On stable cutsets in claw-free graphs and planar graphs

A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let $K_4$ and $K_{1,3}$ (claw) denote the complete (bipartite) graph on 4 and $1+3$ vertices. It is NP-complete to decide whether a line graph (hence a claw-free graph) with maximum degree five or a $K_4$-free graph admits a stable cutset. Here we describe algorithms deciding in polynomial time whether a claw-free graph with maximum degree at most four or whether a (claw, $K_4$)-free graph admits a stable cutset. As a by-product we obtain that the stable cutset problem is polynomially solvable for claw-free planar graphs, and also for planar line graphs.Thus, the computational complexity of the stable cutset problem is completely determined for claw-free graphs with respect to degree constraint, and for claw-free planar graphs. Moreover, we prove that the stable cutset problem remains NP-complete for $K_4$-free planar graphs with maximum degree five.     

Perturbative calculation of Franck-Condon integrals: new hints for a rational implementation

Perturbative approaches to the mode mixing effects in the calculation of Franck-Condon integrals are analyzed and discussed. The zero order multidimensional Franck-Condon integrals are factorized into products of one-dimensional ones, so that recurrence relations can be used without need of storing a huge number of data. Calculations on model systems show that at the second order of perturbation, the method gives results in very good agreement with the exact ones, even in the case of significantly large Duschinsky effect. The accuracy of the results can be substantially improved by grouping together all those modes which are strongly mixed with each other, usually a few ones, for which Franck-Condon integrals can be computed exactly, and using the perturbative approach for treating the smaller mixing between all the other modes.     

Blue-LED Synthesis of Pummerer's Ketones by Peroxidase-Lignin-Catalyzed Oxidative Coupling of Substituted Phenols

Pummerer's ketones resembling the tricyclic scaffold of bioactive natural substances were synthesized by blue-LED driven Horseradish Peroxidase oxidative coupling of substituted phenols in 2-methyltetrahydrofuran by using meso-tetraphenylporphyrin as photosensitizer and dioxygen as primary oxidant. The application of functionalized lignin nanoparticles as a renewable and efficient platform for the immobilization of the enzyme extended the effectiveness of the overall process to heterogeneous catalysis under buffer limiting conditions.     

A Newtonian tale details on notes and proofs in Geneva edition of Newton's Principia

Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scientific aims. The proof of Proposition XLIII is presented and commented as a case study.     

Study on the aggregation and electrochemical properties of Rose Bengal in aqueous solution of cyclodextrins

The interactions of Rose Bengal (RB) with alpha-cyclodextrin (alpha-CD), hydroxypropyl-beta-cyclodextrin (HP-beta-CD), hydroxypropyl-gamma-cyclodextrin (HP-gamma-CD), heptakis(2,3,6-tri-O-methyll)-beta-cyclodextrin (TM-beta-CD) were studied in aqueous solutions of 0.1 M KClO(4) and 0.1 M LiClO(4) by vis absorption, fluorescence spectroscopy as well as electrochemical measurements at 298 K. The spectrophometric results indicate that RB is included in all beta- and gamma-CDs forming complexes with a stoichiometry 1:1 whose stability is slightly higher in KClO(4) than in LiClO(4) solutions. The complex stability constants determined for salt-containing CD solutions are lower than those for water solutions. The complexation of RB with beta- and gamma-CD and the differences between the complexes obtained in the presence of the two salts were confirmed by an electrochemical study.     

Quantum mechanical calculations of conformationally relevant 1H and 13C NMR chemical shifts of N-, O-, and S-substituted calixarene systems

QM GIAO calculations of (13)C and (1)H chemical shift values of the ArCH(2)Ar group in N-, O-, and S-substituted calixarene systems were performed with a hybrid DFT functional MPW1PW91 and 6-31G(d,p) basis set. A good reproduction of experimental data was obtained for some representative calixarenes and for a series of simplified calixarene models. This allowed the derivation of chemical shift surfaces versus phi and chi dihedral angles. The applicability of chemical shift surfaces in the study of calixarene conformational features is illustrated.     

Quantization of the dipole moment and of the end charges in push-pull polymers

A theorem for end-charge quantization in quasi-one-dimensional stereoregular chains is formulated and proved. It is a direct analog of the well-known theorem for surface charges in physics. The theorem states the following: (1) Regardless of the end groups, in stereoregular oligomers with a centrosymmetric bulk, the end charges can only be a multiple of 12 and the longitudinal dipole moment per monomer p can only be a multiple of 12 times the unit length a in the limit of long chains. (2) In oligomers with a noncentrosymmetric bulk, the end charges can assume any value set by the nature of the bulk. Nonetheless, by modifying the end groups, one can only change the end charge by an integer and the dipole moment p by an integer multiple of the unit length a. (3) When the entire bulk part of the system is modified, the end charges may change in an arbitrary way; however, if upon such a modification the system remains centrosymmetric, the end charges can only change by multiples of 12 as a direct consequence of (1). The above statements imply that-in all cases-the end charges are uniquely determined, modulo an integer, by a property of the bulk alone. The theorem's origin is a robust topological phenomenon related to the Berry phase. The effects of the quantization are first demonstrated in toy LiF chains and then in a series of trans-polyacetylene oligomers with neutral and charge-transfer end groups.     

Quasibound continuum states in SiF4 (D2A1) photoionization: photoelectron-vibrational coupling

The authors report a fully vibrationally resolved photoelectron spectroscopy investigation of a nonplanar molecule studied over a range of excitation energies. Experimental results for all four fundamental vibrational modes are presented. In each case significant non-Franck-Condon effects are seen. The vibrational branching ratio for the totally symmetric mode nu1+ is found to be strongly affected by resonant excitation in the SiF4+ (D2A1) photoionization channel. This is shown to be the result of two distinct shape resonances, which for the first time have been both confirmed by theoretical calculations. Vibrationally resolved Schwinger photoionization calculations are used to understand the vibronic coupling for the photoelectrons, both using ab initio and harmonic vibrational wave functions.     

A Practical Approach for the In Vitro Safety and Efficacy Assessment of an Anti-Ageing Cosmetic Cream Enriched with Functional Compounds

(1) Background: Cosmeceuticals are topical products applied to human skin to prevent skin ageing and maintain a healthy skin appearance. Their effectiveness is closely linked to the compounds present in a final formulation. In this article, we propose a panel of in vitro tests to support the efficacy assessment of an anti-ageing cream enriched with functional compounds. (2) Methods: biocompatibility and the irritant effect were evaluated on reconstructed human epidermis (RHE) and corneal epithelium (HCE) 3D models. After a preliminary MTT assay, normal human dermal fibroblasts (NHDF) and keratinocytes (HaCaT) were used to evaluate the extracellular matrix (ECM) protein synthesis, and interleukin-6 (IL-6) and metalloproteinase-1 (MMP-1) production. (3) Results: data collected showed good biocompatibility and demonstrated the absence of the irritant effect in both 3D models. Therefore, we demonstrated a statistical increase in collagen and elastin productions in NHDF cells. In HaCaT cells, we highlighted an anti-inflammatory effect through a reduction in IL-6 levels in inflammatory stimulated conditions. Moreover, the reduction of MMP-1 production after UV-B radiation was demonstrated, showing significant photo-protection. (4) Conclusion: a multiple in vitro assays approach is proposed for the valid and practical assessment of the anti-ageing protection, anti-inflammatory and biocompatible claims that can be assigned to a cosmetic product containing functional compounds.