On the Attainable Order of Collocation Methods for Delay Differential Equations with Proportional Delay

To analyze the attainable order of m-stage implicit (collocation-based) Runge-Kutta methods for the delay differential equation (DDE) y′(t) = by(qt), 0 < q ≤ 1 with y(0) = 1, and the delay Volterra integral equation (DVIE) y(t) = 1 + $\tfrac{b}{q}\int {_0^{qt} }$ y(s) ds with proportional delay qt, 0 < q ≤ 1, our particular interest lies in the approximations (and their orders) at the first mesh point t = h for the collocation solution v(t) of the DDE and the iterated collocation solution u _it(t) of the DVIE to the solution y(t). Recently, H. Brunner proposed the following open problem: “For m ≤ 3, do there exist collocation points c _i = c _i(q), i = 1, 2,..., m in [0,1] such that the rational approximant v(h)is the (m, m)-Padé approximant to y(h)? If these exist, then |v(h) ? y(h)| = O(h ^2m+1) but what is the collocation polynomial M _m(t; q) = K Π _i=1 ^m (t ? c _i) of v(th), t ∈ [0, 1]?” In this paper, we solve this question affirmatively, and give the related results between the collocation solution v(t) of the DDE and the iterated collocation solution u _it(t) of the DVIE. We also answer to Brunner's second open question in the case that one collocation point is fixed at the right end point of the interval.     

The first stereoselective synthesis of (+)-nuciferol and (+)-nuciferal

Using (S)-benzyl 2,3-epoxypropyl ether (1), the first stereoselective synthesis of (+)-nuciferol (14) and (+)-nuciferal (16) has been achieved. Employing the same methodology an enantioselective synthesis of (+)--curcumene (17) is also described.     

Rapid determination of trace quantities of thallium in heat-resisting cobalt and nickel alloys by graphite furnace atomic absorption spectrometry

Summary A simple and rapid analytical method has been developed for the direct determination of trace quantities of thallium in nickel and cobalt-base heatresisting alloys by graphite furnace atomic absorption spectrometry. Hydrofluoric acid, sulphuric acid, and hydrogen peroxide were used for the dissolution of a wide variety of these alloys. The interferences of matrix elements and acids were eliminated. The absorbance of thallium is constant over a wide range of ashing temperatures. Synthetic standard solutions composed of nickel or cobalt matrix and thallium were used for calibration. The detection limit for thallium by this method is 0.2 ppm in the sample. Mechanisms of the interferences are discussed.

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Schnelle Bestimmung von Thalliumspuren in hitzebeständigen Cobalt- und Nickellegierungen durch Atomabsorptions-Spektralphotometrie mit dem Graphitofen

Zusammenfassung Ein Verfahren zur AAS-Bestimmung von Thallium in verschiedenartigen Cobalt- und Nickellegierungen wird beschrieben. Zur Auflösung der Probe werden Flußsäure, Schwefelsäure und Wasserstoffperoxid verwendet. Störungen durch Matrixelemente und durch die Säuren konnten beseitigt werden. Die Thalliumabsorption ist über einen weiten Temperaturbereich bei der Veraschung konstant. Zur Eichung dienen synthetische Lösungen von Cobalt- bzw. Nikkelmatrix und Thallium. Die Nachweisgrenze für Thallium beträgt 0,2 ppm. Die Mechanismen der Störungen werden diskutiert.

     

Antigen�Cantibody interactions of influenza virus hemagglutinin revealed by the fragment molecular orbital calculation

Effective interactions between amino acid residues in antigen?Cantibody complex of influenza virus hemagglutinin (HA) protein can be evaluated in terms of the inter-fragment interaction energy (IFIE) analysis with the fragment molecular orbital (FMO) method, in which each fragment contains the side chain of corresponding amino acid residue. We have carried out the FMO-MP2 (second-order Moeller?CPlesset) calculation for the complex of HA antigen and Fab antibody of influenza virus H3N2 A/Aichi/2/68 and obtained the IFIE values between each amino acid residue in HA and the whole antibody as the sums over the residues contained in the latter. Combining this IFIE data with experimental data for hemadsorption activity of HA mutants, we succeeded in theoretically explaining the mutations in HA observed after the emergence of influenza virus H3N2 A/Aichi/2/68 in an earlier study, except for those of THR83. In the present study, we employ an alternative way of fragment division in the FMO calculation at the carbonyl C site of the peptide bond instead of the C_?? site used in the previous work, which provides revised IFIE values consistent with all the historical mutation data in the antigenic region E of HA including the case of THR83 in the present prediction scheme for probable mutations in HA.     

Possible Existence of {(c\bar{c})} –Nucleus Bound States

Charmonium ( \({c \bar{c}}\) ) bound states in few-nucleon systems, ²H, ⁴He and ⁸Be, are studied via Gaussian Expansion Method (GEM). We adopt a Gaussian potential as an effective \({(c \bar{c})}\) –nucleon (N) interaction. The relation between two-body \({(c \bar{c})}\) –N scattering length \({a_{c\bar{c}-N}}\) and the binding energies B of \({(c \bar{c})}\) –nucleus bound states are given. Recent lattice QCD data of \({a_{c\bar{c}-N}}\) corresponds to \({B \simeq 0.5}\) MeV for \({(c \bar{c})-^{4}}\) He and 2 MeV for \({(c \bar{c})-^{8}}\) Be in our results.     

Porphyrin Network Polymers Prepared via a Click Reaction and Facilitated Oxygen Permeation Through Their Membranes

Network polymers of cobaltporphyrin derivatives are prepared by a facile click reaction via the Michael addition of acetoacetate‐substituted tetraphenyl cobaltporphyrin and tri‐ or tetra‐acrylates. The conversion is saturated for 1 h in the presence of a catalyst, which almost reaches the same gelation point of the formed network polymers. Deeply and homogeneously red‐colored membranes with a sub‐micrometer thickness are yielded on a porous supporting membrane. They are still tough even with a very high content of the rigid porphyrin residue. The oxygen permeability is high, at 10–100 Barrer, and the oxygen/nitrogen permselectivity (P_O2/P_N2) is significantly enhanced with the porphyrin content reaching 30, for the membranes with ca. 70 wt% porphyrin content.

     

Tetraspanin CD9 modulates ADAM17-mediated shedding of LR11 in leukocytes

LR11, also known as SorLA or SORL1, is a type-I membrane protein from which a large extracellular part, soluble LR11 (sLR11), is released by proteolytic shedding on cleavage with a disintegrin and metalloproteinase 17 (ADAM17). A shedding mechanism is presumed to have a key role in the functions of LR11, but the evidence for this has not yet been demonstrated. Tetraspanin CD9 has been recently shown to regulate the ADAM17-mediated shedding of tumor necrosis factor-α and intercellular adhesion molecule-1 on the cell surface. Here, we investigated the role of CD9 on the shedding of LR11 in leukocytes. LR11 was not expressed in THP-1 monocytes, but it was expressed and released in phorbol 12-myristate 13-acetate (PMA)-induced THP-1 macrophages (PMA/THP-1). Confocal microscopy showed colocalization of LR11 and CD9 proteins on the cell surface of PMA/THP-1. Ectopic neo-expression of CD9 in CCRF-SB cells, which are LR11-positive and CD9-negative, reduced the amount of sLR11 released from the cells. In contrast, incubation of LR11-transfected THP-1 cells with neutralizing anti-CD9 monoclonal antibodies increased the amount of sLR11 released from the cells. Likewise, the PMA-stimulated release of sLR11 increased in THP-1 cells transfected with CD9-targeted shRNAs, which was negated by treatment with the metalloproteinase inhibitor GM6001. These results suggest that the tetraspanin CD9 modulates the ADAM17-mediated shedding of LR11 in various leukemia cell lines and that the association between LR11 and CD9 on the cell surface has an important role in the ADAM17-mediated shedding mechanism.     

Development of visual analytical methods for trace determination.

In this paper our recent progress in the field of simple analytical methods is reviewed, with particular focus on the development of rapid, inexpensive, yet sensitive techniques to visualize trace elements of medical, industrial, and environmental importance. Our objective is to solve long-standing practical problems in these fields. We have repeatedly shown that visual perception is remarkably sensitive when used with our new techniques. The applicability of the proposed methods to real samples is also discussed. Making measurements visually is a method free from machinery malfunctions and serves as a simple and sensitive analytical technique, avoiding all of the practical disadvantages associated with sophisticated instrumentation as well as tedious procedures.     

(1‐Pyridinio)perfluorophenacylide: a new stable pyridinium ylide in the enol form

The title compound, C₁₃H₆F₅NO, exists in the enol form and adopts the E configuration about the enol double bond. It is the first example of an enol‐type pyridinium ylide. The enol structure was unambiguously determined on the basis of the significantly longer C—O bond and shorter C—C bond. Intramolecular C—H...O and C—H...F hydrogen bonds are responsible for promotion of the enol form and for the stability of this compound.     

Cholesterol location and orientation in aqueous suspension of large unilamellar vesicles of phospholipid revealed by intermolecular nuclear overhauser effect

The locational and orientational structure and the dynamics of cholesterol in the bilayer membrane were studied by using the solution-state NMR. The intermolecular nuclear Overhauser effect (NOE) was analyzed for large unilamellar vesicles (100 nm in diameter) composed of dimyristoylphosphatidylcholine (DMPC) and cholesterol at cholesterol concentrations of 9-33 mol %. The DMPC headgroups show (1)H-{(1)H}-NOEs with the methyl groups at the hydrophobic terminals of both cholesterol and DMPC, illustrating the significant fluctuation of the bilayer membrane in the vertical (bilayer normal) direction. Cholesterol was found to keep the hydroxyl (OH) group toward the outer water pool on the basis of the following observations: (1) the cross correlation between the DMPC headgroup and the cholesterol terminal methyl group is weaker than those between the DMPC headgroups and (2) the methyl group at the hydrophobic terminal of cholesterol shows strong correlation with the terminal group of the DMPC chain portion. The OH group plays a crucial role in orienting cholesterol with its OH group outward, since cholestane, which has a molecular structure similar to that of cholesterol except for the absence of the OH group, was found to have no orientational preference in the bilayer membrane. The dynamic slowdown at high cholesterol concentrations is demonstrated on the basis of the correlation times for NOE as well as the broadening of the proton linewidths.