New exact solutions of the Yang-Mills equation

New exact classical solutions of the Euclidean Yang-Mills equation are constructed. The exact solutions presented here are characterized by infinite values of topological charges and therefore they are in striking contrast to the well-known instanton and meron solutions which have finite topological charges.     

Synthesis and characterization of a biphenyl-linked hemicryptophane and an endohedral cobalt(II) complex

Hemicryptophanes are covalent molecular cages, constructed from a cyclotriveratrylene-based host unit and a functional unit linked by covalent spacers, which have been designed to accommodate endohedral functionalities in the cavity. In this study, the synthesis and characterization of the rigid, biphenyl-linked hemicryptophane 1 were investigated by NMR, ESI-MS, and X-ray crystallography. The structure of the inclusion complex, in which a dichloromethane molecule was constructed encapsulated within 1, was characterized by X-ray crystallography. An endohedral, cobalt(II) hemicryptophane complex 2 was also synthesized and characterized ESI-MS and X-ray crystallography. The X-ray crystal structure of 2 showed that the biphenyl-linked hemicryptophane had three components—a molecule each of chloroform and acetonitrile, and a cobalt(II) ion—within its cavity.     

Biological identification of peptides that specifically bind to poly(phenylene vinylene) surfaces: recognition of the branched or linear structure of the conjugated polymer

Peptides that bind to poly(phenylene vinylene) (PPV) were identified by the phage display method. Aromatic amino acids were enriched in these peptide sequences, suggesting that a π-π interaction is the key interaction between the peptides and PPV. The surface plasmon resonance (SPR) experiments using chemically synthesized peptides demonstrated that the Hyp01 peptide, with the sequence His-Thr-Asp-Trp-Arg-Leu-Gly-Thr-Trp-His-His-Ser, showed an affinity constant (7.7 × 10(5) M(-1)) for the target, hyperbranched PPV (hypPPV) film. This value is 15-fold greater than its affinity for linear PPV (linPPV). In contrast, the peptide screened for linPPV (Lin01) showed the reverse specificity for linPPV. These results suggested that the Hyp01 and Lin01 peptides selectively recognized the linear or branched structure of PPVs. The Ala-scanning experiment, circular dichroism (CD) spectrometry, and molecular modeling of the Hyp01 peptide indicated that adequate location of two Trp residues by forming the polyproline type II (P(II)) helical conformation allowed the peptide to specifically interact with hypPPV.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

Moment problem of Hamburger,hierarchies of integrable systems,and the positivity of tau-functions

A moment problem of Hamburger is studied to find a parametric Stieltjes measure from given moments. It is shown that if a deformation, or a dynamics, of moments is governed by a hierarchy of a Kac-van Moerbeke system, then the Stieltjes measure can be constructed explicitly by integrating a hierarchy of Moser's nonlinear dynamical system. The positivity of tau-functions is related to the existence of the Stieltjes measure at a deep level.     

Integrable Deformation of Gaussian Distribution and the Ornstein-Uhlenbeck Process

An integrable deformation of one-dimensional Gaussian distribution in terms of a continuous Moser hierarchy is described explicitly. Here the hierarchy governs the level dynamics of the semi-infinite Toda molecule. The action of the second-order flow is shown to be equivalent to that of the Ornstein–Uhlenbeck diffusion process.     

The Critical Effect of Niobium Doping on the Formation of Mesostructured TiO2: Single‐Crystalline Ordered Mesoporous Nb‐TiO2 and Plate‐like Nb‐TiO2 with Ordered Mesoscale Dimples

Highly ordered mesoporous niobium‐doped TiO₂ with a single‐crystalline framework was prepared by using silica colloidal crystals with ca. 30 nm in diameter as templates. The preparation of colloidal crystals composed of uniform silica nanoparticles is a key to obtain highly ordered mesoporous Nb‐doped TiO₂. The XPS measurements of Nb‐doped TiO₂ showed the presence of Nb⁵⁺ and correspondingly Ti³⁺. With the increase in the amount of doped Nb, the crystalline phase of the product was converted from rutile into anatase, and the lattice spacings of both rutile and anatase phases increased. Surprisingly, the increase in the amount of Nb led to the formation of plate‐like TiO₂ with dimpled surfaces on one side, which was directly replicated from the surfaces of the colloidal silica crystals.     

Preparation of highly dispersible and tumor-accumulative, iron oxide nanoparticles Multi-point anchoring of PEG-b-poly(4-vinylbenzylphosphonate) improves performance significantly

This paper describes the preparation of iron oxide nanoparticles, surface of which was coated with extremely high immobilization stability and relatively higher density of poly(ethylene glycol) (PEG), which are referred to as PEG protected iron oxide nanoparticles (PEG-PIONs). The PEG-PIONs were obtained through alkali coprecipitation of iron salts in the presence of the PEG-poly(4-vinylbenzylphosphonate) block copolymer (PEG-b-PVBP). In this system, PEG-b-PVBP served as a surface coating that was bound to the iron oxide surface via multipoint anchoring of the phosphonate groups in the PVBP segment of PEG-b-PVBP. The binding of PEG-b-PVBP onto the iron oxide nanoparticle surface and the subsequent formation of a PEG brush layer were proved by FT-IR, zeta potential, and thermogravimetric measurements. The surface PEG-chain density of the PEG-PIONs varied depending on the [PEG-b-PVBP]/[iron salts] feed-weight ratio in the coprecipitation reaction. PEG-PIONs prepared at an optimal feed-weight ratio in this study showed a high surface PEG-chain surface density (≈0.8 chainsnm(-2)) and small hydrodynamic diameter (<50 nm). Furthermore, these PEG-PIONs could be dispersed in phosphate-buffered saline (PBS) that contains 10% serum without any change in their hydrodynamic diameters over a period of one week, indicating that PEG-PIONs would provide high dispersion stability under in vivo physiological conditions as well as excellent anti-biofouling properties. In fact we have confirmed the prolong blood circulation time and facilitate tumor accumulation (more than 15% IDg(-1) tumor) of PEG-PIONs without the aid of any target ligand in mouse tumor models. The majority of the PEG-PIONs accumulated in the tumor by 96 h after administration, whereas those in normal tissues were smoothly eliminated by 96 h, proving the enhancement of tumor selectivity in the PEG-PION localization. The results obtained here strongly suggest that originally synthesized PEG-b-PVBP, having multipoint anchoring character by the phosphonate groups, is rational design for improvement in nanoparticle as in vivo application. Two major points, viz., extremely stable anchoring character and dense PEG chains tethered on the nanoparticle surface, worked simultaneously to become PEG-PIONs as an ideal biomedical devices intact for prolonged periods in harsh biological environments.