Elements of geometric theory for functions of quaternionic variable

Based on idens in the classical complex case, in this note we present some possible ways of extension of the classical geometric function theory to functions of quaternlonic variables. An univalence result is obtained and certain kinds of starlikeness and of convexity are studied.     

An electrochemical and structural investigation of silicon nanowires as negative electrode for Li-ion batteries

The electrochemical and structural responses of silicon nanowires deposited by chemical vapor deposition are investigated. Transmission electron microscopy and X-ray diffraction experiments show the electrochemical lithiation of SiNWs is not a quantitative process in good agreement with cycling experiments performed as a function of cycling limits. The SiNWs are not deeply lithiated as revealed by TEM micrographs. Our results suggest the existence of two well-defined lithiation steps, first at ∼0.2 V into amorphous silicon and then into crystalline silicon at ∼0.1 V. Cycling SiNWs above 100 mV avoid the lithiation of c-Si which preserves the silicon 3-D architecture and results in good cycling performances. A stable capacity value of ∼500 mAh g⁻¹ is achieved over at least 50 cycles.     

Une caractérisation des variétés complexes compactes parallélisables admettant des structures affines

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections. To cite this article: S. Dumitrescu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Exact results for noise power spectra in linear biochemical reaction networks

We present a simple method for determining the exact noise power spectra and related statistical properties for linear chemical reaction networks. The method is applied to reaction networks which are representative of biochemical processes such as gene expression. We find, for example, that a post-translational modification reaction can reduce the noise associated with gene expression. Our results also indicate how to coarse grain networks by the elimination of fast reactions. In this context we have discovered a breakdown of the sum rule which relates the noise power spectrum to the total noise. The breakdown can be quantified by a sum rule deficit, which is found to be universal, and can be attributed to the high-frequency noise in the fast reactions.     

Some rigidity results for non-commutative Bernoulli shifts

We introduce the outer conjugacy invariants , for cocycle actions σ of discrete groups G on type II₁ factors N, as the set of real numbers t>0 for which the amplification σ^t of σ can be perturbed to an action, respectively, to a weakly mixing action. We calculate explicitly and the fundamental group of σ, , in the case G has infinite normal subgroups with the relative property (T) (e.g., when G itself has the property (T) of Kazhdan) and σ is an action of G on the hyperfinite II₁ factor by Connes–Størmer Bernoulli shifts of weights {t_i}_i. Thus, and coincide with the multiplicative subgroup S of generated by the ratios {t_i/t_j}_i,j, while if S={1} (i.e. when all weights are equal), and otherwise. In fact, we calculate all the “1-cohomology picture” of σ^t,t>0, and classify the actions (σ,G) in terms of their weights {t_i}_i. In particular, we show that any 1-cocycle for (σ,G) vanishes, modulo scalars, and that two such actions are cocycle conjugate iff they are conjugate. Also, any cocycle action obtained by reducing a Bernoulli action of a group G as above on to the algebra pNp, for p a projection in N, p≠0,1, cannot be perturbed to a genuine action.     

Strong rigidity of II1 factors arising from malleable actions of w-rigid groups, II

We prove that any isomorphism θ:M₀≃M of group measure space II₁ factors, , , with G₀ an ICC group containing an infinite normal subgroup with the relative property (T) of Kazhdan-Margulis (i.e. G₀w-rigid) and σ a Bernoulli action of some ICC group G, essentially comes from an isomorphism of probability spaces which conjugates the actions with respect to some identification G₀≃G. Moreover, any isomorphism θ of M₀ onto a “corner” pMp of M, for p∈M an idempotent, forces p=1. In particular, all group measure space factors associated with Bernoulli actions of w-rigid ICC groups have trivial fundamental group and any isomorphism of such factors comes from an isomorphism of the corresponding groups. This settles a “group measure space version” of Connes rigidity conjecture, shown in fact to hold true in a greater generality than just for ICC property (T) groups. We apply these results to ergodic theory, establishing new strong rigidity and superrigidity results for orbit equivalence relations.     

Killing fields of holomorphic Cartan geometries

We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus.     

Analysis of an Euler implicit‐mixed finite element scheme for reactive solute transport in porous media

In this article, we analyze an Euler implicit‐mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, a model for subsurface fluid flow. We prove the convergence of the scheme by estimating the error in terms of the discretization parameters. In doing so we take into account the numerical error occurring in the approximation of the fluid flow. The article, is concluded by numerical experiments, which are in good agreement with the theoretical estimates. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010