Une généralisation du théorème de Kobayashi-Ochiai

We establish relations between the growth of non-degenerate holomorphic maps \(\varphi\) from \({\mathbb{C}}^n\) to X, an n-dimensional compact Kähler manifold, and the positivity of the canonical bundle of X. The general principle is that the growth increases with this positivity. In the extreme case where X is of general type, such maps do not exist, a result of Kobayashi-Ochiai. In the other extreme, if the growth is sufficiently slow (see theorem 1), we show that X is uniruled if projective. K. Kodaira obtained the weaker property that X has no nonzero pluricanonical forms. Our results interpolate between, and include, these two extreme cases.     

Supramolecular structural diversity among first-generation hybrid dendrimers and twin dendrons

Hybrid dendrimers, obtained by complete monofunctionalization of the peripheral amines of a "zero-generation" polyethyleneimine dendrimer, provide structurally diverse lamellar, columnar, and cubic self-organized lattices that are less readily available from other modified dendritic structures. The reaction of tris(2-aminoethyl)amine (TREN) with 4-dodecyloxybenzimidazolide provides only the corresponding zero-generation TREN dendrimer. From the mixture of tri- and disubstituted TREN derivatives obtained from first-generation self-assembling dendritic imidazolides, the hybrid dendrimer and a twin dendron could be separated, purified, and characterized. The hybrid dendrimers display smectic, columnar hexagonal (Phi(h)), and cubic (Pm_3n) lattices. The TREN twin dendrons, on which only two peripheral amines have been acylated, exhibit centered-rectangular columnar (Phi(r-c)), Phi(h), and Pm_3n lattices. The existence of a thermoreversible Phi(h)-to-Pm_3n phase transition in the first-generation hybrid dendrimers and twin dendrons is exploited to elucidate an epitaxial relationship between the two mesophases. We postulate a mechanism by which the transition proceeds. The thermoreversible Phi(h)-to-Pm_3n phase change is accompanied by optical property changes that are suitable for rudimentary signaling or logic functions. This structural diversity reflects the quasiequivalence of flat-taper and conical self-assembling dendrons and the ability of flexible dendrimers to accommodate concomitant conformational and shape changes.     

Fundamental parameter approach to XRF spectroscopy measurements of arsenic in polyester resin skin phantoms

A fundamental parameter (FP) approach that explicitly incorporates the energy‐broadening response of the detector was developed. The ratio between Kα fluorescence peak area and the sum of coherently and incoherently scattered peak areas was used as an indicator of trace element concentration. The peak ratio was theoretically calculated using the FP method. The energy‐broadening response curve of the Si(Li) detector was estimated by matching the theoretical and experimental values of this ratio. The method was implemented for the analysis of the K‐shell x‐ray fluorescence (K‐XRF) spectra of six polyester resin samples corresponding to six different arsenic concentrations. A ¹⁰⁹Cd radioactive source provided the excitation radiation for spectra acquisition. The predicted detector energy resolution expressed as full width at half‐maximum (FWHM) for Fe Kα fluorescence peak (208 ± 5 eV at 6.4 keV) and As Kα fluorescence peak (222 ± 5 eV at 10.5 keV) were in agreement with the experimental measurements. Copyright © 2008 John Wiley & Sons, Ltd.     

Heat transfer and hydraulic performance models for a family of aluminum plate heat exchanger with transversal offset strip fins

This paper presents the experimental analysis of aluminum BPHX, with dimensions of 215 × 80 × 61 mm, having transversal offset strip fins with two pitches of 5 and 6.8 mm using liquid to liquid to measure the heat transfer and pressure drop performance in the Reynolds range of transitional to turbulent regime [10³, 10⁴]. Firstly, the heat exchangers were tested using water on both sides. A heat transfer and friction coefficients empirical correlations were determined, and the resulted functions were compared with two other models presented in the literature. Secondly, the heat exchangers were measured using water and engine oil as hot fluid.     

Injectivity of the Cauchy-stress tensor along rank-one connected lines under strict rank-one convexity condition

In this note, we show that the Cauchy stress tensor \(\sigma\) in nonlinear elasticity is injective along rank-one connected lines provided that the constitutive law is strictly rank-one convex. This means that \(\sigma(F+\xi\otimes\eta)=\sigma(F)\) implies \(\xi \otimes\eta=0\) under strict rank-one convexity. As a consequence of this seemingly unnoticed observation, it follows that rank-one convexity and a homogeneous Cauchy stress imply that the left Cauchy-Green strain is homogeneous, as is shown in Mihai and Neff (Int. J. Non-Linear Mech., 2016, to appear).     

Synthesis and Toxicity Evaluation of New Pyrroles Obtained by the Reaction of Activated Alkynes with 1-Methyl-3-(cyanomethyl)benzimidazolium Bromide

A series of new pyrrole derivatives were designed as chemical analogs of the 1,4-dihydropyridines drugs in order to develop future new calcium channel blockers. The new tri- and tetra-substituted N-arylpyrroles were synthesized by the one-pot reaction of 1-methyl-3-cyanomethyl benzimidazolium bromide with substituted alkynes having at least one electron-withdrawing substituent, in 1,2-epoxybutane, acting both as the solvent and reagent to generate the corresponding benzimidazolium N3-ylide. The structural characterization of the new substituted pyrroles was based on IR, NMR spectroscopy as well as on single crystal X-ray analysis. The toxicity of the new compounds was assessed on the plant cell using Triticum aestivum L. species and on the animal cell using Artemia franciscana Kellogg and Daphnia magna Straus crustaceans. The compounds showed minimal phytotoxicity on Triticum rootlets and virtually no acute toxicity on Artemia nauplii, while on Daphnia magna, it induced moderate to high toxicity, similar to nifedipine. Our research indicates that the newly synthetized pyrrole derivatives are promising molecules with biological activity and low acute toxicity.     

A Dilation Theory Approach to Cubature Formulas. II

An interpretation of multivariate cubature formulas for positive measures in terms of Hilbert space operators leads to a parametrization of all finite‐rank, cyclic and commutative dilations of a given cyclic tuple of self‐adjoint operators. Explicit matricial formulas for these dilations are presented; the abstract dilation problem suggested by the concrete computations is stated at the end of the note.     

Optimal trajectories which are tangent to an affine distribution

In this work we study the trajectories which are tangent to an affine sub-bundle in the tangent bundle of a manifold and which minimize the “total energy”.We give some characterizations of such “regular” trajectories in terms of control theory and geometrical theory. We also build some sufficient conditions of existence for such curves. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Artificial radioactive contamination of sediments along the Romanian sector of the Danube river and the Black Sea coast

The concentrations of⁹⁰Sr,²³⁸Pu,^239,240Pu and²⁴¹Am were determined in 12 sediment samples, collected from the bed of the Romanian sector of the Danube river and the Black Sea coast during 1996–1997. The samples were dissolved using a microwave digestion technique which left the refractory part of the samples undissolved. Part of the samples were also dissolved totally by alkaline fusion. The results obtained after radiochemical separations and measurement of the radionuclides by the two dissolution methods were compared recommending the optimum method. The radioactive contamination of the investigated sector in 1996–1997 is compared with the results obtained for the same locations in 1994–1995 reported in previous papers.