Role of antisymmetric exchange in selecting magnetic chirality in Ba3NbFe3Si2O14

We present an electron spin resonance (ESR) investigation of the acentric Ba(3)NbFe(3)Si(2)O(14), featuring a unique single-domain double-chiral magnetic ground state. Combining simulations of the ESR linewidth anisotropy and the antiferromagnetic-resonance modes allows us to single out the Dzyaloshinsky-Moriya (DM) interaction as the leading magnetic anisotropy term. We demonstrate that the rather minute out-of-plane DM component d(c)=45 mK is responsible for selecting a unique ground state, which endures thermal fluctuations up to astonishingly high temperatures.     

Phase characterization of the reflection on an extreme UV multilayer: comparison between attosecond metrology and standing wave measurements

We characterize the phase shift induced by reflection on a multilayer mirror in the extreme UV range (80-93?eV) using two techniques: one based on high order harmonic generation and attosecond metrology (reconstruction of attosecond beating by interference of two-photon transitions), and a second based on synchrotron radiation and measurements of standing waves (total electron yield). We find an excellent agreement between the results from the two measurements and a flat group delay shift (±40?as) over the main reflectivity peak of the mirror.     

Reaction-Diffusion Equations in Homogeneous Media: Existence,Uniqueness and Stability of Travelling Fronts

The goal of this survey is to describe the construction and some qualitative properties of particular global solutions of certain reaction-diffusion equations. These solutions are known as travelling fronts (or travelling waves) and play an important role in the long-time behaviour of the solutions of the parabolic system. We will mainly focus on the existence of travelling wave solutions and their stability. We will also give some standard tools in elliptic and parabolic theory, which are of general interest.     

Towards factoring in {SL(2,\,\mathbb{F}_{2^n})}

The security of many cryptographic protocols relies on the hardness of some computational problems. Besides discrete logarithm or integer factorization, other problems are regularly proposed as potential hard problems. The factorization problem in finite groups is one of them. Given a finite group G, a set of generators generators for this group and an element ${g\in G}$ , the factorization problem asks for a “short” representation of g as a product of the generators. The problem is related to a famous conjecture of Babai on the diameter of Cayley graphs. It is also motivated by the preimage security of Cayley hash functions, a particular kind of cryptographic hash functions. The problem has been solved for a few particular generator sets, but essentially nothing is known for generic generator sets. In this paper, we make significant steps towards a solution of the factorization problem in the group ${G:=\,SL(2,\,\mathbb{F}_{2^n})}$ , a particularly interesting group for cryptographic applications. To avoid considering all generator sets separately, we first give a new reduction tool that allows focusing on some generator sets with a “nice” special structure. We then identify classes of trapdoor matrices for these special generator sets, such that the factorization of a single one of these matrices would allow efficiently factoring any element in the group. Finally, we provide a heuristic subexponential time algorithm that can compute subexponential length factorizations of any element for any pair of generators of ${SL(2,\,\mathbb{F}_{2^n})}$ . Our results do not yet completely remove the factorization problem in ${SL(2,\,\mathbb{F}_{2^n})}$ from the list of potential hard problems useful for cryptography. However, we believe that each one of our individual results is a significant step towards a polynomial time algorithm for factoring in ${SL(2,\,\mathbb{F}_{2^n})}$ .     

Investigation of the microporosity of high performance concrete by proton nuclear relaxation.

The difference in microporosity features between high and ultra high performance concrete was highlighted by measuring their respective proton spin-lattice relaxation times. A surface fractal dimension was attributed to each formulation and exhibits a correlation with the amount of calcium silicate hydrates.     

ESTIMATION OF PARAMETERS IN A CLOSED PYGMY POPULATION IN CAMEROON

Inspired by Kouakep [16], we consider in this note a wellposed model with differential susceptibility and infectivity adding continuous age structure to an ODE model for a "Baka" pygmy group in the East of Cameroon(Africa).Assuming a very low contribution of carriers to infection compared to acute infection, we estimate a probability p(a)(to develop symptomatic Hepatitis B state at age a) and acute carriers' transmission rate. The value R_0= 2:67 1 of the basic reproduction number estimated from data in the east of Cameroon confirms that HBV is endemic in the Baka pygmy group.     

Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions

We present theorems which provide the existence of invariant whiskered tori in finite-dimensional exact symplectic maps and flows. The method is based on the study of a functional equation expressing that there is an invariant torus.We show that, given an approximate solution of the invariance equation which satisfies some non-degeneracy conditions, there is a true solution nearby. We call this an a posteriori approach.The proof of the main theorems is based on an iterative method to solve the functional equation.The theorems do not assume that the system is close to integrable nor that it is written in action-angle variables (hence we can deal in a unified way with primary and secondary tori). It also does not assume that the hyperbolic bundles are trivial and much less that the hyperbolic motion can be reduced to constant linear map.The a posteriori formulation allows us to justify approximate solutions produced by many non-rigorous methods (e.g. formal series expansions, numerical methods). The iterative method is not based on transformation theory, but rather on successive corrections. This makes it possible to adapt the method almost verbatim to several infinite-dimensional situations, which we will discuss in a forthcoming paper. We also note that the method leads to fast and efficient algorithms. We plan to develop these improvements in forthcoming papers.     

A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition

We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling’s technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.