Given a differentiable manifold, one can unambiguously define the notion of tangent vectors and then directional derivatives.

Given such estimates of first-order derivatives, the gradient magnitude is then computed as:

Given that the derivatives as Schwartz distributions are symmetric, this kind of example belongs in the ' fine ' theory of real analysis.

Given this equivalence, it is valid to assume “ risk neutrality ” when pricing derivatives.

Given a field tensor, a scalar called the Lagrangian density can be constructed from and its derivatives.

Given basic sound blocks, that a machine digitized, one has a bunch of numbers which describe a wave and waves describe words.

Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis.

Given the right overall conditions of the compressed fuel — high enough density and temperature — this heating process will result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given a revisionist makeover, the implied sexuality of the vintage films was enhanced and made explicit in a new wave of erotic thrillers.

Given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the reported significant wave height for a particular day or storm.

Given the unique mapping between densities and wave function, Runge and Gross then treated the Dirac action as a density functional,

Given the right overall conditions of the compressed fuel – high enough density and temperature – this heating process can result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given the right overall conditions of the compressed fuel — high enough density and temperature — this heating process can result in a chain reaction, burning outward from the center where the shock wave started the reaction.

Given that John of Worcester wrote his chronicle after the eruption of the Canterbury – York supremacy struggle, the story of Ealdred renouncing any claims to Worcester needs to be considered suspect.

* Frederick Douglass lecture on Haiti – Given at the World's Fair in Chicago, January 1893.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given unlimited resources, a classical computer can simulate an arbitrary quantum algorithm so quantum computation does not violate the Church – Turing thesis.

* June 9 – Royal Assent Given To The Town Of Milford Haven.

* Shay Given – former goalkeeper for both the Republic of Ireland and Newcastle United F. C ..

Given overwhelming evidence of Louis's collusion with the invaders, the verdict was a foregone conclusion – with 693 deputies voting guilty, none for acquittal, with 23 abstaining.

Given that A. florea is more widely distributed and A. andreniformis is considerably more aggressive, honey is – if at all – usually harvested from the former only.

* The Whole Royal and Magnificent Entertainment Given to King James Through the City of London ( 1603 – 4 ).

Given this information, a timeline of roughly the years 15 – 98 CE can be established for his adult life.

Given this uncertainty, between April – May 2006 at the JINR, a FLNR – PSI team conducted experiments probing the synthesis of this isotope as a daughter in the nuclear reaction < sup > 242 </ sup > Pu (< sup > 48 </ sup > Ca, 3n )< sup > 287 </ sup > Fl.

Given Henry's marital history – banishing his first wife and beheading the second – Mary refused the offer.

Given an adequate supply of food, larvae should pupate and weave a silken cocoon within 1 – 2 weeks after 3 larval stages.

** Masterclasses – Given in public by world renowned filmmakers.

Given that both Jonathan and Peleg Card were scheduled to be tried by the Vermont Committee of Safety ( Peleg died 6 Sep 1777, and it is unknown if the trial was actually held ) it is likely that Philo Card is, in reality, Peleg Card ( 1740 – 1777 ) --- and Stephen ( 1748 – 1798 ) -- ( Source: National Archives of Canada, WO 28 / 10, Reel B-2867, pp. 17 – 18.

Song Jiaoren (; Given name at birth: Liàn 鍊 ; Courtesy name: Dùnchū 鈍初 ) ( 5 April 1882 – 22 March 1913 ) was a Chinese republican revolutionary, political leader and a founder of the Kuomintang ( KMT ).

Given the choice, whether one believes that " the lives of entire peoples and societies have been decisively influenced by exceptional individuals " or, conversely, that whatever happens occurs as a result of impersonal forces oblivious to human intentions – Berlin rejected both options and the choice itself as nonsensical.

Given the subsequent emergence of organized fandom for comic books among adults who grew up reading them during Comics ' Golden Age, it is ironic Wertham at one point in Seduction ( pp. 89 – 90 ) asserts " I have known many adults who have treasured throughout their lives some of the books they read as children.

Given his prestige, Rundstedt was a central figure in the Blomberg – Fritsch Affair which engulfed the German Army in early 1938.

: Given that the particle begins at position x < sub > 1 </ sub > at time t < sub > 1 </ sub > and ends at position x < sub > 2 </ sub > at time t < sub > 2 </ sub >, the physical trajectory that connects these two endpoints is an extremum of the action integral.

Given the initial velocity of a particle launched from the ground, the downward ( i. e. gravitational ) acceleration, and the projectile's angle of projection θ ( measured relative to the horizontal ), then a simple rearrangement of the SUVAT equation

Given the correct bias, professional analog tape recorders could possibly benefit from the use of metal particle tape as consumer cassette decks had ; but the headstacks will wear at a significantly accelerated pace compared to oxide-based material, and therefore outweighing any benefits.

Given a collection ( ensemble ) of particles, the probability of finding a particle at a certain position in phase space is specified by a probability distribution, the Liouville density.

Given a manifold Q, a vector field X on Q ( or equivalently, a section of the tangent bundle TQ ) can be thought of as a function acting on the cotangent bundle, by the duality between the tangent and cotangent spaces.

Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):

Given the absolute magnitude, you can also compute apparent magnitude from its parallax:

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given enough resources, this can result in a vast collection.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given a fixed budget, this can allow an increased sample size.

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

Given r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

We have seen a few cavities of the appropriate size and shape for ivory-bills, but these can be old, or exceptionally large Pileated Woodpecker cavities, or mammal-enlarged Pileated Woodpecker cavities .… Given the results, it is unlikely a population of any meaningful size of Ivory-billed Woodpeckers exists in south Florida.

Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors.

Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in glasses with an amorphous structure.

Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.