Degree complexity of birational maps related to matrix inversion: symmetric case

For q?≥ 3, we let ${\mathcal{S}_q}$ denote the projectivization of the set of symmetric q × q matrices with coefficients in ${\mathbb{C}}$ . We let ${I(x)=(x_{i,j})^{-1}}$ denote the matrix inverse, and we let ${J(x)=(x_{i,j}^{-1})}$ be the matrix whose entries are the reciprocals of the entries of x. We let ${K|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}$ denote the restriction of the composition I ? J to ${\mathcal{S}_q}$ . This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of ${K|\mathcal{S}_q}$ , thus confirming a conjecture of Angles d’Auriac et?al. (J Phys A Math Gen 39:3641–3654, 2006).     

Antioxidant and cytotoxic activity of lichens collected from Bidoup Nui Ba National Park,Vietnam

Research on Chemical Intermediates - Lichens were some of the earliest colonizers of terrestrial habitats on Earth. They represent a unique symbiont between fungi (mycobionts) and algae and/or...     

Intramolecular hydrogen bonding of novel o-hydroxythioacetophenones and related compounds evaluated by deuterium isotope effects on 13C chemical shifts

A new class of compounds, the 2-hydroxythioacetophenones, and related compounds have recently been synthesized. The hydrogen-bond system has been characterized by NMR chemical shifts and deuterium isotope effects on these as well as by DFT calculations. Use of solid-state (13)C NMR has enabled measurements of the intrinsic deuterium isotope effects of the most abundant tautomer of beta-thioxoketones. The compounds show very interesting long-range deuterium isotope effects on the thiocarbonyl carbon. The intramolecular hydrogen bonds of o-hydroxythioacetophenones are found to be slightly stronger than those of the corresponding acetophenones. The reactivity and stability of the compounds can be related to hydrogen bonding and to the presence of electron donating substituents.     

A Generalization of a Theorem of Dehon for Simple t-Designs

A generalization of a theorem of Dehon for simple t-designs is proved. Several new families of 4- and 5-designs having certain additional property regarding their block intersection numbers are obtained by applying this result.The author acknowledges the support of SFB Forschungsschwerpunkt-Geometrie Grant, University of Heidelberg.     

Antibunching and sub-poissonian photon statistics in the Jaynes-Cummings model

Sub-poissonian photon statistics and antibunching by the definition based on the positive derivative of g⁽²⁾ (t, t+τ) as a function of the delay time τ at τ=0 are treated in a single-mode single-two-level-atom model. It is shown, in particular, that sub-poissonian behaviour may be accompanied by bunching or antibunching and photon-antibunching may be accompanied by sub-poissonian or super-poissonian field statistics. It is also shown that the photon-antibunching persists with increasing mean photon number of an initial chaotic state while the sub-Poisson behaviour disappears.     

Spectral Sets and the Drazin Inverse with Applications to Second Order Differential Equations

The paper defines and studies the Drazin inverse for a closed linear operator A in a Banach space X in the case that 0 belongs to a spectral set of the spectrum of A. Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.     

Faster and improved microchip electrophoresis using a capillary bundle

Joule heating generated in CE microchips is known to affect temperature gradient, electrophoretic mobility, diffusion of analytes, and ultimately the efficiency and reproducibility of the separation. One way of reducing the effect of Joule heating is to decrease the cross-section area of microchannels. Currently, due to the limit of fabrication technique and detection apparatus, the typical dimensions of CE microchannels are in the range of 50-200 microm. In this paper, we propose a novel approach of performing microchip CE in a bundle of extremely narrow channels by using photonic crystal fiber (PCF) as separation column. The PCF was simply encapsulated in a poly(methyl methacrylate) (PMMA) microchannel right after a T-shaped injector. CE was simultaneously but independently carried out in 54 narrow capillaries, each capillary with diameter of 3.7 microm. The capillary bundle could sustain high electric field strength up to 1000 V/cm due to efficient heat dissipation, thus faster and enhanced separation was attained.     

A molecular docking simulation study on potent inhibitors against Rhizoctonia solani and Magnaporthe oryzae in rice: silver-tetrylene and bis-silver-tetrylene complexes vs. validamycin and tricyclazole pesticides

Structural Chemistry - Rice, well known as the most important staple food source worldwide, is highly susceptible to many infectious diseases, especially rice sheath blight caused by fungus...