Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations

We consider the derivative nonlinear Schrödinger equations

where the coefficient satisfies the time growth condition

is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type

where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when

     

The inverse scattering problem and the equivalent local potential

We examine the role of the non-locality of the potential in the two-body scattering by taking the nucleon-Σ system as an example. We employ a non-local potential for the nucleon-Σ channel which has the characteristic features of the quark model and reproduces the phase shifts of widely used local potentials. We use inverse scattering methods to obtain the equivalent local potential from the non-local potential, and show that the obtained local potential has a strong short range repulsion.     

Global solvability for the Kirchhoff equations in exterior domains of dimension three

We consider the initial (boundary) value problem for the Kirchhoff equations in exterior domains or in the whole space of dimension three, and show that these problems admit time-global solutions, provided the norms of the initial data in the usual Sobolev spaces of appropriate order are sufficiently small. We obtain uniform estimates of the L¹(R) norms with respect to time variable at each point in the domain, of solutions of initial (boundary) value problem for the linear wave equations. We then show that the estimates above yield the unique global solvability for the Kirchhoff equations.     

Nanoparticles in Emissions and Atmospheric Environment: Now and Future

Journal of Nanoparticle Research -     

Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation

We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear hyperbolic equation of Kirchhoff type with dissipation weak in time. The purpose of this paper is to give time‐decay convergence estimates of the difference between the solutions of the hyperbolic equation above and those of the corresponding parabolic equation, together with the unique existence of the global solutions of the hyperbolic equation above. Copyright © 2009 John Wiley & Sons, Ltd.     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.     

Field performance of proposed foresight tillage depth control system for rotary implements mounted on an agricultural tractor

Indoor experiments to evaluate the response characteristics of the proposed foresight tillage depth control system for rotary implements mounted on an agricultural tractor were done under various conditions and the result of experiments was reported in our previous paper [Lee J, Yamazaki M, Oida A, Nakashima H, Shimizu H. Electro-hydraulic tillage depth control system for rotary implements mounted on agricultural tractor — design and response experiments of a control system, Journal of Terramechanics 1998;35(4):229–238]. Then, the experiments were conducted in an actual field to evaluate the adaptability of the control system to a field. The transient response experiment, by giving the step variation in the set tillage depth through a computer keyboard and the response to the pitching experiment, by giving the compulsory step variation in the pitching angle to the tractor by a pit, which was dug in the experimental field, were conducted under two steps of tractor running speeds, two kinds of sampling frequencies and so on. Besides of the proposed foresight control system, a non-foresight control system and a no-control system were also tried to be served in the field. The result of the field experiments for these control systems will be discussed in this paper.     

Surface treatment of CaCO3 with a mixture of amino- and mercapto-functional silane coupling agents and tensile properties of the rubber composites

In order to reinforce the composite consisting of isoprene rubber (IR) and calcium carbonate (CaCO₃) particles, the surface treatment of CaCO₃ particles with a mixture of amino- and mercapto-functional silane coupling agents was investigated. The quantity of chemisorbed silanes in treated CaCO₃ measured using thermogravimetry was greater for amino- than for mercapto-silane and for the tri- than for the dialkoxy structure. Second, the molecular mobility of polycondensate of the mixtures with the trialkoxy structure measured using ¹H pulse nuclear magnetic resonance had the least molecular mobility, i.e., formed the highest density network. The greater values of stress at 500% strain, fracture stress, and elongation at break were determined for the treatment with amino- and mercapto-functional silanes having a trialkoxy structure from the stress-strain curves of composite. The mixture treatment with dialkoxy structure and with amino- or mercapto-functional silane only did not improve the mechanical properties sufficiently. Interactions between the amino group and the CaCO₃ surface, covalent bonding between the mercapto group and the IR, and high density network formation of trialkoxy silane were important for improving the mechanical properties of the composite.