A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...

The MEG experiment took data at the Paul Scherrer Institute in years 2009–2013 to test violation of lepton flavor conservation law, which originates from an accidental symmetry that Standard Model elementary particle physics has, and published most stringent limit on charged violating decay μ+→e+γ: BR(μ+→e+γ) <4.2×10−13 90% confidence level. detector has been upgraded order reach a sensitivi...

Properties of the law μ of the integral ∫∞ 0 c −Nt− dYt are studied, where c > 1 and {(Nt, Yt), t ≥ 0} is a bivariate Lévy process such that {Nt} and {Yt} are Poisson processes with parameters a and b, respectively. This is the stationary distribution of some generalised Ornstein-Uhlenbeck process. The law μ is parametrised by c, q and r, where p = 1−q−r, q, and r are the normalised Lévy measur...

The main goal of this article is to provide estimates mild solutions Navier–Stokes equations with arbitrary external forces in Rn for n≥2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known and Herz considered works equations. Morrey–Sobolev based weak-Herz space denoted as WK˙p,qαMμs WK˙p,qαN˙μ,rs, respectively, represent new properties interpolations. This class...

We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-v...

We study the distance-profile of the random rooted plane graph Gn with n edges (by a plane graph we mean a planar map with no loops nor multiple edges). Our main result is that the profile and radius of Gn (with 2 O. Bernardi, G. Collet, and É. Fusy In this article, we prove this type of result on the profile for rooted simple maps, that is, maps without loops nor multiple edges, which are clas...

We introduce a natural family of random walks Sn on Z that scale to fractional Brownian motion. The increments Xn := Sn − Sn−1 ∈ {±1} have the property that given {Xk : k < n}, the conditional law of Xn is that of Xn−kn , where kn is sampled independently from a fixed law μ on the positive integers. When μ has a roughly power law decay (precisely, when μ lies in the domain of attraction of an α...

Many physical processes are described by conservative quasilinear systems of equations that admit a supplementary independent conservation law. A typical example is the equations of incompressible fluid dynamics. If for basic equations the conservation laws of the momentum and the volume are chosen then the conservation law of the energy is an additional conservation law. In the present paper a...