On fundamental solutions for non-local parabolic equations with divergence free drift

We are concerned with non-local parabolic equations in the presence of a divergence free drift term. By using the classical Nash approach, we show the existence of fundamental solutions together with continuity estimates, under weak regularity assumptions on the kernel of the non-local term and the velocity of the drift term. As an application, we give an alternative proof of global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case.     

Evaluation of polarization entanglement generated by pulsed spontaneous parametric down-conversion with multi-pairs using four single-photon detectors for quantum state tomography

Quantum state tomography (QST) is widely used to evaluate entanglement generated by spontaneous parametric down-conversion. Two-fold coincidence counts for 16 different configurations have been measured using single-photon detectors to estimate the fidelity (i.e., the probability overlap between ideal and real states) from the reconstructed density matrix. However, multi-pair emission events degrade the fidelity. Here, we numerically analyze pulse-pumped polarization-entangled photon pairs for single-photon detectors that can or cannot count the number of incident photons to estimate the fidelity given by QST. Threshold single-photon detectors are desirable for QST from a practical point of view. Our analysis suggests that using four threshold single-photon detectors for two-fold coincidence measurements offers almost the same fidelity as that given by four photon-number-resolving single-photon detectors. The fidelity estimated by QST becomes poor and loss independent when two threshold single-photon detectors are used.     

Online tool for calculating null points in various inversion recovery sequences

Accurate equations for calculating the inversion time of the null point (TI_null) in inversion recovery (IR) sequences are required for adequate suppression of fat or cerebrospinal fluid (CSF) but are not widely known. The purpose of this study is to elucidate the process of deriving accurate TI_null equations using schematic diagrams that allow the equations to be easily understood, and to devise a convenient online tool for instant calculation of TI_null.     

Sensitive determination of rhodamine 110-labeled monosaccharides in glycoprotein by capillary electrophoresis with laser-induced fluorescence detection

Rhodamine 110 (Rho110) has been used in the highly sensitive analysis of monosaccharides, as it reacts with the reducing carbonyl group of the saccharides. The monosaccharide derivatives were investigated by capillary electrophoresis with laser-induced fluorescence detection. The derivatization was performed at 90 °C for 30 min for all monosaccharides. The derivatized monosaccharides were separated using 200 mM borate (pH 10.5) as running buffer within 20 min. The fluorescence intensities of Rho110-derivatives were significantly decreased by the presence of excess reducing agent, but were greatly increased by the addition of potassium hexacyanoferrate(III). The concentration and mass detection limits for monosaccharides were in the range of 1.4–2.8 nM and 36–70 amol, respectively. We have applied this derivatization method to the analysis of the composition of monosaccharides in glycoproteins (ribonuclease B, fetuin, and erythropoietin) following their subjection to strong acid hydrolysis. The results from these analyses were in good agreements with the reported values established previously.     

Two polymorphs of N1,N4‐bis(5‐hydroxypenta‐1,3‐diynyl)‐N1,N4‐diphenylbenzene‐1,4‐diamine

The title compound, C₂₈H₂₀N₂O₂, forms two conformational polymorphs, (I) and (II), where the molecular structures are similar except for the orientation of the two hydroxy groups. In (I), which was obtained by slow evaporation from chloroform, the two hydroxy groups have an anti conformation. The molecules form a sheet structure within the ac plane, where the hydroxy groups form zigzag hydrogen bonds. In (II), which was obtained by slow evaporation from acetonitrile, the two hydroxy groups have a syn conformation. The molecules form a double‐sheet structure within the ab plane, where the hydroxy groups form 4‐helix hydrogen bonds.     

Odd-even effects in the phase transition behaviour of novel U-shaped liquid crystals

A homologous series of U-shaped dimeric liquid crystals in which two mesogenic groups are connected via catechol has been prepared and the effects of terminal alkyl chains, alkyl spacers and core structures on the transition properties investigated by means of optical microscopy and differential scanning calorimetry. The phase sequence exhibits a pronounced odd-even effect as the length and parity of the spacers is varied, in which the even members favour the nematic and smectic C phases, whereas the odd members favour the nematic and smectic A phases. We discuss the transition behaviour of the U-shaped compounds in terms of molecular shape.     

Seragakinone A, a new pentacyclic metabolite from a marine-derived fungus

A new anthracycline-derived pentacyclic metabolite, seragakinone A (1), was isolated from the mycelium of an unidentified fungus, which was separated from the Okinawan marine rhodophyta Ceralodictyon spongiosum, and the structure was elucidated by spectroscopic data.