9,465 research outputs found
Canonical heights on the jacobians of curves of genus 2 and the infinite descent
We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computations involve only working with the Kummer surface and so lengthy computations with divisors in the Jacobian are avoided. We use this height algorithm to give an algorithm to perform the infinite descent stage of computing the Mordell-Weil group. This last stage is performed by a lattice enlarging procedure
Regularity and stochastic homogenization of fully nonlinear equations without uniform ellipticity
We prove regularity and stochastic homogenization results for certain
degenerate elliptic equations in nondivergence form. The equation is required
to be strictly elliptic, but the ellipticity may oscillate on the microscopic
scale and is only assumed to have a finite th moment, where is the
dimension. In the general stationary-ergodic framework, we show that the
equation homogenizes to a deterministic, uniformly elliptic equation, and we
obtain an explicit estimate of the effective ellipticity, which is new even in
the uniformly elliptic context. Showing that such an equation behaves like a
uniformly elliptic equation requires a novel reworking of the regularity
theory. We prove deterministic estimates depending on averaged quantities
involving the distribution of the ellipticity, which are controlled in the
macroscopic limit by the ergodic theorem. We show that the moment condition is
sharp by giving an explicit example of an equation whose ellipticity has a
finite th moment, for every , but for which regularity and
homogenization break down. In probabilistic terms, the homogenization results
correspond to quenched invariance principles for diffusion processes in random
media, including linear diffusions as well as diffusions controlled by one
controller or two competing players.Comment: Published in at http://dx.doi.org/10.1214/13-AOP833 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The Distribution of Revenues From State-Collected Consumer Taxes
VĂ€rdegrundsarbetet i förskolan dĂ€r genus och likabehandling stĂ„r i fokus Ă€r ett Ă€mne som skall arbetas aktivt med och det var detta som var grunden i underökning. Undersökningen utgick ifrĂ„n tvĂ„ frĂ„gor som handlade om pedagogernas kompetens i genusvetenskap samt vilka genuspedagogiska strategier som de anvĂ€nde i arbetet med barnen. För att undersöka detta sĂ„ valde jag att anvĂ€nda mig av en halvstrukturerad enkĂ€t dĂ€r de flesta frĂ„gorna var av öppen karaktĂ€r för att kunna fĂ„nga vad pedagogernas kunskap om de olika genusvetenskapliga begreppen. De slutna frĂ„gorna fĂ„ngade vilka genuspedagogiska strategier som pedagogerna anvĂ€nde i sitt arbete med barnen. 40 enkĂ€ter delades ut till pedagogerna i ett rektorsomrĂ„de. FrĂ„n resultatdelen kunde det utlĂ€sas att det var mĂ„nga olika definitioner pĂ„ de genusvetenskapliga begreppen och att flertalet av pedagogerna inte hade samma syn som forskningen kring om det beror pĂ„ det sociala eller det biologiska nĂ€r barnen positionerar sig som pojkar eller flickor. Resultatet visade ocksĂ„ att endast ett fĂ„tal pedagogerna anvĂ€nder sig av det komplicerande och normkritiska arbetssĂ€ttet med barnen och att lite fler Ă€n hĂ€lften tycker att de har tillrĂ€ckligt med kunskap för att arbeta med genus. Slutsatser som kunde dras frĂ„n resultaten frĂ„n enkĂ€ten Ă€r att pedagogernas kompetenser i de genusvetenskapliga begreppen Ă€r pĂ„ olika nivĂ„ och att de varierar vĂ€ldigt mycket. DĂ€rför drog jag den slutsatsen att det Ă€r dĂ€rför som det komplicerande och normkritiska arbetet inte anvĂ€nds i arbetet med genus i förskolan. ĂndĂ„ sĂ„ ansĂ„g flertalet av de pedagoger som inte arbetade med det komplicerande och normkritiska arbetet att de Ă€ndĂ„ hade tillrĂ€ckligt med kunskap i genus. Kompetens i ett Ă€mne gör att det Ă€r möjligt att ta ut svĂ€ngarna, att verkligen se hur barnen gör genus i barngruppen och att ifrĂ„gasĂ€tta normer i samhĂ€llet tillsammans med barnen
Fundamental solutions of homogeneous fully nonlinear elliptic equations
We prove the existence of two fundamental solutions and
of the PDE for
any positively homogeneous, uniformly elliptic operator . Corresponding to
are two unique scaling exponents which
describe the homogeneity of and . We give a sharp
characterization of the isolated singularities and the behavior at infinity of
a solution of the equation , which is bounded on one side. A
Liouville-type result demonstrates that the two fundamental solutions are the
unique nontrivial solutions of in
which are bounded on one side in a neighborhood of the origin as well as at
infinity. Finally, we show that the sign of each scaling exponent is related to
the recurrence or transience of a stochastic process for a two-player
differential game.Comment: 35 pages, typos and minor mistakes correcte
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