Problems with agriculture in the beginning of the 19th century would also occur just when industrialists began abandoning the city of Bragança.

Problems began early as he was only given five weeks to go from concept to finished product.

Problems began to arise when Carpenter learned that the next Eddie Murphy vehicle, The Golden Child, featured a similar theme and was going to be released around the same time as Big Trouble in Little China.

Problems began in the new century.

Problems began on the boat journey over, with disputes developing about aspects of the trip and a rift developed between tour manager and coach, Mr Mair, an Australian and seven forwards.

Problems began when Island also leased discs from other US labels that interested them and released them on UK Sue too-which was not in the agreement.

In 2009 and 2010 Side One Dummy began working with Fake Problems, Anti-Flag, Audra Mae Jesse Malin and The Black Pacific.

She gave up broadcasting in 1964 to raise her family and did not return full-time until 1971, when she presented If You Think You've Got Problems, a programme in which a broad range of human problems were discussed, many of which would not have been allowed when she began her association with Woman's Hour.

Problems began when the LCMS began exploratory talks with leaders of the American Lutheran Church ( ALC ).

Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions.

Problems that continue to put a drag on growth include low foreign investment levels, bureaucratic red tape, and very widespread corruption which causes 51. 43 trillion Rupiah or 5. 6573 billion US Dollar or approximately 1. 4 % of GDP to be lost on a yearly basis.

Problems include wide-spanned chords, which can be difficult for people with small hands ; chords that require unusual hand positions that can initially be uncomfortable, and fast scales, trills and arpeggios.

Problems include reliability, cost, questions about how great the need is, and the fact that many smart building tasks such as turning on a lamp at dusk can be performed equally well by simpler, cheaper, and often more reliable, mechanical or electro-mechanical devices.

Problems such as pollution and social injustice may then be seen as failures to properly account for capital, rather than as inherent failures of capitalism itself.

Problems can be caused if the format of configuration files changes.

Problems are recorded so they can be reported to

Problems related to the construction of Golomb Rulers are provably shown to be NP-hard, where it is also noted that no known NP-complete problem has similar flavor to finding Golomb Rulers.

Problems have been raised for this view because the mental states seem to be reduced to mere physical causes.

According to Article 75 of the Constitution of Moldova, "( 1 ) Problems of utmost gravity or urgency confronting the Moldovan society or State shall be resolved by referendum.

Problems that are EXPTIME-complete might be thought of as the hardest problems in EXPTIME.

Problems can also be identified from a single significant incident, indicative of a single error, for which the cause is unknown, but for which the impact is significant.

Early in September 2004, Michael Cullen, the deputy prime minister of New Zealand, announced that Irving would not be permitted to visit the country, where he had been invited by the National Press Club to give a series of lectures under the heading " The Problems of Writing about World War II in a Free Society ".

Problems in coping with one's environment are thought, by Bar-On, to be especially common among those individuals lacking in the subscales of reality testing, problem solving, stress tolerance, and impulse control.

* In the 1997 music video for the highly popular song " Mo Money Mo Problems " by Notorious B. I. G, rap moguls Sean Combs and Mase, appear to be dancing in front of the Unisphere.

In many cases, such as in Constraint Satisfaction Problems, one can dramatically reduce the search space by means of Constraint propagation, that is efficiently implemented in Constraint programming languages. The search space for problems can also be reduced by replacing the full problem with a simplified version.

Problems with activities such as cutting meat and eating can be addressed by using specialized cutlery, kitchen utensils, or dishes.

Problems can be contrasted with tactical puzzles often found in chess columns or magazines in which the task is to find the best move or sequence of moves ( usually leading to mate or gain of material ) from a given position.

Problems in Ramsey theory typically ask a question of the form: " how many elements of some structure must there be to guarantee that a particular property will hold?

Problems to be solved include, East Timor-Indonesia Boundary Committee meetings to survey and delimit land boundary ; and Indonesia is seeking resolution of East Timorese refugees in Indonesia.

Problems occurred when the Coens and cinematographer Roger Deakins decided that these shots would be more effective with a wide-angle lens.

Problems such as this, where model parameters ( the location of the activity ) have to be estimated from measured data ( the SQUID signals ) are referred to as inverse problems ( in contrast to forward problems where the model parameters ( e. g. source location ) are known and the data ( e. g. the field at a given distance ) is to be estimated.