The order-interval hypergraph of a finite poset and the König property

We study the hypergraph H(P) whose vertices are the points of a finite poset and whose edges are the maximal intervals in P (i.e. sets of the form I = {{v ε P: p ν q}}, p minimal, q maximal). We mention resp. show that the problems of the determination of the independence number , the point covering number τ, the matching number v and the edge covering number p are NP-complete. For interval orders we describe polynomial algorithms and prove the König property (v = τ) and the dual König property (a = p). Finally we show that the (dual) König property is preserved by product.     

The Uncountable Lattice of All Subfunctors of the Functor of Rational Representations

In set theory the cardinality of the continuum \(|{\mathbb R}|\) is the cardinal number of some interesting sets, like the Cantor set or the transcendental numbers. We will prove that the cardinal number of all subfunctors of the functor of rational representations \(k \otimes_{{\mathbb Z}} R_{{\mathbb Q}}\), taking values on odd order groups over the field k of characteristic 2, is equal to \(|{\mathbb R}|\). When the characteristic q?>?0 of the field k is not necessarily even, we will present a formula giving the dimension of the evaluations S _C,k(G), of the simple functor S _C,k, at any group G of order prime to q and being associated to a suitable cyclic group C.     

Quantitative study of fluorescence excitation and emission spectra of bean leaves

A quantitative and comprehensive knowledge of leaf fluorescence is required for the interpretation of fluorescence signals at the canopy level and also for the modelling of leaf and canopy fluorescence. In this work we present full range fluorescence excitation and emission spectra of intact leaves, expressed in units of apparent spectral fluorescence yield, from both the adaxial and the abaxial sides of the leaves, and for both front-side and back-side geometries. Emission spectra were measured for incident radiations in the blue and the green spectral range. The red/far-red fluorescence ratio depended on the measurement geometry and on the excitation wavelength. Excitation spectra were measured for emissions at 687 and 760 nm. When the abaxial side was illuminated, the measured spectra always had a larger intensity compared to adaxial side that is explained by the higher scattering of the spongy tissues. At 760 nm, the spectra had the same shape for front-side and back-side geometry, indicating that scattering predominated. At 687 nm, the shape of the spectra was very different for front-side and back-side geometry due to re-absorption of red fluorescence within the leaf. The comparison of excitation spectra measured from the adaxial or the abaxial side revealed differences in carotenoid absorption.     

Linear forms in logarithms and the mathematical method of diophantine equations: applications in chemistry and physics

Journal of Mathematical Chemistry - In this paper, we established the bound of n in term of p of the following equation $${\mathcal {F}}_n=2^p\quad {\text {with}}\quad n,p\ge 0 $$ where...     

Instability of the magnetohydrodynamics system at vanishing Reynolds number

The aim of this note is to study the dynamo properties of the magnetohydrodynamics system at vanishing R _m . Improving the analysis in Gérard-Varet (SIAM J Math Anal 37(3):815–840, 2006), we shall establish a generic Lyapunov instability result.     

Developing imprinted polymer nanoparticles for the selective separation of antidiabetic drugs

In this study, new molecularly imprinted polymer (MIP) nanoparticles are designed for selective recognition of different drugs used for the treatment of type 2 diabetes mellitus, i.e. sitagliptin (SG) and metformin (MF). The SG‐ and MF‐imprinted polymer nanoparticles are synthesized by free‐radical initiated polymerization of the functional monomers: methacrylic acid and methyl methacrylate; and the crosslinker: ethylene glycol dimethacrylate. The surface morphology of resultant MIP nanoparticles is studied by atomic force microscopy. Fourier transform infrared spectra of MIP nanoparticles suggest the presence of reversible, non‐covalent interactions between the template and the polymer. The effect of pH on the rebinding of antidiabetic drugs with SG‐ and MF‐imprinted polymers is investigated to determine the optimal experimental conditions. The molecular recognition characteristics of SG‐ and MF‐imprinted polymers for the respective drug targets are determined at low concentrations of SG (50–150 ppm) and MF (5–100 ppm). In both cases, the MIP nanoparticles exhibit higher binding response compared to non‐imprinted polymers. Furthermore, the MIPs demonstrate high selectivity with four fold higher responses toward imprinted drugs targets, respectively. Recycled MIP nanoparticles retain 90% of their drug‐binding efficiency, which makes them suitable for successive analyses with significantly preserved recognition features.     

Thomas Bayes’ walk on manifolds

Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.     

Novel copolymers of styrene. 7. Some ring-disubstituted butyl 2-cyano-3-phenyl-2-propenoates

Novel trisubstituted ethylenes, ring-disubstituted butyl 2-cyano-3-phenyl-2-propenoates, RPhCH?C(CN)CO₂C₄H₉ (where R is 2-bromo-5-methoxy, 3-bromo-4-methoxy, 5-bromo-2-methoxy, 2-chloro-3-methoxy, 3-chloro-4-methoxy, 2-chloro-6-methyl, 3-chloro-4-methyl, 2-fluoro-4-methoxy) were prepared and copolymerized with styrene. The monomers were synthesized by the piperidine catalyzed Knoevenagel condensation of ring-substituted benzaldehydes and butyl cyanoacetate, and characterized by CHN analysis, IR, ¹H and ¹³C-NMR. All the ethylenes were copolymerized with styrene in solution with radical initiation (ABCN) at 70°C. The compositions of the copolymers were calculated from nitrogen analysis and the structures were analyzed by IR, ¹H and ¹³C-NMR. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200-500ºC range with residue (1-6% wt.), which then decomposed in the 500–800ºC range.