Related papers: Notes on the Sigma invariants

We have reviewed the comment in [3], posted on arXiv.org concerning our recent work in [1]. We reply to the comment in this paper.

This paper is a sequel to "Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey…

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of the Milnor link…

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…

Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…

First I will explain my motivation to introduce the $\delta$-invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of…

These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.

We remark on the Garnier system in two variables.

We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.

We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are…

We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable…

This is a position paper written as an introduction to the special volume on quantum algorithms I edited for the journal Mathematical Structures in Computer Science (Volume 20 - Special Issue 06 (Quantum Algorithms), 2010).

A consistent approach to the description of integral coordinate invariant functionals of the metric on manifolds ${\cal M}_{\alpha}$ with conical defects (or singularities) of the topology $C_{\alpha}\times\Sigma$ is developed. According to…

We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…

This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…

In this paper, we present the invalidities of the results in [3], because of their definition of a semi-invariant submanifold of an almost complex contact metric manifold is not true .

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.