Non-separating even cycles in highly connected graphs

We prove that every k-connected graph (k ≥ 5) has an even cycle C such that G-V (C) is still (k-4)-connected. The connectivity bound is best possible.     

Determination of bisphenol A in human breast milk by HPLC with column-switching and fluorescence detection

A highly sensitive HPLC method was developed for the determination of xenoestrogenic compound, bisphenol A (BPA) in human breast milk samples. After a two-step liquid-liquid extraction, BPA was derivatized with fluorescent labeling reagent, 4-(4,5-diphenyl-1H-imidazol-2-yl)benzoyl chloride (DIB-Cl). The excess fluorescent reagent could be removed effectively using a column-switching system. The separation of DIB-BPA from endogenous materials in milk was carried out on two C(18) columns and fluorescence intensity was monitored at 475 nm with the excitation of 350 nm. A good linearity (r = 0.994) was observed of BPA in the concentration range of 0.2-5.0 ng mL(-1) in breast milk, and the detection limit was 0.11 ng mL(-1) at a signal-to-noise ratio of 3. Intra- and inter-day precision (RSD, %) were less than 8.7 and 10.4, respectively. Twenty-three breast milk samples of healthy lactating women were analyzed for the BPA concentration; the mean value was 0.61 +/- 0.20 ng mL(-1), with no correlation to the lipid content of milk samples.     

Experimental and theoretical investigations of isomerization reactions of ionized acetone and its dimer

Ionization dynamics of acetone and its dimer in supersonic jets is investigated by a combination of experimental and theoretical techniques, both of which have recently been developed. In experiments, the neutral and the cationic structures are explored by infrared predissociation spectroscopy with the vacuum-ultraviolet photoionization detection schemes. Reaction paths following the one-photon ionization of the acetone monomer and its dimer have been studied by the joint use of several theoretical methods including the ab initio molecular dynamics, the global reaction route mapping, the intrinsic reaction coordinate, and the artificial force induced reaction calculations. Upon one-photon ionization, the dimer isomerizes to the H-bonded form, in which the enol cation of acetone is bound to the neutral molecule, while this enolization is energetically forbidden in the acetone monomer. The enolization of the dimer cation occurs through a two-step proton-transfer from the methyl group of the ionized moiety, and is catalyzed by the neutral moiety within the dimer cation.     

Biomimetic Peptide Catalytic Bond-Forming Utilizing a Mild Brønsted Acid

Since the global peptide drug market demand has been predicted to increase, highly efficient and inexpensive mass scale peptides are required. However, the production process raises questions about the cost of energy input, scale-up production, raw materials, and solvents treatment. This paper introduces 2 methods for the 2–4 mer oligopeptides bond formation for batch reaction utilizing 50–100 mol% of a mild Brønsted acid under the mild condition. One of the methods has been capably adapted to flow synthesis at room temperature using organic solvents with boiling points below 100 °C. The method applies the tert-butoxycarbonyl amino methoxy group, forming the desired dipeptide without solvent at mild temperatures. Furthermore, the conversion of the carboxylic acid leaving the group to phenyl ester promotes peptide bond formation, and the reaction were applied to di, tri, and tetrapeptide bond formation in excellent yield without notable racemization at ambient temperature (up to >99 % yield and 99 : 1 dr). Finally, this study proposes this new production method to overcome the limited scale-up production by reaction device scale: liquid phase biomimetic catalytic peptide flow synthesis utilizing a mild Brønsted acid.     

Chiral Dinuclear EuIII,TbIII, and YIII Complexes Supported by P-Stereogenic Linear Tetraphosphine Tetraoxide

A P-stereogenic linear tetraphosphine tetraoxide, (R,R)- or (S,S)-dpmppm(=O)₄, was synthesized to prepare C₂ dinuclear M(hfa)₃ complexes (M=Eu, Tb, Y) as the first example of lanthanide(III) complexes with P-chiral multidentate phosphine oxides. The mononuclear M(hfa)₃ complexes (M=Eu, Y) with a P-chiral diphosphine dioxide, tpdpb(=O)₂, were also prepared, and comparison of their photophysical properties for the Eu^III complexes revealed that significant chiral induction from the P-chiral centers arises on the achiral M(hfa)₃ units through intramolecular π-π stacking constraint in the dinuclear system.     

Circularly Polarized Luminescence and Circular Dichroism of Bichromophoric Difluoroboron-β-diketonates: Inversion and Enhanced Chirality Based on Spatial Arrangements and Self-Assembly

We synthesized two bichromophoric difluoroboron-β-diketonates (DFB) connected in para and meta positions by using cyclohexane diamine as a chiral bridge ( para and meta (R/S)-CyDFB ). TD-DFT calculations revealed that the variation in connectivity of the DFB units leads to different spatial arrangements and a chirality inversion of the bichromophoric DFB. Higher g_abs values were obtained in (R/S)-CyDFB connected in para as compared to meta position. Aggregation of para (R/S)-CyDFB in mixture of solvents increase the g_lum values as compared to its monomeric form. Ultrasonication and heating induced the formation of highly ordered nano-helical wires of para (R/S)-CyDFB that increased the g_lum values to 0.015. On the other hand, meta (R/S)-CyDFB failed to form highly ordered self-assembled wires due to hindered H-binding sites. These observations indicate that the chiroptical properties of DFB bi-chromophore system can be modulated with self-assembly and spatial arrangement of the chromophores.     

Optical properties of Au–Ag core–shell nanorods on glass and ITO substrates

Gold-silver core–shell nanorods were deposited on glass and ITO plates. SEM observations indicated that some of these nanorods were standing on the ITO plate. The extinction spectra of the plates were measured by varying the angles of incidence of p-polarized monitor light. Deconvolution of these spectra gave six bands in the visible region. The dependence of the peak intensities on the incident angles indicated that the bands at 390 and 420 nm originated from surface plasmon bands in the transverse direction of the nanorods.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Nonlinear oscillations of fourth order quasilinear ordinary differential equations

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.