Synthesis and characterization of phenoxarsin-10-yl 2-R2N-cyclopent-1-ene-1-carbodithioate (R = H,C2H5, cyclo-C6H11CH2) and the crystal and molecular structure of the 2-amino (R = H) derivative

Phenoxarsin-10-yl derivatives of 2-amino-cyclopent-1-ene-1-carbodithioic acid, (ACDA), and its N-alkyl derivativesO(C₆H₄)₂ AsS₂C—C₅H₆— NHR-2 (R = H, CH₂CH₃, CH₂C₆H₁₁,), have been prepared by reacting O(C₆H₄)₂AsCI with the corresponding ACDA 1,1-dithioic acid. The compounds were obtained by stirring stoichiometric amounts of the reagents in ethanol, over 24 h, at room temperature. The scale of the preparations were in the order of 2 mmol and the yields of the compounds ca 75%. The reactions were carried out in absolute ethanol. The compounds were characterized by IR, mass and NMR (¹H, ¹³C) spectroscopy. The molecular structure of O(C₆H₄)₂AsS₂C—C₅H₆—NH₂-2 was determined using X-ray diffractometry, achieving an R-value of 6.3%; this compound is monomeric and contains an asymmetric monometallic biconnective 1,1-dithiolato ligand [As—S(1) 2.272(2) å, As … S(2) 3.125(2) å]. An intramolecular hydrogen bond is established between one hydrogen atom of the NH₂ group and the sulfur [S(2)] atom involved in the secondary interaction to arsenic. The dihedral angle (150.3(3)°) of the phenoxarsine moiety is practically unaffected by substitution of chlorine on arsenic by the carbodithioato ligand.     

Lagrange Inversion and Schur Functions

Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. We also present a q-analogue of this result, which is related to the q-Lagrange inversion formula of Andrews, Garsia, and Gessel, as well as the operator of Bergeron and Garsia.     

On the Collision between two PNG Droplets

In this article we study the interface generated by the collision between two crystals growing layer by layer on a one-dimensional substrate through random decomposition of particles. We relate this interface with the notion of β-path in an equivalent directed polymer model and, by using asymptotics results from J. Baik and E. Rains, J. Stat. Phys., 100:523–541 (2000). and some hydrodynamic tools introduced by E. Cator and P. Groeneboom, Ann. Probab., 33:879–903 (2005), we derive a law of large numbers for such a path and obtain some bounds for its fluctuations. 2000 Mathematics Subject Classification: 60C05, 60K35     

On Harmonic and C-Harmonic 1-Differentiable Forms on Sasakian Manifolds

In this paper, we firstly extend some classical operators on Sasakian manifolds acting to 1-differentiable forms on Sasakian manifolds. Next in a similar manner with the study of C-harmonic forms, we define and extend such a study for the case of 1-differentiable forms on Sasakian manifolds.     

Flasque resolutions of reductive group schemes

We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.     

Approaching minimum time control of timed continuous Petri nets

This paper considers the problem of controlling timed continuous Petri nets under infinite server semantics. The proposed control strategy assigns piecewise constant flows to transitions in order to reach the target state. First, by using linear programming, a method driving the system from the initial to the target state through a linear trajectory is developed. Then, in order to improve the time of the trajectory, intermediate states are added by means of bilinear programming. Finally, in order to handle potential perturbations, we develop a closed loop control strategy that follows the trajectory computed by the open loop control by calculating a new state after each time step. The algorithms developed here are applied to a manufacturing system.     

Visible-Light Assisted Covalent Surface Functionalization of Reduced Graphene Oxide Nanosheets with Arylazo Sulfones

We present an environmentally benign methodology for the covalent functionalization (arylation) of reduced graphene oxide (rGO) nanosheets with arylazo sulfones. A variety of tagged aryl units were conveniently accommodated at the rGO surface via visible-light irradiation of suspensions of carbon nanostructured materials in aqueous media. Mild reaction conditions, absence of photosensitizers, functional group tolerance and high atomic fractions (XPS analysis) represent some of the salient features characterizing the present methodology. Control experiments for the mechanistic elucidation (Raman analysis) and chemical nanomanipulation of the tagged rGO surfaces are also reported.     

Functional Liquid Crystal Elastomers Based on Dynamic Covalent Chemistry

The marriage of liquid crystal elastomers with dynamic covalent chemistry can be a new paradigm for the development of dynamic and intelligent polymers with versatile functionalities, which is of paramount significance for many emerging applications such as adaptive optics, soft robotics, bioinspired camouflage, 3D/4D printing technology and beyond. Read more in the Review by Wang, Feng et al. ( 10.1002/chem.202201957 )