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, the action groupoid is the set with source and target maps s ( g, x )

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 realistic models are tailored to a specific problem and include the transition state theory, the calculation of the potential energy surface, the Marcus theory and the Rice – Ramsperger – Kassel – Marcus ( RRKM ) theory.

More sophisticated space elevator designs reduce the energy cost per trip by using counterweights, and the most ambitious schemes aim to balance loads going up and down and thus make the energy cost close to zero.

More special cases are the coupled oscillators where the energy alternates between two forms of oscillation.

More precisely, it is a low energy expansion based on the spontaneous chiral symmetry breaking of QCD, which is an exact symmetry when quark masses are equal to zero, but for the u, d and s quark, which have small mass, it is still a good approximate symmetry.

More correctly, radiosity B is the energy per unit area leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy:

More complex systems may carry out all of these functions: generate electricity, recover thermal energy, and also act as a roof covering.

More generally, where an observer detects electromagnetic radiation outside the visible spectrum, " redder " amounts to a technical shorthand for " increase in electromagnetic wavelength " — which also implies lower frequency and photon energy in accord with, respectively, the wave and quantum theories of light.

* News story: More evidence for dark energy being the cosmological constant

More abstract and invisible divine energy centres, called Chakras, are associated with its Rise.

More generally, the nth ionization energy is the energy required to strip off the nth electron after the first electrons have been removed.

More specifically, the energy Eigen states form a basis-any wavefunction may be written as a sum over the discrete energy states or an integral over continuous energy states, or more generally as an integral over a measure.

More interesting processes occur when the chemical substrate undergoes internal energy transitions before re-emitting the energy from the absorption event.

More widely, passive solar technologies include the solar furnace and solar forge, but these typically require some external energy for aligning their concentrating mirrors or receivers, and historically have not proven to be practical or cost effective for widespread use.

More often a diode is used to prevent voltage spikes by providing a path for the current to recirculate through the winding until the energy is dissipated as heat.

More recently, the development of renewable energy sources, especially offshore wind power, has created further opportunities for support services.

More recently, the endosymbionts that are found in the gills have been subject to study the bioconversion of cellulose for fuel energy research.

Morrow ) and defined by Max More in 1988, is " the extent of a living or organizational system's intelligence, functional order, vitality, energy, life, experience, and capacity and drive for improvement and growth.

These include " Seasons Change " by Exposé, " Thinking of You " by Sa-Fire, " One More Try " by Timmy T, " Because I Love You ( The Postman Song )" by Stevie B, and " If Wishes Came True " by Sweet Sensation.

More formally, a multivariate random variable is a column vector X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub >)< sup > T </ sup > ( or its transpose, which is a row vector ) whose components are scalar-valued random variables on the same probability space ( Ω,, P ), where Ω is the sample space, is the sigma-algebra ( the collection of all events ), and P is the probability measure ( a function returning every event's probability ).

More recently, that ad campaign was lampooned by American Dad, in the episode A. T. the Abusive Terrestrial.

Faith No More collaborated with the Boo-Yaa T. R. I. B. E.

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

More than 5, 000 businesses have operations within Richardson's, including many of the world's largest telecommunications / networking companies: AT & T, Ericsson, Verizon, Cisco Systems, Samsung, MetroPCS, Texas Instruments, TriQuint Semiconductor, and Fujitsu.

More recent translations in English have been published by T. G. Allen ( 1974 ) and Raymond O. Faulkner ( 1972 ).

More rarely, bands will do an entire album of cover songs originally by a particular artist, such as The The's Hanky Panky, which consists entirely of Hank Williams songs, or Booker T. & the M. G.

More subtle uses of alter egos can be seen in artists who redefine their image for an album, such as Christina Aguilera as Xtina and the members of My Chemical Romance as members of an outlaw gang known as the Fabulous Killjoys, and artists who describe their stage personalities as different from their private ones, such as Beyoncé Knowles ' identity as Sasha Fierce, Katy Perry's identity as Kathy Beth Terry in music video " Last Friday Night ( T. G. I. F.

More generally, where < sup > T </ sup >, an n-dimensional random vector, one uses instead of tX:

More generally, T is not invertible if it is not bounded below ; that is, if there is no c > 0 such that || Tx || ≥ c || x || for all.

More precisely, ζ ( X, s ) can be written as a finite alternating product < dl >< dd ></ dl > where each P < sub > i </ sub >( T ) is an integral polynomial.

More recent studies indicate substantially decreased enplanements due in-part to soaring fuel costs, and easier access to Logan International Airport since completion of improvements to the Southeast Expressway, Third Harbor Tunnel, bus services between T. F.

More precisely, when T < sub > 0 </ sub > is Fredholm from X to Y, there exists ε > 0 such that every T in L ( X, Y ) with || T − T < sub > 0 </ sub >|| < ε is Fredholm, with the same index as that of T < sub > 0 </ sub >.

More dates were announced and the band played festival dates at Glastonbury, T in the Park and Oxegen 2009 as well as headlining shows in Manchester, Newcastle, Wolverhampton, Goldsmiths College and the East Anglian Railway Museum in Colchester.

More generally, if we have a differentiable tensor field T of rank and a differentiable vector field Y ( i. e. a differentiable section of the tangent bundle TM ), then we can define the Lie derivative of T along Y.