Calculating the mislin genus for a certain family of nilpotent groups

It is known that the Mislin genus of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. In this paper, we compute explicitly that structure under the following additional assumptions: The torsion subgroup TN is abelian, the epimorphism N→N/TN splits and all automorphisms of TN commute with cinjugation by elements of N. Among the groups satisfying these conditions are all nilpotent split extensions of a finite cyclic group by a finitely free abelian group. We further prove that the function M ? M × N^k­1 k ≥ 2, which is in general a surjective homomorphism from the genus of N onto the genus of N^k , is an isomorphism at least in an imporatnt special case. Applications to the study of non-cancellation phenomena in group theory are given.     

Finding lower bounds on the complexity of secret sharing schemes by linear programming

Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants.By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program non-Shannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of non-representable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme.     

D‐Fructose‐6‐phosphate Aldolase in Organic Synthesis: Cascade Chemical‐Enzymatic Preparation of Sugar‐Related Polyhydroxylated Compounds

D ‐Fructose‐6‐phosphate aldolase (FSA) is a key biocatalyst for the alternative synthetic construction of biologically active products with known therapeutic and research interest or novel structures relevant to drug discovery. Novel aldol addition reactions of dihydroxyacetone and hydroxyacetone to a variety of aldehydes catalyzed by FSA are presented (see scheme).

     

Implicational (semilinear) logics III: completeness properties

This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers (Cintula and Noguera in Arch Math Logic 49(4):417–446, 2010; Arch Math Logic 53(3):353–372, 2016).     

Synthesis of new bis-BINOL-2,2′-ethers and bis-H8BINOL-2,2′-ethers evaluation of their Titanium complexes in the asymmetric ethylation of benzaldehyde

The preparation by means of different synthetic paths of a series of bis-BINOL and bis-H₈BINOL ligands is described. The ligands consist of two BINOL or H₈BINOL fragments, joined by diverse linkages through the oxygen at the 2′-position of the arylic fragments. These ligands were applied to the Ti(OⁱPr)₄ catalyzed asymmetric alkylation of benzaldehyde with Et₂Zn. The performance of these catalysts is very sensitive to the nature of the ether linkage. The ligand with a propylene link shows better enantioselectivity (ca. 70%) than those with two or four carbon atoms joining the BINOL fragments. Furthermore, using the propylene link, but replacing (R)-BINOL by (R)-H₈BINOL, a significant improvement in the stereoselectivity of the catalysts was achieved (ca. 80% ee in (R)-1-phenylpropan-1-ol). A cooperative effect was observed between the chirality at the BINOL fragment and that of a (S,S)-4,5-bis(methylene)-2,2-dimethyl-1,3-dioxolane link, derived from tartaric acid. When this chiral link combines with two (S)-BINOL fragments, the alkylation of benzaldehyde in toluene produces 70% ee of (S)-1-phenylpropan-1-ol, while the (R)-BINOL derivative ligand with the same link, in identical conditions, yields only 40% ee of the (R)-alcohol.     

Symmetrically multilateral-bargained allocations in multi-sided assignment markets

We extend the notion of symmetrically pairwise-bargained (SPB) allocations (Rochford, J Econ Theory, 34:262–281, 1984) to balanced assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent’s payoff remains invariant after a negotiation process between all agents based on what they could receive—and use as a threat—in their preferred alternative matching to any given optimal matching. We prove that, for balanced multi-sided assignment games, the set of SMB is always nonempty and that, unlike the two-sided case, it does not coincide in general with the kernel (Davis and Maschler, Naval Res Logist Q 12:223–259, 1965). We also give an answer to an open question formulated by Rochford by introducing a kernel-based set whose intersection with the core coincides with the set of SMB.     

Structural properties of water confined by phospholipid membranes

Biological membranes are essential for cell life and hydration. Water provides the driving force for the assembly and stability of many cell components. Here, we study the structural properties of water in a phospholipid membrane. We characterize the local structures, inspecting the intermediate range order (IRO) and adopting a sensitive local order metric recently proposed by Martelli et al. that measures and grades the degree of overlap of the local environment with the structures of perfect ice. Close to the membrane, water acquires a high IRO and changes its dynamical properties; i.e., its translational and rotational degrees of freedom slow in a region that extends over ≃ 1 nm from the membrane interface. Surprisingly, we show that at distances as far as ≃ 2:5 nm from the interface, although the bulk-like dynamics are recovered, the IRO of water is still slightly higher than that in the bulk under the same thermodynamic conditions. Therefore, the water-membrane interface has a structural effect at ambient conditions that propagates further than the often-invoked 1-nm length scale. Consequently, this should be considered when analyzing experimental data of water confined by membranes and could help us to understand the role of water in biological systems.     

High-temperature emission spectroscopy of methane

A high-enthalpy source (HES) has been developed in Rennes either to heat gases up to 2000 K in local thermodynamic equilibrium (LTE) or to generate hypersonic expansions. The HES prototype has been associated with a high-resolution Bruker IFS 120 HR Fourier transform spectrometer to record emission spectra of hot gases, in LTE conditions. A series of emission spectra of methane has been obtained at 1005, 1365, 1485, 1625 and 1820 K in the pentad spectral region located around 3000 cm⁻¹, at Doppler-limited resolution (0.02 cm⁻¹). Spectra have been corrected for the transmission function that strongly affects the infrared radiation emitted by the hot gas. Line-integrated absorption cross sections have been extracted from the corrected spectra using an improved procedure for the calculation of the total partition function Q of methane at high temperature. This calculation included anharmonicity and rovibrational interaction effects, and was based on a multi-resolution fully converged direct partition sum. It has been shown that, as the temperature increases above 1000 K, the commonly used harmonic and rigid rotor double approximation to estimate Q leads to underestimated values.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.