Fluorescent Probes Based on Nucleophilic Substitution–Cyclization for Hydrogen Sulfide Detection and Bioimaging

The design, synthesis, properties, and cell imaging applications of a series of 2‐pyridyl disulfide based fluorescent probes (WSP1, WSP2, WSP3, WSP4 and WSP5) for hydrogen sulfide detection are reported. The strategy is based on the dual‐nucleophilicity of hydrogen sulfide. A hydrogen sulfide mediated tandem nucleophilic substitution‐cyclization reaction is used to release the fluorophores and turn on the fluorescence. The probes showed high sensitivity and selectivity for hydrogen sulfide over other reactive sulfur species, including cysteine and glutathione.     

Symmetry of solitary waves

It is shown that all supercritical solitary wave solutions to the equations for water waves are symmetric, and monotone on either side of the crest. The proof is based on the Alexandrov method of moving planes. Further a priori estimates, and asymptotic decay properties of solutions are derived     

Crystal Structure Refinements of Cellulose Polymorphs using Solid State 13C Chemical Shifts

Force field methods in combination with chemical shift target functions are used to investigate the structures of cellulose I and II. Since diffraction investigations of biopolymers like cellulose II are only of poor resolution, different models for the structure are discussed in the literature. These models were used as the starting point for force field optimizations with ¹³C chemical shift target functions. In these optimizations additionally to the total energy a pseudo-energy is minimized that depends harmonically on the difference between calculated and observed chemical shifts. In the case of cellulose II all four criteria: (i) total energy, (ii) pseudo-energy, (iii) chemical shift rms (root mean square) difference, and (iv) deviation from the diffraction data favour the structure model of Kolpak and Blackwell with two antiparallel carbohydrate chains. The CH₂–OH group of one chain is in tg and that of the other chain in gt conformation. The chemical shift optimized fractional coordinates for cellulose II, I and I are presented together with the calculated and experimental ¹³C chemical shifts.     

Asymptotic Analysis of Finite Deformation in a Nonlinear Transversely Isotropic Incompressible Hyperelastic Half-space Subjected to a Tensile Point Load

The Boussinesq problem, that is, determining the deformation in a hyperelastic half-space due to a point force normal to the boundary, is an important problem of engineering, geomechanics, and other fields to which elasticity theory is often applied. While linear solutions produce useful Greens functions, they also predict infinite displacements and other physically inconsistent results nearby and at the point of application of the load where the most critical and interesting material behavior occurs. To illuminate the deformation due to such a load in the region of interest, asymptotic analysis of the nonlinear Boussinesq problem has been considered in the context of isotropic hyperelasticity. Studies considering transversely isotropic materials have also been broadly used in the linear theory, but have not been treated within the nonlinear framework. In this paper we extend the nonlinearly elastic isotropic analysis to transverse isotropy, producing a more general theory which also better encompasses applications involving layered media. The governing equations for nonlinearly elastic, transversely isotropic solids are derived, conservation laws of elastostatics are invoked, asymptotic forms of the deformation solutions are hypothesized, and the differential equations governing deformation near the point load are determined. The analysis also develops sequences of simple tests to determine if a transversely isotropic material can possibly sustain a finite deflection under the point load. The results are applied to a variety of transversely isotropic materials, and the effects of the anisotropy considered is demonstrated by comparison of the resulting deformation with similar asymptotic solutions in the isotropic theory. Mathematics Subject Classifications (2000) 74B20, 74E10, 74G10, 74G15, 74G70.     

Arithmetic inflection formulae for linear series on hyperelliptic curves

Over the complex numbers, Plücker's formula computes the number of inflection points of a linear series of fixed degree and projective dimension on an algebraic curve of fixed genus. Here, we explore the geometric meaning of a natural analog of Plücker's formula and its constituent local indices in ${\mathbb{A}}^1$-homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.     

Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, up to the action of the universal cover of ${\text{GL}}_2^{+}(\mathbb{R})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel–Mukai fourfolds.