Syzygies of torsion bundles and the geometry of the level ℓ modular variety over \overline{\mathcal{M}}_{g}

We formulate, and in some cases prove, three statements concerning the purity or, more generally, the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of ? in its Jacobian. These statements can be viewed an analogues of Green’s Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space $\mathcal{R}_{g,\ell}$ of twisted level ? curves of genus g and use this to derive results about the birational geometry of $\mathcal{R}_{g, \ell}$ . For instance, we prove that $\mathcal{R}_{g,3}$ is a variety of general type when g>11 and the Kodaira dimension of $\mathcal{R}_{11,3}$ is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.     

Eigenvalue distribution of some fractal semi-elliptic differential operators

We consider differential operators of type and Sierpinski carpets . The aim of the paper is to investigate spectral properties of the fractal differential operator acting in the anisotropic Sobolev space where is closely related to the trace operator . Received September 15, 1999; in final form January 24, 2000 / Published online December 8, 2000     

Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a non-linear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass; hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for e.g., Wolbachia in a mosquito population. Therefore, the (infinite dimensional) non-linearity arises in the recruitment term. First, we establish global existence of solutions and the principle of linearised stability for our model. Then, in our main result, we formulate simple conditions which guarantee the existence of non-trivial steady states of the model. Our method utilises an operator theoretic framework combined with a fixed-point approach. Finally in the last section, we establish a sufficient condition for the local asymptotic stability of the positive steady state.     

Comparison of thermally and chemically reduced graphene oxides by thermal analysis and Raman spectroscopy

Journal of Thermal Analysis and Calorimetry - In this paper, a numerical simulation of jet impingement quenching is provided. The VOF method in the basic solver of the OpenFOAM CFD package is...     

Diversity in the Interaction of Amino Acid- and Peptide-Based Hydroxamic Acids with Some Platinum Group Metals in Solution

Complexes that incorporate both ligand(s) and metal(s) exhibiting cytotoxic activity can especially be interesting to develop multifunctional drug molecules with desired activities. In this review, the limited number of solution results collected in our laboratory on the complexes of Pd(II) and two other platinum group metals—the half-sandwich type, [(η⁶-p-cym)Ru(H₂O)₃]²⁺, and [(η⁵-Cp*)Rh(H₂O)₃]²⁺—with hydroxamic acid derivatives of three amino acids, two imidazole analogues, and four small peptides are summarized and evaluated. Unlike the limited number of coordination sites of these metal ions (four and three for Pd(II) and the organometallic cations, respectively), the ligands discussed here offer a relatively high number of donor atoms as well as variation in their position within the ligands, resulting in a large versatility of the likely coordination modes. The review, besides presenting the solution equilibrium results, also discusses the main factors, such as (N,N) versus (O,O) chelate; size of chelate; amino-N versus imidazole-N; primary versus secondary hydroxamic function; differences between hydrolytic ability of the metal ions studied; and hydrolysis of the coordinated peptide hydroxamic acids in their Pd(II) complexes, which all determine the coordination modes present in the complexes formed in measurable concentrations in these systems. The options for the quantitative evaluation of metal binding effectivity and selectivity of the various ligands and the comparison with each other by using solution equilibrium data are also discussed.