On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices

In this paper, we characterize the games in which Johnston, Shapley-Shubik and Penrose-Banzhaf-Coleman indices are ordinally equivalent, meaning that they rank players in the same way. We prove that these three indices are ordinally equivalent in semicomplete simple games, which is a newly defined class that contains complete games and includes most of the real-world examples of binary voting systems. This result constitutes a twofold extension of Diffo Lambo and Moulen’s result (Diffo Lambo and Moulen, 2002) in the sense that ordinal equivalence emerges for three power indices (not just for the Shapley-Shubik and Penrose-Banzhaf-Coleman indices), and it holds for a class of games strictly larger than the class of complete games.     

A Koszul complex over skew polynomial rings

We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence.     

The picard group of the variety of plane cuspidal cubics of ?3

We give a compactification of the varietyU of non-degenerate plane cuspidal cubics of ℙ³. We construct this compactification by means of the projective bundleX of a suitable vector bundleE. We describe the intersection ring ofX and, as a consequence, we obtain the intersection numbers ofU that satisfy 10 conditions of the following kinds:ρ, that the plane determined by the cuspidal cubic go through a point;c, that the cusp be on a plane;q, that the cuspidal tangent intersect a line;μ, that the cuspidal cubic intersect a line. Moreover, we prove that the Picard group of the varietyU is a product of two infinite cyclic groups generated byρ andc−q.     

Structurally Defined Water-Soluble Metallofullerene Derivatives towards Biomedical Applications

Endohedral metallofullerenes (EMFs) are excellent carriers of rare-earth element (REE) ions in biomedical applications because they preclude the release of toxic metal ions. However, existing approaches to synthesize water-soluble EMF derivatives yield mixtures that inhibit precise drug design. Here we report the synthesis of metallobuckytrio (MBT), a three-buckyball system, as a modular platform to develop structurally defined water-soluble EMF derivatives with ligands by choice. Demonstrated with PEG ligands, the resulting water-soluble MBTs show superb biocompatibility. The Gd MBTs exhibit superior T₁ relaxivity than typical Gd complexes, potentially superseding current clinical MRI contrast agents in both safety and efficiency. The Lu MBTs generated reactive oxygen species upon light irradiation, showing promise as photosensitizers. With their modular nature to incorporate other ligands, we anticipate the MBT platform to open new paths towards bio-specific REE drugs.     

Dihydrogen and Ethylene Activation by a Sterically Distorted Distibene

Herein, we report the synthesis of a sterically distorted distibene ( [4]₂ ) and its transition-metal-like reactivity towards two fundamental feedstock chemicals: H₂ and ethylene. Although [4]₂ exhibits an unusually long Sb=Sb distance and noticeable backbone distortion in the solid state, NMR data suggest that [4]₂ remains predominantly as a dimer in solution, even at high temperatures. However, it was proposed that the elusive reactivity of [4]₂ toward H₂ and ethylene results from reversible dissociation of [4]₂ into the transient stibinidene ( [4] ), which could be observed by NMR spectroscopic techniques.     

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of ClO(2) and C(4)H(4)O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies.     

Pseudoephedrine‐Directed Asymmetric α‐Arylation of α‐Amino Acid Derivatives

Available α‐amino acids undergo arylation at their α position in an enantioselective manner on treatment with base of N′‐aryl urea derivatives ligated to pseudoephedrine as a chiral auxiliary. In situ silylation and enolization induces diastereoselective migration of the N′‐aryl group to the α position of the amino acid, followed by ring closure to a hydantoin with concomitant explulsion of the recyclable auxiliary. The hydrolysis of the hydantoin products provides derivatives of quaternary amino acids. The arylation avoids the use of heavy‐metal additives, and is successful with a range of amino acids and with aryl rings of varying electronic character.     

Purification of Uranium‐based Endohedral Metallofullerenes (EMFs) by Selective Supramolecular Encapsulation and Release

Supramolecular nanocapsule 1 ?(BArF)₈ is able to sequentially and selectively entrap recently discovered U₂@C₈₀ and unprecedented Sc₂CU@C₈₀, simply by soaking crystals of 1 ?(BArF)₈ in a toluene solution of arc‐produced soot. These species, selectively and stepwise absorbed by 1 ?(BArF)₈, are easily released, obtaining highly pure fractions of U₂@C₈₀ and Sc₂CU@C₈₀ in one step. Sc₂CU@C₈₀ represents the first example of a mixed metal actinide‐based endohedral metallofullerene (EMF). Remarkably, the host–guest studies revealed that 1 ?(BArF)₈ is able to discriminate EMFs with the same carbon cage but with different encapsulated cluster and computational studies provide support for these observations.     

Development of an analytical procedure for the determination of emerging and priority organic pollutants in leafy vegetables by pressurized solvent extraction followed by GC–MS determination

A new multiresidue method for the determination of 13 emerging and priority pollutants in lettuce, including pesticides, pharmaceuticals, personal care products, polycyclic aromatic hydrocarbons (PAHs), and phenolic estrogens, has been developed using matrix solid-phase dispersion combined to pressurized fluid extraction (PFE) followed by gas chromatography coupled to mass spectrometry determination. A sequential optimization strategy based on solvent optimization first, followed by experimental design, was performed in order to maximize target analyte extraction with the aid of response surface methodology. Firstly, a full factorial design was applied to choose the significant variables in PFE; extraction time and temperature were found to have the biggest overall effect on response for most of analytes. They were later optimized performing a central composite design and the variable response of these factors was modeled for all analytes. It was found that marked differences in physicochemical nature exerted a strong influence on extraction conditions and yield. Therefore, the effect of parameters on the response was rather different for some compounds. To overcome this conflicting behavior, a multiple response simultaneous optimization was applied using the desirability function to achieve global optimal operating conditions. The optimal conditions were attained at 13.5 min (two extraction cycles) and 104 °C in the PFE by using hexane acetone mixture (1:1). Limit of detection and limit of quantitation values were found to be between 6.6 and 58 and 7.6 and 61.7 μg kg⁻¹, respectively.     

Hydrodynamic Effects in Soft‐matter Self‐assembly: The Case of J‐Aggregates of Amphiphilic Porphyrins

Chiral J‐aggregates of achiral amphiphilic porphyrins (4‐sulfonatophenyl and aryl meso‐substituted porphyrins) show several effects under the hydrodynamic forces of common stirring. These effects can be classified as pure mechanic (e. g. elasticity, plasticity and breaking of the self‐assembly non‐covalent bonding) and chemically selective as detected in the formation/growth of the nanoparticles. Diastereoselective, enantioselective and, depending on the sign of chiral shear forces, even enantiospecific selections have been described. Some types of these effects have been reported in other type of J‐aggregates. Reversible and irreversible structural effects have been studied by atomic force imaging. The determination of the optical polarization properties (linear and circular) of their solutions is best done using Mueller matrix polarimetry methods.