More explicitly, it is stating that for every indexed family of nonempty sets there exists an indexed family of elements such that for every.

More explicitly it can be written as:

More explicitly, an energy T < sub > R </ sub > S is not available to do useful work, where T < sub > R </ sub > is the temperature of the coldest accessible reservoir or heat sink external to the system.

More explicitly stated:

Ackroyd notes that More explicitly " approved of Burning " After the case of John Tewkesbury, a London leather-seller found guilty by More of harbouring banned books and sentenced to burning for refusing to recant, More declared: he " burned as there was neuer wretche I wene better worthy.

More, relying on legal precedent and the maxim " qui tacet consentire videtur " ( literally, who ( is ) silent is seen to consent ), understood that he could not be convicted as long as he did not explicitly deny that the King was Supreme Head of the Church, and he therefore refused to answer all questions regarding his opinions on the subject.

It is not known whether the king or his Lord Chancellor, Thomas More, explicitly approved the plan.

More recently Paul Ernest has explicitly formulated a social constructivist philosophy of mathematics.

More explicitly, an injective continuous map f: X → Y between topological spaces X and Y is a topological embedding if f yields a homeomorphism between X and f ( X ) ( where f ( X ) carries the subspace topology inherited from Y ).

More recently, the space opera series Firefly used an explicitly Western theme for its portrayal of frontier worlds.

" More explicitly: that the expressionists rejected the ideology of realism.

More explicitly: For every symmetric real matrix A there exists a real orthogonal matrix Q such that D = Q < sup > T </ sup > AQ is a diagonal matrix.

More recent films that have explicitly explored parallel universes are: the 2000 film The Family Man, the 2001 cult movie Donnie Darko, which deals with what it terms a " tangent universe " that erupts from our own universe ; Super Mario Bros. ( 1993 ) has the eponymous heroes cross over into a parallel universe ruled by humanoids who evolved from dinosaurs ; The One ( 2001 ) starring Jet Li, in which there is a complex system of realities in which Jet Li's character is a police officer in one universe and a serial killer in another, who travels to other universes to destroy versions of himself, so that he can take their energy ; and FAQ: Frequently Asked Questions ( 2004 ), the main character runs away from a totalitarian nightmare, and he enters into a cyber-afterlife alternative reality.

More explicitly, one can equivalently write

More explicitly, suppose for example that, and that, and so on.

More explicitly, Kosmann's local expression given in 1972 is:

More recently, the common good rhetoric is being used by political actors in an explicitly religious context, such as Kansans for Faithful Citizenship.

More explicitly, F is, up to isomorphisms in C, characterized by the following universal property:

More explicitly, a coequalizer can be defined as an object Q together with a morphism q: Y → Q such that q ∘ f = q ∘ g. Moreover, the pair ( Q, q ) must be universal in the sense that given any other such pair ( Q ′, q ′) there exists a unique morphism u: Q → Q ′ for which the following diagram commutes:

More explicitly this means that apart from the topological obstruction there is no other obstruction to the existence of a holonomic solution.

More recently, it has been explicitly described by some cartoon characters, including Roger Rabbit, Bonkers D. Bobcat, and Yakko, Wakko, and Dot, who say that toons are allowed to bend or break natural laws for the purposes of comedy.

More explicitly, in refusing to judge tropes as entities unto themselves, Longinus promotes the appreciation of literary devices as they relate to passages as a whole.

More, the U.S. action was hailed by a principal opposition leader, Dr. Juan Bosch, as having saved `` many lives and many troubles in the near future ''.

More than 20, 000 people were forced to leave the Democratic Republic of the Congo in 2009, an action the DR Congo said was in retaliation for regular expulsion of Congolese diamond miners who were in Angola illegally.

In Anime Essentials: Every Thing a Fan Needs to Know, Giles Poitras wrote " More humorous and less serious looking than the characters in the Lodoss War series, the stars of Slayers provide action and laughs ".

More than 30, 000 soldiers had been killed in action.

Collaborations with Bill Sharpe of Shakatak helped little, though two singles the duo recorded, " Change Your Mind ", did see chart action, reaching No. 17 and " No More Lies " reaching No. 35 in 1988 in Britain.

More recently, a Quinnipiac poll from June 2009 finds that 55 % of Americans feel that affirmative action should be discontinued, yet 55 % support affirmative action for disabled people.

More specifically, MS destroys oligodendrocytes, the cells responsible for creating and maintaining a fatty layer — known as the myelin sheath — which helps the neurons carry electrical signals ( action potentials ).

More than a hundred Australian thalidomide survivors are involved in the class action, according to Rowe's lawyer.

More than 86, 000 troops, 11, 000 administrative personnel and thousands of civilian porters actually completed the breakout ; the remainder, largely wounded or ill soldiers, continued to fight a delaying action after the main force had left, and then dispersed into the countryside.

More precise theory shows that during the action of the laser field, the time-averaged effective potential of H < sub > 2 </ sup >< sup >+</ sup > is formed which binds the electron even if very strong electromagnetic field is present in similarity to the hydrogen molecule ion and prevents ionization.

More recent historians, such as Donald Kagan and R. J. Buck, have tended to support this analysis, pointing to the role that Thrasybulus played in crafting Athenian strategy in all these battles, and specifically to the decisive action he took at Cyzicus, which saved Alcibiades's force from being swamped, and turned a potential Athenian defeat into a stunning victory.

Bosley Crowther for one wrote in The New York Times, " More and more, Walt Disney's craftsmen have been loading their feature films with so-called ' live action ' in place of their animated whimsies of the past, and by just those proportions has the magic of these Disney films decreased ," citing the ratio of live action to animation at two to one, concluding that is " approximately the ratio of its mediocrity to its charm.

More familiar Rosenman compositions include the action music for the face off between the Bird-of-Prey and a whaling ship in open water, and the atmospheric music ( reminiscent of the composer's work in Fantastic Voyage ) during the probe's communication.

More recently the Blaser company has introduced a new straight-pull action where locking is achieved by a series of concentric ' blades '.

More typically, the excitatory potentials from several synapses must work together at nearly the same time to provoke a new action potential.

More balls generally adds to the amount of action in a game, but can result in stalemate with many blocks.

More than a man of ideas, Morazán was a man of action wrote biographer Rafael Eliodoro Valle.

More than a century passed, however, before any action was taken.

More technically, when H is invariant under the action of a certain group of transformations G:

Most recently, Helping Unite More People In Trouble ( HUMPIT ) consisted of many naked ( or nearly naked ) Portlanders marched from 1st Avenue to 23rd Avenue on Burnside Street ; arousing people to take action to end the plight of troubled Portlanders.

More specifically, the damage was done to a part of the nerve tract called the arcuate fasciculus, which the mechanism of action is unknown but it is shown to connect the posterior ( back ) of the brain to the anterior ( front ) and vice versa.

More likely, the volcano weathered away ; hot volcanic gases and steam turned hard rock into soft clay that were easily eroded by glacial action.