Fonctions séparément harmoniques,un théorème de type Terada

Given D a domain in , G an open set in and E a subset of D verifying the harmonic analogue of Local Polynomial Condition of Leja at some point in D. We prove that if f(x, y) is a complex function defined on D × G such that– f(x, ) is harmonic on G for every fixed x E,– f(, y) is harmonic on D for every fixed y G,then f is harmonic in (x, y) on D × G.     

Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial Conditions

We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.     

Nuclear Physics in Norway, 1933–1955

In the late 1940s and the 1950s, Norwegian nuclear scientists, engineers, and administrators were deeply split over their nation’s goals, organization, politics, and tools for research in nuclear physics. One faction was determined to build a nuclear reactor in Norway, while another fiercely opposed the reactor plans and focused on particle accelerators. The first faction comprised scientific entrepreneurs and research technologists, the second academic scientists, most of whom began their research careers in nuclear physics in the 1930s. To understand this conflict, I trace the development of nuclear research in Norway from the early 1930s to the mid-1950s, placing it within an international context. Roland Wittje is working on his habilitation thesis in the History of Science Unit at the University of Regensburg, Germany.     

Constructing rational and multi‐wave solutions to higher order NEEs via the Exp‐function method

In this paper, we present an application of some known generalizations of the Exp‐function method to the fifth‐order Burgers and to the seventh‐order Korteweg de Vries equations for the first time. The two examples show that the Exp‐function method can be an effective alternative tool for explicitly constructing rational and multi‐wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered. Copyright © 2011 John Wiley & Sons, Ltd.     

Degree conditions for group connectivity

Let G be a 2-edge-connected simple graph on n≥13 vertices and A an (additive) abelian group with |A|≥4. In this paper, we prove that if for every uv∉E(G), max{d(u),d(v)}≥n/4, then either G is A-connected or G can be reduced to one of K_2,3,C₄ and C₅ by repeatedly contracting proper A-connected subgraphs, where C_k is a cycle of length k. We also show that the bound n≥13 is the best possible.     

Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression

In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences generally neglected in the derived expressions of the critical buckling load published in the literature. The elastic multiple Donnell shells continuum approach is employed for modelling the multi-walled carbon nanotubes. The validation of the proposed formula is made by comparison with a numerical solution. The influence of the neglected terms is also studied.     

The effect of chiral doping in achiral smectic liquid crystals on the de Vries characteristics: smectic layer thickness,electro-optics and birefringence

An addition of chiral dopant to two achiral smectic liquid crystals from a homologous series, by varying weight percentages with known low values of layer shrinkage, leads to chiral smectic-C* phase with a finite value of the spontaneous polarisation. The electro-optical response arising from changes in the induced apparent tilt angle brought about by a weak electric field in the SmA* phase gives rise to power law dependency on the reduced temperature. The critical exponent γ of the power law depends on the dopant concentration but its value is found to be greater than the typical value of 1.32. This implies that the short-range correlation extends from two dimensions to three dimensions in these materials in the SmA phase. The layer thickness of smectic layers in the guest–host system remains unaltered up to the 15 wt % addition of the chiral dopant to two achiral smectics. The system thus retains the low layer shrinkage of the achiral smectic as evidenced by measurements of the layer thickness from X-ray scattering and thickness measurements from optical interferometry. Results on the optical birefringence and the apparent tilt angle lead us to the conclusion of having successfully obtained chiral smectic materials for devices with de Vries characteristics by chiral doping.     

de Sitter Tunneling,Emission Spectrum and Entropy/Area Quantum

The Banerjee-Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case of a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It is interestingly found that the area of the CH is quantized by Δ A=4l_pl², as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.     

De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

Analytical model for thermal resistance due to multiple moving circular contacts on a coated bodyModèle analytique pour la résistance thermique due à des contacts circulaires mobiles multiples à la surface d'un solide revêtu

The heat transfer at the interface of two solids in sliding/rolling contact depends on the constriction phenomenon which occurs at the vicinity of asperities. In order to study this problem, the micro-contacts are represented by multiple moving circular heat sources on the surface of a body. The studied body is constituted of a substrate and a surface coating. The thermal constriction resistance due to those contacts is determined analytically in this paper. The solution is developed by using the integral Fourier transforms, and it is valid regardless of the velocity and the relative contact size values. To cite this article: A. Baïri, C. R. Mecanique 331 (2003).