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Heuristics on pairing-friendly elliptic curves
Elliptic curves finite fields pairing-based cryptography
2011/8/23
Abstract: We present a heuristic asymptotic formula as $x\to \infty$ for the number of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value b...
Calabi-Yau Problem for Legendrian curves in C^3 and applications
Calabi-Yau Problem Legendrian curves C^3 and applications
2011/8/22
Abstract: We construct a complete, bounded Legendrian immersion in C^3. As direct applications of it, we show the first examples of a weakly complete bounded flat front in hyperbolic 3-space, a weakly...
Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise
Euler-Lagrange equation phase response curve limit-cycle oscillators Poisson noise
2011/7/6
We consider optimization of phase response curves for stochastic synchronization of non-
interacting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional
shape for suf...
Hierarchical Abstraction of Phase Response Curves of Synchronized Systems of Coupled Oscillators
Coupled Oscillators Response Curves Synchronized Systems
2011/7/6
We prove that a group of injection-locked oscillators, each
modelled using a nonlinear phase macromodel, responds as a single
oscillator to small external perturbations. More precisely, we show that...
Null mannheim curves in the minkowski 3-space E13
Mannheim curve null curve Minkowski space
2011/4/6
In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E 13. We get the necessary and sufficient conditions for the nul...
Algebraic arctic curves in the domain-wall six-vertex model
Algebraic arctic domain-wall six-vertex model
2011/1/20
The arctic curve, i.e. the spatial curve separating ordered (or ‘frozen’) and disordered (or ‘temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root...
A New Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples
elliptic curves rank pythagorean triples
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves in the form of y2 = x(x−a2)(x−b2) that have positive ranks. We first generate a list of pythagorean triples (a, b, c) ...
A new family of elliptic curves with positive ranks arising from the Heron triangles
Elliptic curves Ranks Torsion group Heron’s Triangle
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves with positive ranks.
The Plateau problem for polygonal boundary curves in Minkowski 3-space
maximal immersions with singularities integrable systems
2011/2/21
We apply Garnier’s method to solve the Plateau problem for maximal surfaces in Minkowski 3-space. Our study relies on the improved version we gave in [4] of Garnier’s resolution [12] of the Plateau pr...
We prove that the Chow quotient parametrizing configurations of n points in Pd which generically lie on a rational normal curve is isomorphic to M0,n, generalizing the well-known d = 1 result of Kapra...
Uniqueness of models in persistent homology: the case of curves
Persistent Betti numbers reflections matching distance
2011/2/28
We consider generic curves in R2, i.e. generic C1 functions f : S1 → R2.We analyze these curves through the persistent homology groups of a filtration induced on S1 by f. In particular, we consider th...
This is the first in a projected series of three papers in which we construct the second flip in the log minimal model program for Mg. We introduce the notion of a weakly proper algebraic stack.
From $L$-series of elliptic curves to Mahler measures
Mahler measure L-value of elliptic curve hypergeometric series
2011/1/21
We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hyper-geometric expressions for L-values of CM elliptic curves o...
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2010/12/28
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for t...
The rationality of the moduli spaces of trigonal curves of odd genus
trigonal curve rationality of moduli
2011/1/18
The moduli spaces of trigonal curves of odd genus g ≥ 5 are proven to be rational.