Center cyclicity of a family of quartic polynomial differential system

In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as

$$\dot{z} = i z + z \bar{z}\big(A z^2 + B z \bar{z} + C \bar{z}^2 \big),$$

where \({A,B,C \in \mathbb{C}}\). We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.

     

Nucleophilic Aromatic Substitution on Pentafluorophenyl‐Substituted Dipyrranes and Tetrapyrroles as a Route to Multifunctionalized Chromophores for Potential Application in Photodynamic Therapy

The application of porphyrinoids in biomedical fields, such as photodynamic therapy (PDT), requires the introduction of functional groups to tune their solubility for the biological environment and to allow a coupling to other active moieties or carrier systems. A valuable motif in this regard is the pentafluorophenyl (PFP) substituent, which can easily undergo a regiospecific nucleophilic replacement (S_NAr) of its para‐fluorine atom by a number of nucleophiles. Here, it is shown that, instead of amino‐substitution on the final porphyrinoid or BODIPY (boron dipyrromethene), the precursor 5‐(PFP)‐dipyrrane can be modified with amines (or alcohols). These dipyrranes were transformed into amino‐substituted BODIPYs. Condensation of these dipyrranes with aldehydes gave access to trans‐A₂B₂‐porphyrins and trans‐A₂B‐corroles. By using pentafluorobenzaldehyde, it was possible to introduce another para‐fluorine atom, which enabled the synthesis of multifunctionalized tetrapyrroles. Furthermore, alkoxy‐ and amino‐substituted dipyrranes were applied to the synthesis of A₃B₃‐hexaphyrins. The polar porphyrins that were prepared by using this method exhibited in vitro PDT activity against several tumor cell lines.     

Mononuclear rearrangements of heterocycles in water/β-CD: information on the real site of reaction from structural modifications of substrates and from proton concentration dependence of the reactivity

The effect of β-cyclodextrin (β-CD) on the reactivity in the base-catalyzed pathway for the rearrangement in water of some (Z)-hydrazones of 3-benzoyl-1,2,4-oxadiazoles (1b-f) into the relevant triazoles (2b-f) was investigated, finding different behavior as a function of the proton concentration. ESIMS and ¹H NMR data evidence the formation of host-guest complexes. The whole of the experimental and calculated (MM2) data enabled us to draw some intriguing conclusions concerning the influence of the structures of the substrates and the nature of the formed host-guest complexes on the real site of the reaction.     

A microfluidic device for parallel 3-D cell cultures in asymmetric environments

We demonstrate a concept for how a miniaturized 3-D cell culture in biological extracellular matrix (ECM) or synthetic gels bridges the gap between organ-tissue culture and traditional 2-D cultures. A microfluidic device for 3-D cell culture including microgradient environments has been designed, fabricated, and successfully evaluated. In the presented system stable diffusion gradients can be generated by application of two parallel fluid flows with different composition against opposite sides of a gel plug with embedded cells. Culture for up to two weeks was performed showing cells still viable and proliferating. The cell tracer dye calcein was used to verify gradient formation as the fluorescence intensity in exposed cells was proportional to the position in the chamber. Cellular response to an applied stimulus was demonstrated by use of an adenosine triphosphate gradient where the onset of a stimulated intracellular calcium release also depended on cell position.     

A new insight into using chlorine leaving group and nucleophile carbon kinetic isotope effects to determine substituent effects on the structure of SN2 transition states

Chlorine leaving group k(35)/k(37), nucleophile carbon k(11)/k(14), and secondary alpha-deuterium [(kH/kD)alpha] kinetic isotope effects (KIEs) have been measured for the SN2 reactions between para-substituted benzyl chlorides and tetrabutylammonium cyanide in tetrahydrofuran at 20 degrees C to determine whether these isotope effects can be used to determine the substituent effect on the structure of the transition state. The secondary alpha-deuterium KIEs indicate that the transition states for these reactions are unsymmetric. The theoretical calculations at the B3LYP/aug-cc-pVDZ level of theory support this conclusion; i.e., they suggest that the transition states for these reactions are unsymmetric with a long NC-C(alpha) and reasonably short C(alpha)-Cl bonds. The chlorine isotope effects suggest that these KIEs can be used to determine the substituent effects on transition state structure with the KIE decreasing when a more electron-withdrawing para-substituent is present. This conclusion is supported by theoretical calculations. The nucleophile carbon k(11)/k(14) KIEs for these reactions, however, do not change significantly with substituent and, therefore, do not appear to be useful for determining how the NC-C(alpha) transition-state bond changes with substituent. The theoretical calculations indicate that the NC-C(alpha) bond also shortens as a more electron-withdrawing substituent is placed on the benzene ring of the substrate but that the changes in the NC-C(alpha) transition-state bond with substituent are very small and may not be measurable. The results also show that using leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is more complicated than previously thought. The implication of using both chlorine leaving group and nucleophile carbon KIEs to determine the substituent effect on transition-state structure is discussed.     

Monosolvation of R-1-phenyl-2,2,2-trifluoroethanol with amines: configurational effects on the excitation, ionization, and fragmentation of diastereomeric complexes

Wavelength and mass selected resonant two-photon ionization spectra of molecular clusters between R-1-phenyl-2,2,2-trifluoroethanol (FER) and methylamine (M) or the enantiomers of 2-aminobutane (AR and AS) were recorded after supersonic molecular beam expansion and analyzed with the aid of ab initio molecular orbital calculations. The experimental results agree with theoretical calculations pointing to the predominance of the two most stable conformers of monosolvated FER whose CF3 group establishes intense NH...F interactions with the selected amines so as to orient them away from the aromatic ring. This reduces the enantioselectivity of FER toward the 2-aminobutane enantiomers as compared to that exhibited by the R-1-phenylethanol (ER) analogue, where obviously NH...F interactions are absent.     

Intercomparison exercise on difficult to measure radionuclides in activated concrete—statistical analysis and comparison with activation calculations

Journal of Radioanalytical and Nuclear Chemistry - This paper reports the results obtained in a Nordic Nuclear Safety Research project during the second intercomparison exercise for the...     

On the average volume of sections of convex bodies

The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: \(as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|} d\sigma \left( \xi \right)\). We study the question whether there exists an absolute constantC > 0 such that for every n, for every centered convex body K in R ⁿ and for every 1 ≤ k ≤ n ? 2,

$$as\left( K \right) \leqslant {C^k}{\left| K \right|^{\frac{k}{n}}}\mathop {\max }\limits_{|E \in G{r_{n - k}}} {\kern 1pt} as\left( {K \cap E} \right)$$

. We observe that the case k = 1 is equivalent to the hyperplane conjecture. We show that this inequality holds true in full generality if one replaces C by CL _K orCd_ovr(K, BP _k ⁿ ), where L _K is the isotropic constant of K and dovr(K, BP _k ⁿ ) is the outer volume ratio distance of K to the class BP _k ⁿ of generalized k-intersection bodies. We also compare as(K) to the average of as(K ∩ E) over all k-codimensional sections of K. We examine separately the dependence of the constants on the dimension when K is in some classical position. Moreover, we study the natural lower dimensional analogue of the average section functional.

     

Dissymmetry effects on the laser spectroscopy of supersonically expanded rare gas/chiral arene heteroclusters

The R2PI-TOF spectra of supersonically expanded rare gas/chiral arene heteroclusters have been rationalized in terms of the distortion of the pi-electron density reflecting the different dipole and quadrupole momenta induced in the rare gas atoms by interaction with the opposite pi-faces of the chiral arene itself.