Publications related to Natural logarithm

Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does n ...

Elsevier2015

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces

P_\Lambda := span\{y \mapsto y^\nu | \nu \in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma := [-1,1]^d

, based on the sa ...

MATHICSE2015

Exponential convergence of the hp version of isogeometric analysis of 1D

Annalisa Buffa

We establish exponential convergence of the hp-version of isogeometric analysis for second order elliptic problems in one spacial dimension. Specifically, we construct, for functions which are piecewise analytic with a finite number of algebraic singularit ...

Springer, Cham2014

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai

We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a ce ...

2014

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013

Solving a $6120$-bit DLP on a Desktop Computer

Robert Granger, Jens Markus Zumbrägel

In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relat ...

Springer Berlin Heidelberg2013

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling

László Forró, Arnaud Magrez, Claudio Grimaldi, Richard Gaal, Marijana Mionic Ebersold, Rita Smajda, Primoz Rebernik Ribic

The statistical analysis of the length distribution of catalytic chemical vapour deposition synthesized multi-walled carbon nanotubes cut by planetary ball milling is reported. The nanotube lengths follow a log-normal distribution in a broad range of grind ...

Amer Inst Physics2013

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

Yuri Faenza, Hans Raj Tiwary

We show that the binary logarithm of the nonnegative rank of a nonnegative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new con ...

Springer Berlin Heidelberg2012

Multielectron redox chemistry of lanthanide Schiff-base complexes

Marinella Mazzanti

Multielectron redox chemistry, which is essential in metal catalysed chemical transformations, is not easily accessible in lanthanide complexes. Here we explored the reductive chemistry of lanthanide complexes with tetradentate Schiff bases acting as redox ...

2012

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Pramod Rastogi, Sai Siva Gorthi

Simultaneous measurement of multidimensional displacements using digital holographic interferometry involves multi-directional illumination of the deformed object and requires the reliable estimation of the resulting multiple interference phase distributio ...

Optical Society of America2012

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Asymptotics of action variables near semi-toric singularities

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Exponential convergence of the hp version of isogeometric analysis of 1D

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Solving a $6120$-bit DLP on a Desktop Computer

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

Multielectron redox chemistry of lanthanide Schiff-base complexes

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Asymptotics of action variables near semi-toric singularities

Solving a $6120$-bit DLP on a Desktop Computer

MATHICSE Technical Report : Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

Multielectron redox chemistry of lanthanide Schiff-base complexes

Exponential convergence of the hp version of isogeometric analysis of 1D

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling