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The Picard – Fuchs equation can be cast into the form of Riemann's differential equation, and thus solutions can be directly read off in terms of Riemann P-functions.
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Picard and –
* 1900 – Leo Picard, German-Israeli geologist ( d. 1997 )
* 1856 – Charles Émile Picard, French mathematician ( d. 1941 )
* 1620 – Jean Picard, French astronomer ( d. 1682 )
* 1969 – Michel Picard, Canadian professional ice hockey player
Nevanlinna gave a fuller account of the theory in the monographs La théoreme de Picard – Borel et la théorie des fonctions méromorphes ( 1929 ) and Eindeutige analytische Funktionen ( 1936 ).
Q also lost a wager he made with Picard, detailing that if he failed to turn Riker, then he has to stay out of humanity's path – forever.
* 1961 – Luc Picard, Canadian actor and comedian
Likewise, Banach's fixed point theorem, based on earlier methods developed by Charles Émile Picard, was included in his dissertation, and was later extended by his students ( for example in the Banach – Schauder theorem ) and other mathematicians ( in particular Bouwer and Poincaré and Birkhoff ).
Based on other surveys and figures, Laurent Hendschel wrote in 1999 that between 30 and 40 % people were bilingual in Wallonia ( Walloon, Picard ), among them 10 % of the younger population ( 18 – 30 years old ).
* November 23 – Dominique-France Picard, queen of Egypt
* July 21 – Jean Picard, French astronomer ( d. 1682 )
* July 12 – Jean Picard, French astronomer ( b. 1620 )
Charles Émile Picard ForMemRS (; 24 July 1856 – 11 December 1941 ) was a French mathematician.
He also made important contributions in the theory of differential equations, including work on Picard – Vessiot theory, Painlevé transcendents and his introduction of a kind of symmetry group for a linear differential equation, the Picard group.
In the theory of differential equations, Lipschitz continuity is the central condition of the Picard – Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem.
Although the issue of existence and uniqueness of solutions of ordinary differential equations has a very satisfactory answer with the Picard – Lindelöf theorem, that is far from the case for partial differential equations.
* 22 October 1908 – Alfred Picard succeeds Thomson as Minister of Marine.
* 1972 – 1975: Laurent A. Picard
Existence and uniqueness then follow from the Picard – Lindelöf theorem for the solutions of ODEs with prescribed initial conditions.
" Within the Friedmann – Lemaître – Robertson – Walker ( FLRW ) model, the presently most popular shape of the Universe found to fit observational data according to cosmologists is the infinite flat model, while other FLRW models that fit the data include the Poincaré dodecahedral space and the Picard horn.
Having gained his law degree, he became a trainee ( 1881 – 1884 ) with Edmond Picard, a renowned criminal lawyer, who also played a pivotal role on the Brussels artistic scene.
Caricature of Ernest PicardLouis Joseph Ernest Picard ( 24 December 1821 – 13 May 1877 ) was a French politician.
Picard and Fuchs
These formulas give the explicit numbers of rational curves of all degrees in a large class of Calabi – Yau manifolds, in terms of the Picard – Fuchs equations of the corresponding mirror manifolds.
In mathematics, the Picard – Fuchs equation, named after Charles Émile Picard and Lazarus Fuchs, is a linear ordinary differential equation whose solutions describe the periods of elliptic curves.
The Picard – Fuchs equation is then
* J. Harnad, Picard – Fuchs Equations, Hauptmoduls and Integrable Systems, Chapter 8 ( Pgs.
:( Provides further examples of Picard – Fuchs equations satisfied by modular functions of genus 0, including non-triangular ones, and introduces Inhomogeneous Picard – Fuchs equations as special solutions to isomonodromic deformation equations of Painlevé type.
Picard and equation
The existence of solutions to this first-order ordinary differential equation is given by the Picard – Lindelöf theorem ( more generally, the existence of such curves is given by the Frobenius theorem ).
An older proof of the Picard – Lindelöf theorem constructs a sequence of functions which converge to the solution of the integral equation, and thus, the solution of the initial value problem.
The integrability follows because the equation defining the curve is a first-order ordinary differential equation, and thus its integrability is guaranteed by the Picard – Lindelöf theorem.
Picard and can
Picard is able to give the cadet confidence to pilot the shuttle away from the planet by bouncing off its atmosphere so they can retrieve him.
When the network destabilizes, Picard orders the fleet to retreat and reform the net, but Data observes that he can trace the source of the disruption.
The geographical spread of Picard and Chtimi among the Langues d ' oïl | Oïl languages ( other than French ) can be seen in shades of green and yellow on this map.
The Abel-Jacobi theorem states that the torus thus built is a variety, the classical Jacobian of a curve, that indeed parametrizes the degree 0 line bundles, that is, it can be identified with its Picard variety of degree 0 divisors modulo linear equivalence.
The Picard – Lindelöf theorem, which gives sufficient conditions for unique solutions to exist, can be used to rule out the existence of singular solutions.
( It can be shown that for, if a single branch of the square root is chosen, then there is a local solution which is unique using the Picard – Lindelöf theorem.
* As Spock, Picard, and Data escape the room after knocking Sela unconscious, the reflection of a member of the production crew chewing gum can be clearly seen in the reflection of an ornamental object on the desk.
" Kate's a strong, confident woman with a crusty edge who can hold her own with Captain Picard.
Picard replies that there is nothing the Enterprise can do as regrettably the Federation Prime Directive prohibits any interference with the natural development of the Boraalan civilization ; it is not for them to decide that one group shall survive while the rest of the planet perishes.
The basic statement can be formulated in terms of the Picard variety Pic ( C ) of a smooth curve C, and the subset of Pic ( C ) corresponding to divisor classes of divisors D, with given values n of deg ( D ) and r of l ( D ) in the notation of the Riemann – Roch theorem.
Captain Picard and Commander Riker greet Starbase Commander Quinteros and a pair of small humanoid aliens known as Bynars whose species have become so interconnected with their computer technology that their language and thought patterns have become as near to that of a computer's as a biological lifeform's can.
Dr. Crusher does everything she can to extend Riker's and Odan's chances while the Enterprise races to meet the Trill ship, and has a deeply emotional moment with Captain Picard.
It can then be shown, by using the Banach fixed point theorem, that the sequence of " Picard iterates " is convergent and that the limit is a solution to the problem.
Q congratulates Picard for being able to think in multiple timelines simultaneously in order to solve the puzzle, which is proof that humanity can still evolve, much to the surprise of the Q Continuum.
Norman can be classified as one of the northern Oïl languages along with Picard and Walloon.
A bend can be modified by most of the lines of partition — like the engrailed bend in the coat of Cleethorpes Borough Council, England, and the wavy bend in the coat of Picard, Canada.
The problem of finding which integrals of elementary functions can be expressed with other elementary functions is analogous to the problem of solutions of polynomial equations by radicals in algebraic Galois theory, and is solved by Picard – Vessiot theory.
Lore then explains that he can communicate with the crystalline entity and suggests that Captain Picard show a demonstration of force by beaming an object toward the crystal and then destroying it with a phaser.
Captain Picard offers any help the Enterprise can provide, including returning the aliens to their homeworlds and replicating other parts for the two other aging Ornaran freighters.
The ownership of the cargo barrel is brought up, and Picard learns it contains " Felicium ", medicine for a lethal plague that all Ornarans carry-a medicine that can only be manufactured from a plant on Brekka.
It is possible to see her waving good-bye in her last scene ( at about 42: 17, as Picard and Crusher leave the cargo bay, she can be seen in the background managing a brief wave before the cargo bay doors close ).
In 1887 van Rysselberghe already experimented with this style, as can be seen in his Madame Oscar Ghysbrecht ( 1887 ) and Madame Edmond Picard ( 1887 ).
They decide to mount a rescue mission to save Picard, but studies of the cane device reveal that due to instability of the portal, only one person can return.
Alternatively, the Picard group can be defined as the sheaf cohomology group
For integral schemes the Picard group can be shown to be isomorphic to the class group of Cartier divisors.
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