The intersection of a matroid and a simplicial complex

A classical theorem of Edmonds provides a min-max formula relating the maximal size of a set in the intersection of two matroids to a ``covering" parameter. We generalize this theorem, replacing one of the matroids by a general simplicial complex. One application is a solution of the case of a matroidal version of Ryser's conjecture. Another is an upper bound on the minimal number of sets belonging to the intersection of two matroids, needed to cover their common ground set. This, in turn, is used to derive a weakened version of a conjecture of Rota. Bounds are also found on the dual parameter--the maximal number of disjoint sets, all spanning in each of two given matroids. We study in detail the case in which the complex is the complex of independent sets of a graph, and prove generalizations of known results on ``independent systems of representatives" (which are the special case in which the matroid is a partition matroid). In particular, we define a notion of -matroidal colorability of a graph, and prove a fractional version of a conjecture, that every graph is -matroidally colorable.

The methods used are mostly topological.

     

Methyltrifluoropyruvate imines possessing N-oxalyl and N-phosphonoformyl groups--precursors to a variety of alpha-CF3-alpha-amino acid derivatives

Convenient routes to methyl 2-oxalylimino- and 2-(phosphonoformimido)-3,3,3-trifluoropropanoates have been elaborated, based on the reaction of methyl trifluoropyruvate with ethyl oxamate or diethyl carbamoylphosphonate, respectively, followed by dehydration. The compounds obtained are useful synthetic intermediates toward a variety of novel 3,3,3-trifluoroalanine derivatives that are potential drug candidates.     

Vapor–liquid–solid growth and Sb doping of Ge nanowires from a liquid Au-Sb-Ge ternary alloy

Single-crystalline Sb-doped Ge nanowires (NWs) with excellent structural properties and uniform composition have been synthesized with high yield by vapor–liquid–solid (VLS) growth by low-temperature thermal evaporation from a mixture of Ge and Sb powders. During deposition, both the Ge and the Sb dopant became incorporated in the VLS seed nanoparticle. In situ annealing experiments during transmission electron microscopy establish that a liquid ternary Au-Sb-Ge alloy constitutes the active phase of the VLS seed drop at high temperatures, which governs the growth of the one-dimensional Ge NW and its doping by Sb.     

A new mechanism for gravitational-wave emission in core-collapse supernovae

We present a new theory for the gravitational-wave signatures of core-collapse supernovae. Previous studies identified axisymmetric rotating core collapse, core bounce, postbounce convection, and anisotropic neutrino emission as the primary processes and phases for the radiation of gravitational waves. Our results, which are based on axisymmetric Newtonian supernova simulations, indicate that the dominant emission process of gravitational waves in core-collapse supernovae may be the oscillations of the protoneutron star core. The oscillations are predominantly of mode character, are excited hundreds of milliseconds after bounce, and typically last for several hundred milliseconds. Our results suggest that even nonrotating core-collapse supernovae should be visible to current LIGO-class detectors throughout the Galaxy, and depending on progenitor structure, possibly out to megaparsec distances.     

On the Frobenius Problem of Numerical Semigroups

We define the minimal transversal of a numerical semigroup with respect to one of its elements and use it to calculate the Frobenius number, genus, and the Hilbert function of the semigroup. We give various examples for the use of this method.     

The Effect of Metal‐Ligand Affinity on Fe3O4_Supported Co–Rh Catalysts for Dicyclopentadiene Hydroformylation

The catalytic performances of Co‐Rh/Fe₃O₄ catalysts modified with phosphine ligands (PPh₃) and its analogues on dicyclopentadiene hydroformylation were evaluated. Among these catalysts, Co‐Rh/Fe₃O₄ modified with tris(p‐trifluoromethylphenyl)phosphine was determined to be effective for monoformyltricyclodecanes production, whereas Co‐Rh/Fe₃O₄ modified with PPh₃ or tri‐p‐tolylphosphine was effective for the diformyltricyclodecanes production. To investigate the ligand effects, the complex catalyst system (Co‐Rh/Fe₃O₄ and phosphine ligand) was subjected to pretreatment with syngas and then characterized by thermogravimetry and differential thermal analysis (TG‐DTA). It was determined that the threshold decomposition temperature reflected the corresponding Rh‐phosphine interaction strength, affecting the catalytic selectivity toward different products. A weak Rh‐phosphine interaction was desirable to produce monoformyltricyclodecanes with fast reaction kinetics, whereas a strong Rh‐phosphine complex was required for the synthesis of diformyltricyclodecanes. In addition to the selectivity rule shown in the PPh₃ series, experiments with other ligands also demonstrated similar selectivity trends.     

Enhanced In situ Activity of Peroxidases and Lignification of Root Tissues after Exposure to Non-Thermal Plasma Increases the Resistance of Pea Seedlings

Improving the germination of economically important crops and the condition of young plants is a major challenge currently facing agricultural practice. Pea (Pisum sativum L.) is one of the four most important cultivated legumes, along with groundnut (Arachis hypogaea L.), soybean (Glycine max L.) and beans (Phaseolus vulgaris L.). Due to the high protein content (23–33%), there is an interest in growing this crop as a source of protein for humans and animals. In this study, we focused on the effect of Cold Atmospheric Pressure Plasma (CAPP) on the decontamination and germination of pea seeds, on young seedling growth and production parameters, and on increasing their resistance and mechanical strength. We can state that germination increased by 10 to 25% after plasma treatment, and the most significant decontamination effect was detected when using non-thermal plasma generated in the ambient air (A-variants) and in the nitrogen atmosphere (N-variants). The increased in situ activity of peroxidases (POX) in the cell walls of A-variants and N-variants is also closely related to the increase in the mechanical strength of the cell walls and thus contributes to the higher resistance of these seedlings. This is also illustrated by the differences in lignin deposition among the different variants after CAPP treatment. To our knowledge, this is the first study concerning the influence of CAPP on the lignification of root tissues and on increasing the strength and resistance of plants.

     

Folding control and unfolding free energy of yeast iso-1-cytochrome c bound to layered zirconium phosphate materials monitored by surface plasmon resonance

The free energy change (Delta G degrees ) for the unfolding of immobilized yeast iso-1-cytochrome c (Cyt c) at nanoassemblies was measured by surface plasmon resonance (SPR) spectroscopy. Data show that SPR is sensitive to protein conformational changes, and protein solid interface exerts a major influence on bound protein stability. First, Cyt c was self-assembled on the Au film via the single thiol of Cys-102. Then, crystalline sheets of layered alpha-Zr(O(3)POH)(2).H(2)O (alpha-ZrP) or Zr(O(3)PCH(2)CH(2)COOH)(2).xH(2)O (alpha-ZrCEP) were adsorbed to construct alpha-ZrP/Cyt c/Au or alpha-ZrCEP/Cyt c/Au nanoassemblies. The construction of each layer was monitored by SPR, in real time, and the assemblies were further characterized by atomic force microscopy and electrochemical studies. Thermodynamic stability of the protein nanoassembly was assessed by urea-induced unfolding. Surprisingly, unfolding is reversible in all cases studied here. Stability of Cyt c in alpha-ZrP/Cyt c/Au increased by approximately 4.3 kJ/mol when compared to the unfolding free energy of Cyt c/Au assembly. In contrast, the protein stability decreased by approximately 1.5 kJ/mol for alpha-ZrCEP/Cyt c/Au layer. Thus, OH-decorated surfaces stabilized the protein whereas COOH-decorated surfaces destabilized it. These data quantitate the role of specific functional groups of the inorganic layers in controlling bound protein stability.