A threshold property for intersections in a finite set

Let F be any family of subsets of a finite set E and let n be an integer, n<|F|. Under what condition does the knowledge of cardinals of m-intersections in F, for all m≤n, univocally determine the cardinal of any intersection in F, and what is the minimal condition? We give a complete answer to that. For any n, this determination property is satisfied by n if and only if |E|<2ⁿ, without further condition on F.     

Carbon nanotubes as nanoparticles collector

This communication reports on a new method for the collection of nanoparticles using carbon nanotubes (CNT) as collecting surfaces, by which the problem of agglomeration of nanoparticles can be circumvented. CNT (10–50 nm in diameter, 1–10 μm in length) were grown by thermal CVD at 923 K in a 7 v/v% C₂H₂ in N₂ mixture on electroless nickel-plated copper transmission electron microscopy (TEM) grids and Monel coupons. These samples were then placed downstream of an arc plasma reactor to collect individual copper nanoparticles (5–30 nm in diameter). It was observed that the Cu nanoparticles preferentially adhere onto CNT and that the macro-particles (diameter >1 μm), a usual co-product obtained with metal nanoparticles in the arc plasma synthesis, are not collected. Cu–Ni nanoparticles, a catalyst for CNT growth, were deposited on CNT to grow multibranched CNT. CNT-embedded thin films were produced by re-melting the deposited nanoparticles.     

Topological Entropy and Secondary Folding

A convenient measure of a map or flow’s chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with ‘secondary folding’: material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.     

Regular subsets of valued fields and Bhargava’s v-orderings

We generalize notions and results obtained by Amice for regular compact subsets S of a local field K and extended by Bhargava to general compact subsets of K. Considering any ultrametric valued field K and subsets S that are regular in a generalized sense (but not necessarily compact), we show that they still have strong properties such as having v-orderings ${\{a_n\}_{n\geq0}}$ which satisfy a generalized Legendre formula, which are very well ordered and well distributed sequences in the sense of Helsmoortel and which remain v-orderings when a finite number of the initial terms of the sequence are deleted.     

An articulatory basis for the labial-to-coronal effect: /pata/ seems a more stable articulatory pattern than /tapa/

This paper investigates the coordination between the jaw, the tongue tip, and the lower lip during repetition with rate increase of labial-to-coronal (L(a)C(o)) consonant-vowel-consonant-vowel disyllables (e.g., /pata/) and coronal-to-labial (C(o)L(a)) ones (e.g., /tapa/) by French speakers. For the two types of disyllables: (1) the speeding process induces a shift from two jaw cycles per disyllable to a single cycle; (2) this shift modifies the coordination between the jaw and the constrictors, and (3) comes with a progression toward either a L(a)C(o) attractor [e.g., (/pata/ or /tapa/) --> /patá/ --> /ptá/] or a C(o)L(a) one (e.g., /pata/ or /tapa/ --> /tapá/ --> /tpá/). Yet, (4) the L(a)C(o) attractor is clearly favored regardless of the initial sequencing. These results are interpreted as evidence that a L(a)C(o) CVCV disyllable could be a more stable coordinative pattern for the lip-tongue-jaw motor system than a C(o)L(a) one. They are discussed in relation with the so-called LC effect that is the preference for L(a)C(o) associations rather than C(o)L(a) ones in CV.CV disyllables in both world languages and infants' first words.     

Impact of bidirectional charge transfer and molecular distortions on the electronic structure of a metal-organic interface

Interface energetics are of fundamental importance in organic and molecular electronics. By combining complementary experimental techniques and first-principles calculations, we resolve the complex interplay among several interfacial phenomena that collectively determine the electronic structure of the strong electron acceptor tetrafluoro-tetracyanoquinodimethane chemisorbed on copper. The combination of adsorption-induced geometric distortion of the molecules, metal-to-molecule charge transfer, and molecule-to-metal back transfer leads to a net increase of the metal work function.     

Alkylation of H-phosphinate esters under basic conditions

An efficient and general procedure was developed for the direct alkylation of H-phosphinate esters with LHMDS at low temperature. The simplicity of the reaction allows the use of various H-phosphinate esters and takes place with a wide range of electrophiles. The approach can be employed to access some GABA analogues or precursors to GABA analogues. The isolated yields are moderate to good. This is the first report of an alkylation with a secondary iodide or a primary chloride.     

Toward selective reactions with C-H bonds: a rationale for the regio- and stereochemistry of dichlorocarbene insertions into cyclic hydrocarbons

DFT calculations have been performed to study the course of dichlorocarbene insertion reactions into alkanes and to better understand the regio- and stereoselectivities observed. At the B3LYP/6-31G(d) level of theory, the selectivity of dichlorocarbene insertions into a number of hydrocarbons agrees well with the obtained experimental results. The reactivity of a specific C-H bond is determined by the capacity of the remaining alkyl fragment to effectively delocalize the partial positive charge buildup during the reaction. This activity can readily be estimated by calculation of the hydride transfer potential (HTP). A comparison with the structure and the stability of the corresponding cation is useful to emphasize the origins of the selectivity. Dichlorocarbene is also predicted to react efficiently with acidic C-H bonds through a nucleophilic-electrophilic mechanism. In principle, an attack of a carbene on an appropriately substituted three-membered ring may lead to fragmentation of the molecule.     

Foiled carbenes revisited: When sigma-stabilization surpasses pi-stabilization

The bicyclic alkenylidenes 9 (bicyclo[3.2.1]oct-2-en-8-ylidene) and 17 (bicyclo[3.3.1]non-2-en-9-ylidene) were claimed to be stabilized foiled carbenes. Our B3LYP and MP2 computations confirm previous experimental data. Moreover, they show that these carbenes are very reactive and rearrange rapidly, mainly through a 1,2-vinyl shift by overcoming a low barrier (1.2 to 5.4 kcal/mol). This is in contrast to the high barriers (up to 30 kcal/mol) predicted for the same type of rearrangements in norborn-2-en-7-ylidene derivatives. In 17 and bicyclo[4.1.1]oct-2-en-7-ylidene (23), the divalent carbon atom is even bent away from the double bond!     

Nonaqueous capillary electrophoresis in pharmaceutical analysis

This review presents different solvents and electrolytes commonly used as BGEs in NACE for the analysis of pharmaceutical compounds. Most NACE applications carried out since 1998 for the analysis of compounds of pharmaceutical interest are presented in four tables: (i) analysis of drugs and related substances, (ii) analysis of chiral substances, (iii) analysis of phytochemical extracts and (iv) analysis of drugs in biological fluids. These selected examples are used to illustrate the interest in NACE versus conventional aqueous CE.