From a fundamental physics perspective, mass is the number describing under which the representation of the little group of the Poincaré group a particle transforms.

From May to July 2006, several groups presented papers that filled in the details of Perelman's proof of the Poincaré conjecture, as follows:

From left to right: Top row-Archimedes, Aristotle, Alhazen | Ibn al-Haytham, Leonardo da Vinci, Galileo Galilei, Antonie van Leeuwenhoek ; Second row-Isaac Newton, James Hutton, Antoine Lavoisier, John Dalton, Charles Darwin, Gregor Mendel ; Third row-Louis Pasteur, James Clerk Maxwell, Henri Poincaré, Sigmund Freud, Nikola Tesla, Max Planck ; Fourth row-Ernest Rutherford, Marie Curie, Albert Einstein, Niels Bohr, Erwin Schrödinger, Enrico Fermi ; Bottom row-J. Robert Oppenheimer, Alan Turing, Richard Feynman, E. O. Wilson, Jane Goodall, Stephen Hawking

From 1936 to 1938, Hassler Whitney and Eduard Čech developed the cup product ( making cohomology into a graded ring ) and cap product, and realized that Poincaré duality can be stated in terms of the cap product.

From the latter, it follows by the Poincaré lemma that in a coordinate chart it is possible to introduce an electromagnetic field potential A < sub > α </ sub > such that

: From the point of view of the definition, this is an expression of the Poincaré Duality isomorphism where is the quotient of the field of fractions of by, considered as a-module, and where is the conjugate-module to ie: as an abelian group it is identical to but the covering transformation acts by.

From the early 1960s on, he mostly worked on the Poincaré conjecture.

In his article, " From the Imaginary Signifier: Identification, Mirror ," Christian Metz argues that viewing film is only possible through scopophilia ( pleasure from looking, related to voyeurism ), which is best exemplified in silent film.

From this premise, Charles Hartshorne argues further that:

Despite arguments that realism cannot be achieved in reality shows because the outcomes may or may not have been scripted, Geoff King argues in his book, Spectacle of the Real: From Hollywood to Reality TV and Beyond that even though the contestants are in a fabricated setting and the situation has been set up for a certain outcome, as in real love shows such as The Bachelor and The Bachelorette, these contestants still harbor feelings that make their participation in the show real to them.

In his 1989 Contingency, Irony, and Solidarity, Richard Rorty argues that Derrida ( especially in his book, The Post Card: From Socrates to Freud and Beyond ) purposefully uses words that cannot be defined ( e. g. Différance ), and uses previously definable words in contexts diverse enough to make understanding impossible, so that the reader will never be able to contextualize Derrida's literary self.

Tommy tells Jane that he cannot marry her, and she argues with him, but he continues to daydream about his true love (" Go Home With Bonnie Jean " ( reprise ) and " From This Day On " ( reprise )).

From their debates has emerged a multifarious populist nationalism which argues that anti-imperialist nationalism in China has provided a valuable public space for popular participation outside the country's political institutions and that nationalist sentiments under the postcolonial condition represent a democratic form of civic activity.

From the perspective of religious thought, Eliade argues, hierophanies give structure and orientation to the world, establishing a sacred order.

Korten's 2006 book The Great Turning: From Empire to Earth Community argues that the development of empires about 5, 000 years ago initiated unequal distribution of power and social benefits to a small portion of the population they controlled.

From this, given Mary ’ s high rank, he argues that baptism by water is inferior to the spiritual act of baptism.

From this point on, as Andrew Roberts in particular argues, Halifax set his face firmly towards a policy of deterrence based on increased rearmament, including the reintroduction of conscription ; strengthening of alliances and economic support to Eastern Europe ; and a firmer line towards Germany, Italy and Japan in the hope that increased British resolution would increase the risks of a combination of all three ( of note, when war did begin, neither Japan nor Italy was prepared to join in until the pendulum had swung much further in Germany's favour ).

Walter Kaufmann argues in From Shakespeare to Existentialism that, though Jaspers was certainly indebted to Kierkegaard and Nietzsche, he was closest to Kant's philosophy.

From a spiritual viewpoint, Father Etienne Richer argues that devotional scapular is one of key Roman Catholic sacramentals that harmonize with Catholic Liturgy in the meditative process.

In 2007 they published the controversial From Little Things Big Things Grow: Strategies for building revolutionary socialist organisations by Mick Armstrong, which argues their orientation for building a cadre organisation in times of revolutionary downturn and a critique of the Australian Labor Party: The Labor Party: A Marxist Analysis by Armstrong and Bramble.

From this ( so Chalmers argues ) it follows that such a world is logically possible.

Chalmers states ; " From the conceivability of zombies, proponents of the argument infer their metaphysical possibility " and argues that this inference, while not generally legitimate, is legitimate for phenomenal concepts such as consciousness since we must adhere to " Kripke's insight that for phenomenal concepts, there is no gap between reference-fixers and reference ( or between primary and secondary intentions ).

From that point on, Marx argues, labour power at work is transformed into capital, specifically variable capital which accomplishes the valorisation process.

From an entirely different starting point, the Sapir – Whorf hypothesis argues that individuals experience the world based on the grammatical structures they habitually use.

In Simon Prideaux's " From Organisational Theory to the New Communitarium of Amitai Etzioni ," he argues that Etzioni's communitarian methods are based upon earlier functionalist definitions of organisations.

From this argument Ridley argues that society operates best in groups of around 150 individuals, which he suggests is the level at which humans are capable of being sure about which members to cooperate with and which to exclude.

From this, Block argues that such a machine could continue a conversation with a person on any topic, because the computer would be programmed with every sentence that it was possible to use.

From this he argues that the photons exhibit wave behavior, including high fringe visibility but no which-way information, up to the point they hit the detector: " In other words the two-peaked distribution is an interference pattern and the photon behaves as a wave and exhibits no particle properties until it hits the plate.

From a different perspective, U. S. historian Joseph Tainter in The Collapse of Complex Societies ( 1988 ) argues that complex societies are the exception, rather than the norm, arise from special circumstances, and are a problem solving response.

McPheeters argues that the scene was inspired and influenced by dystopian films such as Death Wish, Taxi Driver, The Warriors, and Escape From New York.

In Lessons of October, Leon Trotsky, who was one of the leaders of the Russian October Revolution and considered second only to Lenin, argues that the Petrograd Soviet essentially entered a state of armed insurrection before October 25: " From the moment when we, as the Petrograd Soviet, invalidated Kerensky's order transferring two-thirds of the garrison to the front, we had actually entered a state of armed insurrection ... the outcome of the insurrection of October 25 was at least three-quarters settled, if not more, the moment that we opposed the transfer of the Petrograd garrison ; created the Military Revolutionary Committee ( October 16 )...".

From 1613 on, if the lists exist, they contain between twenty to thirty names.

From listening to their recordings, one had difficulty determining if the Crickets, the name of Buddy's band, were white or black singers.

From a theoretical perspective, both tao and dao transliterations if pronounced according to English spelling conventions are equally close to, or far from, the Standard Chinese pronunciation of 道.

From the above properties an important feature arises: Looking at two triangles ABD and BCD with the common edge BD ( see figures ), if the sum of the angles α and γ is less than or equal to 180 °, the triangles meet the Delaunay condition.

From the eigenvalues and the eigenvectors of A it is possible to determine if an initial point will converge or diverge to the equilibrium point at the origin.

From the Eastern Orthodox perspective, a council is accepted as being ecumenical if it is accepted by the Eastern Orthodox church at large – clergy, monks and assembly of believers.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical ( are one and the same ) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness.

From a geometric perspective, a function f is holomorphic at z < sub > 0 </ sub > if and only if its exterior derivative df in a neighborhood U of z < sub > 0 </ sub > is equal to f ′( z ) dz for some continuous function f ′.

And He is called Angel and Apostle ; for He declares whatever we ought to know, and is sent forth to declare whatever is revealed ; as our Lord Himself says, “ He that heareth Me, heareth Him that sent Me .” From the writings of Moses also this will be manifest ; for thus it is written in them, “ And the Angel of God spoke to Moses, in a flame of fire out of the bush, and said, I am that I am, the God of Abraham, the God of Isaac, the God of Jacob, the God of thy fathers ; go down into Egypt, and bring forth My people .” And if you wish to learn what follows, you can do so from the same writings ; for it is impossible to relate the whole here.

From the British point of view, it was regarded as highly desirable to keep Romania and its oil out of German hands ; since Germany had hardly any natural supplies of oil, the ability of the Royal Navy to successfully impose a blockade represented a British trump card both to deter war, and if necessary, win a war.

From time to time Lord Rayleigh participated in the House of Lords ; however, he spoke up only if politics attempted to become involved in science.

From this the sum of the interior angles can be easily confirmed, even if some interior angles are more than 180 °: going clockwise around, it means that one sometime turns left instead of right, which is counted as turning a negative amount.

From this we learn that, although Pius's defenders still say that he paid a golden ransom in a vain effort to save Rome's Jews from transportation to the death camps, the most he did was indicate a willingness to chip in if the Jews could not raise the sum demanded.

From this time, there was a growing acceptance of the position of Prime Minister and the title was more commonly used, if only unofficially.

From licenses MR and upward there is also a " B " Condition which may apply to your license if you do your testing in a Synchromesh or Automatic Transmission Vehicle.

From the 1830s until the 1940s, mechanical calculating machines such as adders and multipliers were built and improved, but they could not perform an " if / goto " and therefore are not true computers.

:: From the fact that if this match is scratched it will light, it follows that if it does not light it was not scratched.

:: From the fact that if this match is scratched it will light, it follows that if it were not to light it would not have been scratched.

From an investor's point of view, shares offer the potential for higher returns and capital gains if the company does well.

From him we learn that the Sudovians lived secluded from the Samlandish, would marry within their own tribe and did not allow intermarriage with the neighbouring Prussian population " even if begged ".

From version 3. 9. 2, the holder of the copyright, the University of Washington, changed the license so that even if the source code was still available, they did not allow modifications and changes to Pine to be distributed by anyone other than themselves.

From their superficially tadpole-like forms, leaf or paddle-shaped tails, and various degrees of streamlining, it is assumed that all vetulicolians discovered thus far were swimming animals that spent much, if not all, of their time living in the water column.