The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

Geometric analysis of anharmonic downward distortion following paths

A mathematical aspect of the anharmonic downward distortion following (ADDF) path is discussed. The ADDF method is utilized as an automated reaction path search method, which can explore transition state geometries on a potential energy surface from a potential minimum. We show that the maximum number of the ADD stationary paths intersecting the potential minimum is 2^{f + 1} ? 2 , where f denotes the degree of freedom of the system. We also show that the bifurcation of the ADD stationary path is essential to detect all the transition states connected from a given minimum. The ADDF computation is demonstrated for a H₂O molecule in which pitchfork bifurcation is observed.     

2′,4′-BNA/LNA with 9-(2-Aminoethoxy)-1,3-diaza-2-oxophenoxazine Efficiently Forms Duplexes and Has Enhanced Enzymatic Resistance**

Artificial nucleic acids are widely used in various technologies, such as nucleic acid therapeutics and DNA nanotechnologies requiring excellent duplex-forming abilities and enhanced nuclease resistance. 2′-O,4′-C-Methylene-bridged nucleic acid/locked nucleic acid (2′,4′-BNA/LNA) with 1,3-diaza-2-oxophenoxazine (BNAP ( B^H )) was previously reported. Herein, a novel B^H analogue, 2′,4′-BNA/LNA with 9-(2-aminoethoxy)-1,3-diaza-2-oxophenoxazine (G-clamp), named BNAP-AEO ( B^AEO ), was designed. The B^AEO nucleoside was successfully synthesized and incorporated into oligodeoxynucleotides (ODNs). ODNs containing B^AEO possessed up to 10⁴-, 152-, and 11-fold higher binding affinities for complementary (c) RNA than those of ODNs containing 2′-deoxycytidine ( C ), 2′,4′-BNA/LNA with 5-methylcytosine ( L ), or 2′-deoxyribonucleoside with G-clamp ( P^AEO ), respectively. Moreover, duplexes formed by ODN bearing B^AEO with cDNA and cRNA were thermally stable, even under molecular crowding conditions induced by the addition of polyethylene glycol. Furthermore, ODN bearing B^AEO was more resistant to 3′-exonuclease than ODNs with phosphorothioate linkages.     

Terahertz time-domain spectroscopy as a novel tool for crystallographic analysis in cellulose: the potentiality of being a new standard for evaluating crystallinity

Cellulose - Given that terahertz (THz) radiation responds to intermolecular forces such as hydrogen bonds, THz time-domain spectroscopy (THz-TDS) has expanded possibilities in cellulose research....     

Total Synthesis of the Antibiotic Kendomycin: A Macrocyclization Using the Tsuji–Trost Etherification

A highly stereocontrolled, convergent total synthesis of kendomycin [(?)‐TAN2162], an ansa‐macrocyclic antibiotic, is reported. The key of the strategy is an unprecedented Tsuji–Trost macrocyclic etherification, followed by a transannular Claisen rearrangement to construct the 18‐membered carbocyclic framework. The oxa‐six‐ and five‐membered rings were also stereoselectively constructed respectively by a cascade oxidative cyclization at an unfunctionalized benzylic position and using a one‐pot epoxidation/5‐exo‐tet epoxide opening.     

The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

High-throughput characterization of local conductivity of Nd0.9Ca0.1Ba2Cu3O7−δ thin film by the low-temperature scanning microwave microscope

We developed a scanning microwave microscope (SμM) designed for high-throughput electric-property screening as well as for rapid construction of electronic phase diagrams at low temperatures. As a sensor probe, we used a high-Qλ/4 coaxial cavity resonator to which a thin needle with ball-tip end was attached. The sensor module was mounted on the low-temperature XYZ stage, which allowed us to map out the change of resonance frequency and quality factor due to the local tip-sample interaction at low temperatures. From the measurements of combinatorial thin films, such as Ti_1−xCo_xO_2−δ and Nd_0.9Ca_0.1Ba₂Cu₃O_7−δ (NCBCO), it was demonstrated that this SμM system has enough performance for the high-throughput characterization of sample conductance under variable temperature conditions.     

Stimulation of Microvascular Networks on Sulfonated Polyrotaxane Surfaces with Immobilized Vascular Endothelial Growth Factor

Modulation of material properties and growth factor application are critical in constructing suitable cell culture environments to induce desired cellular functions. Sulfonated polyrotaxane (PRX) surfaces with immobilized vascular endothelial growth factors (VEGFs) are prepared to improve network formation in vascular endothelial cells. Sulfonated PRXs, whereby sulfonated α‐cyclodextrins (α‐CDs) are threaded onto a linear poly(ethylene glycol) chain capped with bulky groups at both terminals, are coated onto surfaces. The molecular mobility of sulfonated PRX surfaces is modulated by tuning the number of threading α‐CDs. VEGF is immobilized onto surfaces with varying mobility. Low mobility and VEGF‐immobilization reinforce cell proliferation, yes‐associated protein activity, and rhoA, pdgf, ang‐1, and pecam‐1 gene expression. Highly mobile surfaces and soluble VEGF weakly affect these cell responses. Network formation is strongly stimulated in vascular endothelial cells only on low‐mobility VEGF‐immobilized surfaces, suggesting that molecular mobility and VEGF immobilization synergistically control cell function.