Gröbner Flags and Gorenstein Algebras

The goal of this paper is to study the Koszul property and the property of having a Gröbner basis of quadrics for classical varieties and algebras as canonical curves, finite sets of points and Artinian Gorenstein algebras with socle in low degree. Our approach is based on the notion of Gröbner flags and Koszul filtrations. The main results are the existence of a Gröbner basis of quadrics for the ideal of the canonical curve whenever it is defined by quadrics, the existence of a Gröbner basis of quadrics for the defining ideal of s 2n points in general linear position in P ⁿ , and the Koszul property of the generic Artinian Gorenstein algebra of socle degree 3.     

Interactions between spherical colloids mediated by a liquid crystal: a molecular simulation and mesoscale study

Monte Carlo simulations and dynamic field theory (DyFT) are used to study the interactions between dilute spherical particles, dispersed in nematic and isotropic phases of a liquid crystal. A recently developed simulation method (expanded ensemble density of states) was used to determine the potential of mean force (PMF) between the two spheres as a function of their separation and size. The PMF was also calculated by a dynamic field theory that describes the evolution of the local tensor order parameter. Both methods reveal an overall attraction between the colloids in the nematic phase; in the isotropic phase, the overall attraction between the colloids is much weaker, whereas the repulsion at short range is stronger. In addition, both methods predict a new topology of the disclination lines, which arises when the particles approach each other. The theory is found to describe the results of simulations remarkably well, down to length scales comparable to the size of the molecules. At separations corresponding to the width of individual molecular layers on the particles' surface, the two methods yield different defect structures. We attribute this difference to the neglect of density inhomogeneities in the DyFT. We also investigate the effects of the size of spherical colloids on their interactions.     

2-Aminopyridiniomethylphosphonite: A hydrogen-bonded polymer from the hydrolysis of 1,3,4-diazaphospholo[1,2-a]pyridine

Condensation of 2-aminopyridine and chloromethyldichlorophosphane yields 1,3,4-diazaphospholo[1,2-a]pyridine 2 . Methanol adds to 2 while diethylamine does not; with additional elemental sulfur, in both cases the sulfides 4, 6 of the respective adducts are formed. Hydrolysis of 2 specifically opens the PN-bond and gives the zwitterionic 2-aminopyridinio-methylphosphonite 7 . The compound crystallizes with one molecule water in the monoclinic space group P 2₁/c with a = 25.490(7)Å, b = 7.365(4)Å, c = 9.088(3)Å, β = 100.06(3)°, and Z = 8 with two independent molecules of 7 and of water. In the crystal hydrogen bonds connect the molecules of 7 to form double-chain structured polymers. The individual double-chains are linked to each other by hydrogen-bonded water molecules.     

Slopes and Abelian Subvariety Theorem

In this article, we show how to modify the proof of the Abelian Subvariety Theorem by Bost (Périodes et isogénies des variétés abeliennes sur les corps de nombres, Séminaire Bourbaki, 1994-95, Theorem 5.1) in order to improve the bounds in a quantitative respect and to extend the theorem to subspaces instead of hyperplanes. Given an abelian variety A defined over a number field κ and a non-trivial period γ in a proper subspace W of t_AK with K a finite extension of κ, the Abelian Subvariety Theorem shows the existence of a proper abelian subvariety B of , whose degree is bounded in terms of the height of W, the norm of γ, the degree of κ and the degree and dimension of A. If A is principally polarized then the theorem is explicit.     

Microwave-assisted solid-phase synthesis of hydantoin derivatives

A microwave-assisted synthesis of 3,5- and 1,3,5-substituted hydantoins starting from various resins for solid-phase combinatorial chemistry has been developed. The hydantoins were synthesized from pre-loaded resins with amino acids via treatment with isocyanate or phenylisocyanate and subsequent intramolecular cyclization. Both reactions were performed under microwave irradiation. We studied the cyclative cleavage leading to hydantoin compounds dependent on the nature of the amino acid and the nucleofuge properties of the resin.     

Navier–Stokes equations and forward–backward SDEs on the group of diffeomorphisms of a torus

We establish a connection between the strong solution to the spatially periodic Navier–Stokes equations and a solution to a system of forward–backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier–Stokes equations in terms of diffusion processes.     

Exploiting catalytic chain transfer polymerization for the synthesis of carboxylated latexes via sulfur‐free RAFT

We present a systematic study of incorporating carboxyl groups into latex particles to enhance colloidal stability and the physical properties of the latex. Statistical copolymers of methacrylic acid and methyl methacrylate) were synthesized via catalytic chain transfer polymerization (CCTP) in emulsion. The vinyl‐terminated oligomers were in turn successfully utilized as chain transfer agents for the formation of diblock and pseudo triblock copolymers via sulfur‐free reversible addition–fragmentation chain transfer polymerization (SF‐RAFT). These copolymers were characterized using ¹H NMR, size exclusion chromatography (SEC), dynamic light scattering (DLS), dynamic mechanical analysis (DMA), contact angle measurements and matrix‐assisted laser desorption/ionization time of flight mass spectroscopy (MALDI‐TOF‐MS) techniques. © 2019 The Authors. Journal of Polymer Science Part A: Polymer Chemistry published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, E1–E9     

Modelling synergistic action of laccase-based biosensor utilizing simultaneous substrates conversion

The response of a laccase-based amperometric biosensor that acts in a synergistic manner was modelled digitally. A mathematical model of the biosensor is based on a system of non-linear reaction diffusion equations. The modelling biosensor comprises three compartments, an enzyme layer, a dialysis membrane and an outer diffusion layer. By changing input parameters the biosensor action was analysed with a special emphasis to the influence of the species concentrations on the synergy of the simultaneous substrates conversion. The digital simulation was carried out using the finite difference technique.     

A Degenerate Birdcage with Integrated Tx/Rx Switches and Butler Matrix for the Human Limbs at 7 T

The theoretically known degeneracy condition of the band-pass birdcage coil has rarely been exploited in transmit coil designs. We have created an eight-channel degenerate birdcage for the human limbs at 7 T, with dedicated Tx/Rx switches and a Butler matrix. The coil can be split into two half cylinders, as required for its application to patients with limited mobility. The design of the coil, the Butler matrix, and Tx/Rx switches relied on a combination of analytical, circuital, and numerical simulations. The birdcage theory was extended to the degenerate case. The theoretical and practical aspects of the design and construction of the coil are presented. The performance of the coil was demonstrated by simulations, workbench, and scanner measurements. The fully assembled prototype presents good performance in terms of efficiency, B₁ homogeneity, and signal-to-noise ratio, despite the asymmetry introduced by the splittable design. The first in vivo images of the knee are also shown. A novel RF coil design consisting of an eight-channel splittable degenerate birdcage has been developed, and it is now available for 7 T MRI applications of the human lower limbs, including high-resolution imaging of the knee cartilages and of the patellar trabecular structure.