Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern

For a {0, 1}-pattern of finite length, an empirical process is introduced in order to describe the number of overlapping occurrences of the pattern at each level t[0,1] in a sequence of the corresponding indicators of i.i.d. [0, 1]-valued observations of length n. A method for obtaining the exact finite-dimensional distributions of the empirical process is given. The weak convergence of the process to a Gaussian process in D[0,1] as n tends to infinity is also established. The limiting process depends on the given pattern. The exact covariance function is compared with the asymptotic covariance function in a numerical example.     

A two-step procedure for the preparation of mono-protected bis-N-heterocyclic alkyl ether systems

A two-step convenient sequence for the synthesis of previously inaccessible mono-Boc-protected bis-N-heterocyclic alkyl substituted ether derivatives 4 is described. Mitsunobu protocol was applied to the preparation of pyridinyl ether precursor 5. The reduction of the electron rich pyridinyl system 5 has been achieved catalytically using the combination of PtO₂-H₂SO₄ or PtO₂-pTsOH under a hydrogen atmosphere maintained by a gas balloon at ambient temperature.     

Brønsted acid catalyzed formal insertion of isocyanides into a C-O bond of acetals

The Br?nsted acid catalyzed formal insertion of an isocyanide into a C-O bond of an acetal is described. A diverse array of acyclic and cyclic acetals can be applied to the catalytic insertion to form alpha-alkoxy imidates. Functional groups, such as nitro, cyano, halogen, ester, and alkoxy groups, are tolerant to the reaction conditions employed. The course of the reaction is highly dependent on the structure of the isocyanide. The use of an electron-deficient aryl isocyanide, such as 2c and 2d, is required to selectively obtain the monoinsertion product. When aryl isocyanides containing alkyl substituents, such as 2a and 2b, are employed, two molecules of the isocyanide are incorporated, and the double-insertion product is obtained. The reaction of tert-octyl isocyanide also induces a double incorporation, but the subsequent acid-mediated fragmentation leads to the 2-alkoxy imidoyl cyanide. The monoinsertion products, alpha-alkoxy imidates, can readily be hydrolyzed to alpha-alkoxy esters, realizing the formal carbonylation of an acetal.     

Molecular simulation of crystallization in n-alkane ultrathin films: effects of film thickness and substrate attraction

Crystallization in n-alkane ultrathin films supported by solid substrates is investigated by molecular dynamics simulation. We consider a relatively short n-alkane, undecane C11H24, on a flat substrate of varied degree of attraction. By the use of the united atom model for n-alkane, we reveal several characteristics of the thin film crystallization. It is found that the crystalline films consist of thin crystalline lamellae where chains are either parallel or perpendicular to the substrate. The relative amount of both types of lamellae changes systematically with film thickness, substrate attraction, and crystallization temperature; thicker films on substrates of higher attraction comprise dominant parallel lamellae, while thinner films on substrates of weaker attraction prefer the perpendicular lamellae. A clue to the morphogenesis is suggested to be the marked preference of the chain ends to locate on the free surface and on the effectively repulsive substrate. It is also shown that the perpendicular crystals, both on the free surface and on the solid substrate, have melting points higher than that of the bulk.     

Highly enantioselective conjugate addition of thiols using mild scandium triflate catalysis

A Sc complex of (4S,5S)-diphenyl PYBOX 1 was found to serve as a catalyst for the asymmetric conjugate addition reactions between various thiols and 3-crotonoyl-2-oxazolidinone, affording the corresponding adducts in good yields and high enantioselectivies (up to 92% ee). A new improved method for making (4S,5S)-diphenyl PYBOX is presented.     

Organic hybrid of chlorinated polyethylene and hindered phenol. II. Influence of the chemical structure of small molecules on viscoelastic properties

The viscoelastic properties and stabilities of those properties of organic hybrids consisting of chlorinated polyethylene (CPE) and tetrakis[methylene‐3‐(3‐5‐di‐tert‐butyl‐4‐hydroxy phenyl)propionyloxy]methane (AO‐60) and triethylene glycol bis[3‐(3‐tert‐butyl‐4‐hydroxy‐5‐methyl phenyl)propionyloxy] (AO‐70) were investigated. The CPE/AO‐70 hybrids show only one transition, whereas for the CPE/AO‐60 hybrids, one novel relaxation appears above the glass‐transition temperature of CPE. This relaxation on the higher temperature side in the mechanical spectrum for CPE/AO‐60 is associated with the appearance of the AO‐60‐rich phase. Furthermore, the stabilities of the viscoelastic properties and microstructures of the organic hybrids consisting of CPE and multifunctional hindered phenols are dominated by the strength of the intermolecular interaction between CPE and phenols and the conformations of the middle skeletal parts of hindered phenols. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1496–1503, 2000     

A novel approach to the characterization of end groups in styrene–methyl methacrylate copolymers by pyrolysis–gas chromatography

The end groups of styrene–methyl methacrylate (St‐MMA) copolymers polymerized radically with 2,2′‐azobisisobutyronitrile (AIBN) as an initiator, which are difficult to characterize even by NMR, were investigated by pyrolysis–gas chromatography. On the resulting pyrograms, characteristic products that formed from the end‐group moiety due to AIBN, such as 2‐cyanopropane, 2‐cyanopropen, and various compounds consisting of an isobutyronitrile group and a monomer unit, were observed together with those from the main chain, such as St and MMA monomers and various dimeric and trimeric products. The relative abundance between the recombination and disproportionation termination reactions in the copolymerization process was estimated from the relative intensities between the characteristic peaks of the end group and those of the main chain. Thus, the estimated abundance for the termination reactions suggested that the polymerization process for this particular copolymer system terminated preferentially by recombination rather than by disproportionation. Furthermore, the relative abundance between the monomer units adjacent to the chain‐end AIBN residues was estimated on the basis of the peak intensities of the products consisting of an isobutyronitrile group and either monomer unit, which reflected the penultimate neighboring structure of the end group in the polymer chain. Thus, the observed results suggested that the isobutyronitrile radical formed by the dissociation of AIBN in the initiation reaction was predominantly adjoined by St monomer rather than by MMA monomer. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1880–1888, 2000     

Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

This study thoroughly examines various higher-order three and four-node beam elements for use in the absolute nodal coordinate formulation (ANCF). The paper carefully investigates which potential benefits and drawbacks the utilization of higher-order ANCF beam elements without in-slope vectors has in the case of the usage of full three-dimensional elasticity. When the elastic forces for shear-deformable ANCF beam elements are calculated using full three-dimensional elasticity—especially in the form of the St. Venant–Kirchhoff material law—Poisson locking severely deteriorates the accuracy of the numeric results. As shown in this paper, an existing approach to preventing this locking phenomenon for three-node beam elements can still produce unsatisfying results in load cases involving bidirectional bending. The results of this study show that enriching the polynomial basis used to approximate the beam kinematics provides a natural solution to this issue. As will be seen, these findings for three-node elements can also be extended to four-node elements. When using a sufficient approximation order in transverse directions, satisfying accuracy can be achieved both in conventional one-dimensional bending and in the above-mentioned bidirectional load case.     

Visualization of Magnetization Transfer Effect in Polyethylene Glycol Impregnated Waterlogged Wood

To visualize the condition of impregnation of polyethylene glycol (PEG) in waterlogged wood, we demonstrated magnetic transfer (MT) magnetic resonance imaging (MRI) through a series of process of PEG impregnation. Three different samples were examined; reference wood, 10 cm cut wood, and 5 cm cut wood. During this study, the upper section sample was kept immersed in water, for the middle and lower sections the concentration of PEG solution was changed at 20 wt% intervals from 20 to 100 wt%. The impregnated periods of each PEG solution concentration were 14 days. Then, MR imaging were performed with/without MT pulse. The MTR value for both 10 cm- and 5 cm-samples were shown to decrease at 20 wt% PEG at peak concentration. When the sample volume was large, e.g., 10 cm-sample, the MTR value decreased to 100 wt% PEG concentration. In contrast, when a sample volume was small, e.g., 5 cm-sample, MTR value decreased to 60 wt% PEG concentration. In conclusion, MTR analysis makes it possible to nondestructively visualize and evaluate the inner condition concerning the PEG impregnation method for waterlogged wood.