Double Molecular Encapsulation of Tetrahydrofuran by an Amphiphilic Calix-[4]-arene

The crystal structure of para-octanoylcalix-[4]-arene·2 tetrahydrofuran complex reveals double inclusion of the guest molecules, one deep in the aromatic cavity and the other held in a four-fingered molecular hand formed by the aliphatic chains, the inclusion changes the molecular packing from a bilayer system in the absence of guest, to a head-to-tail antiparallel chain packing.     

The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations

In this Note, we formulate sufficient conditions for regularity of a so called suitable weak solution (v;p) in a sub-domain D of the time–space cylinder Q_T by means of requirements on one of the eigenvalues or on the eigenvectors of the symmetrized gradient of velocity. To cite this article: J. Neustupa, P. Penel, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

7,8‐(Dichloromethano)homo[70]fullerene,an Unusual,but Unexceptional,Methanoannulene

The crystal structure of 7,8‐(dichloromethano)homo[70]fullerene shows that addition of the dichlorocarbene (:CCl₂) to C₇₀ gives a surprisingly normal methano‐bridged [9]annulene. The structural changes caused by the addition are highly localized; the C(7)? C(8) distance lengthens by 0.705(2) Å but no other distance changes by more than 0.022(3) Å. Bond angles within the [9]annulene increase by as much as 7.8(1)°, but changes outside the C₉ ring are much smaller. The nearly ellipsoidal molecules form hexagonally close‐packed layers that interact in pairs through short Cl???C, and possibly short Cl???Cl and C???C, interactions.     

A Frequency Selection Criterion in Spatially Developing Flows

The possible existence of global modes or self-excited linear resonances in spatially developing systems is explored within the framework of the WKBJ approximation. It is shown that the existence and properties of the dominant global mode may be deduced from the variations of the local absolute frequency ω₀ with distance X. The main results are summarized in two theorems: (1) A system with no region of absolute instability does not sustain temporally growing global modes with an O(1) growth rate. (2) If the singularity X, closest to the real X-axis of the complex function ω₀(X) is a saddle point, the most unstable global mode has, to leading order in the WKBJ approximation, a complex frequency ω₀(X_s). Thus, it will be temporally growing only if ω₀(X_s) is positive.     

Plants and Fibonacci

The universality of many features of plant patterns and phyllotaxis has mystified and intrigued natural scientists for at least four hundred years. It is remarkable that, to date, there is no widely accepted theory to explain the observations. We hope that the ideas explained below lead towards increased understanding     

Maximum variance unimodal distributions

A new sufficient condition for the variance of a unimodal distribution in ?a, b? to have the least upper bound $\text{(b ? a)}{}^2\text{12}$ is derived. This condition is more general than the condition found by Jacobson (1969). A new proof that the least upper bound for all unimodal distributions in ?a, b? is $\text{(b ? a)}{}^2\text{9}$ is also given. These results are used to construct a new estimator of the variance of such distributions.     

Correction to a constructive decomposition and Fulkerson's characterization of permutation matrices

The purpose of this note is to point out an error in the paper [2], named in the title above, published under my authorship in this Journal in 1971.