Distance-based classifier by data transformation for high-dimension,strongly spiked eigenvalue models

Annals of the Institute of Statistical Mathematics - We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data...     

Effect of Coulomb Damping on Buckling of a Two-Rod System

This paper describes a significant influence of a slight Coulomb damping on buckling, using a simple two rods system. Coulomb damping produces equilibrium regions around the well-known stable and unstable steady states under the pitchfork bifurcation which occurs in the case without Coulomb damping. Also, the stability of the states in the equilibrium regions is examined by using the phase portrait. As a consequence, due to the slight Coulomb damping, it is theoretically clarified that the states in the equilibrium regions are locally stable, even in the neighborhood of the unstable steady states under the pitchfork bifurcation in the case without Coulomb damping, i.e., even in the neighborhood of the unstable trivial steady states in the postbuckling and the unstable nontrivial steady states under the subcritical pitchfork bifurcation. Furthermore, the experimental results are in qualitative agreement with the theoretically predicted phenomena.     

Effect of Lateral Linear Stiffness on Nonlinear Characteristics of Hunting Motion of a Railway Wheelset

Railway wheelset experiences the problem of hunting above a critical speed, which is a kind of self-excited oscillation. At the critical speed, it is known that the system undergoes a subcritical Hopf bifurcation. Therefore, for clarifying the nonlinear characteristics of hunting it is very important to detect, for example, the nonlinear forces in the wheelset due to the creep forces acting between the wheels and rails, and the nonlinear component of the resorting forces by the suspensions. However, it is impossible to determine each force quantitatively. In the present paper, it is first shown, by using the center manifold theory and the method of normal form, that the nonlinear characteristics of the bifurcation in a wheelset model with two degrees of freedom are governed by a single parameter, hence each nonlinear force need not be detected when examining the nonlinear characteristics. Also, a method of determining the governing parameter from experimentally observed radiuses of the unstable limit cycle is proposed. Next, we experimentally investigate the variation of the parameter due to the presence of linear spring suspensions in the lateral direction and discuss the variation of the nonlinear characteristics of the hunting motion, which depends on the lateral stiffness. As a result, the improvement of the stability of the wheelset against the disturbance by the linear spring suspensions is clarified.     

Cationic addition polymerization of 1,4‐dioxene using gacl3 as lewis acid catalyst: Long‐lived species‐mediated polymerization

Effective cationic addition polymerization of 1,4‐dioxene, a six‐membered cyclic olefin with two oxygen atoms adjacent to the double bond, was performed using a simple metal halide catalyst system in dichloromethane. The polymerization was controlled when the reaction was conducted using GaCl₃ in conjunction with an isobutyl vinyl ether–HCl adduct as a cationogen at –78°C to give polymers with predetermined molecular weights and relatively narrow molecular weight distributions. The long‐lived properties of the propagating species were further confirmed by a monomer addition experiment and the analyses of the product polymers by ¹H NMR and MALDI–TOF–MS. Although highly clean propagation proceeded, the apparent rate constant changed during the controlled cationic polymerization of 1,4‐dioxene. The reason for the change was discussed based on polymerization results under various conditions. The obtained poly(1,4‐dioxene) exhibited a very high glass transition temperature (T_g) of 217°C and unique solubility. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Living cationic polymerization of vinyl ethers with a naphthyl group: Decisive effect of the substituted position on naphthalene ring

Living cationic polymerization of a vinyl ether with a naphthyl group [2‐(2‐naphthoxy)ethyl vinyl ether, βNpOVE] was achieved using base‐assisting initiating systems with a Lewis acid. The Et_1.5AlCl_1.5/1,4‐dioxane or ethyl acetate system induced the living cationic polymerization of βNpOVE in toluene at 0 °C. The living nature of this reaction was confirmed by a monomer addition experiment, followed by ¹H NMR and matrix‐assisted laser desorption ionization time‐of‐flight mass spectrometry (MALDI‐TOF‐MS) analyses. In contrast, the polymerization of αNpOVE was not fully controlled; under similar conditions, it produced polymers with broad molecular weight distributions. The ¹H NMR and MALDI‐TOF‐MS spectra of the resultant poly(αNpOVE) revealed that the products had undesirable structures derived from Friedel–Crafts alkylation. The higher reactivity of αNpOVE in electrophilic substitution reactions, such as the Friedel–Crafts reaction, was attributable to the greater electron density of the naphthyl ring, which was calculated based on frontier orbital theory. The naphthyl groups significantly affected the properties of the resultant polymer. For example, the glass transition temperatures (T_g) of poly(NpOVE)s are higher by approximately 40 °C than that of poly(2‐phenoxyethyl vinyl ether). © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Synthesis of fluorine‐containing star‐shaped poly(vinyl ether)s via arm‐linking reactions in living cationic polymerization

Various types of fluorine‐containing star‐shaped poly(vinyl ether)s were successfully synthesized by crosslinking reactions of living polymers based on living cationic polymerization. Star polymers with fluorinated arm chains were prepared by the reaction between a divinyl ether and living poly(vinyl ether)s with fluorine groups (C₄F₉, C₆F₁₃, and C₈F₁₇) at the side chain using cationogen/Et_1.5AlCl_1.5 in a fluorinated solvent (dichloropentafluoropropanes), giving star‐shaped fluorinated polymers in high yields with a relatively narrow molecular weight distribution. The concentration of living polymers for the crosslinking reaction and the molar feed ratio of a bifunctional vinyl ether to living polymers affected the yield and molecular weight of the star polymers. Star polymers with block arms were prepared by a linking reaction of living block copolymers of a fluorinated segment and a nonfluorinated segment. Heteroarm star‐shaped polymers containing two‐ or three‐arm species were synthesized using a mixture of different living polymer species for the reaction with a bifunctional vinyl ether. The obtained polymers underwent temperature‐induced solubility transitions in various organic solvents, and their concentrated solutions underwent sol–gel transitions, based on the solubility transition of a thermoresponsive fluorinated segment. Furthermore, a slight amount of fluorine groups were shown to be effective for physical gelation when those were located at the arm ends of a star polymer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Living cationic polymerization of isobutyl vinyl ether using a variety of metal oxides as heterogeneous catalysts: Robust,reusable, and environmentally benign initiating systems

Cationic polymerization of isobutyl vinyl ether (IBVE) was examined using a variety of metal oxides in conjunction with IBVE–HCl adduct as a cationogen in toluene at 0 °C. Iron oxides (α‐Fe₂O₃, γ‐Fe₂O₃, and Fe₃O₄) induced living polymerization in the presence of an added base, ethyl acetate or 1,4‐dioxane, to give polymers with very narrow molecular weight distributions (MWDs). Conversely, with other metal oxides such as Ga₂O₃, In₂O₃, ZnO, Co₃O₄, and Bi₂O₃, polymers with bimodal MWDs, including long‐lived species along with uncontrolled higher molecular weight portions, were produced in the presence of an added base. A small amount of nBu₄NCl or 2,6‐di‐tert‐butylpyridine (DTBP) suppressed the uncontrolled portion to induce controlled reactions with Ga₂O₃, In₂O₃, and ZnO. The roles of these reagents are discussed in terms of the nature of the active sites of the catalyst surface and the polymerization mechanisms. In addition, the reusability of the catalyst, the effect of stirring before and during polymerization, and the estimation of the number of active sites are also described. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 916–926, 2010     

Selectively degradable alternating copolymers of isobutyl vinyl ether and plant‐derived aldehydes with acyclic side chains: Effects of side group structures on copolymerization behaviors

Side group structures of aldehydes were demonstrated to have decisive effects on cationic copolymerizations with alkyl vinyl ether (VE). Alternating copolymerizations of isobutyl VE (IBVE) and plant‐derived aldehydes with acyclic side chains such as trans‐2,cis‐6‐nonadienal, trans‐2‐nonenal, and citral proceeded under appropriate reaction conditions with the EtSO₃H/GaCl₃ initiating system. In addition, some aldehydes copolymerized in a well‐controlled fashion to yield alternating copolymers with controlled molecular weights and narrow molecular weight distributions. Quantitative and selective acid hydrolysis of the resulting alternating copolymers, based on the acetal structures in the main chains, was also achieved to give other conjugated aldehydes as nearly sole degradation products. Copolymerization results of IBVE and various plant‐derived aldehydes with acyclic or cyclic side groups suggested that electron‐donating ability and bulkiness of the side groups were most likely responsible for the alternating and/or controlled copolymerization behaviors. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4684–4693