Abstract:
It has been proved theoetically and numerically that the highly relativistic electron beam can be accelerated efficiently via the Compton scattering induced by nonlinear Landau and cyclotron damping of the lower-hybrid waves.

Abstract:
We show that a strongly $\lambda$-spirallike function of order $\alpha$ can be extended to a $\sin(\pi\alpha/2)$-quasiconformal automorphism of the complex plane for $-\pi/2<\lambda<\pi/2$ and $0<\alpha<1$ with $|\lambda|<\pi\alpha/2.$ In order to prove it, we provide several geometric characterizations of a strongly $\lambda$-spirallike domain of order $\alpha.$ We also give a concrete form of the mapping function of the standard strongly $\lambda$-spirallike domain $U_{\lambda,\alpha}$ of order $\alpha.$ A key tool of the present study is the notion of $\lambda$-argument, which was developed by Y. C. Kim and the author.

Abstract:
It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this characterization to a hyperbolic domain in the Riemann sphere in terms of the spherical metric.

Abstract:
This paper examines optimal consumption/portfolio choices under stochastic habit formation in which it is uncertain how deep consumers would become in the habit of consuming in future. By extending Shroder and Skiadas [1] to stochastic habit formation, the optimization problem with stochastic habit forming preferences is transformed into that with simple time-additive preferences. Optimal portfolios are composed of the tangency portfolio and habit hedging portfolio. Resulting risk premia are characterized by consumption beta, which is proportionate to the covariance with consumption changes, and habit beta, defined by using the covariance with habit.

Abstract:
A layer
structured titanate Cs_{2}Ti_{5}O_{11}·(1 + x)H_{2}O
(x = 0.70) has
been prepared in a solid state reaction using Cs_{2}CO_{3} and anatase
type TiO_{2} at 900°C. Ion exchange reactions of Cs^{+} in
the interlayer space were studied in aqueous solutions. The single phases of Li^{+}, Na^{+} and H^{+} exchange products were obtained. The
three kinds of resulting titanates were evaluated for use as the cathodes in
rechargeable sodium batteries after dehydrations by
heating at 200°C in a vacuum. The
electrochemical measurements showed that they exhibited the reversible Na^{+} intercalation-deintercalation in a voltage range of 0.5 - 3.5 V or 0.7 - 4.0 V. The Li^{+} exchange product showed the best performance of the
discharge-charge capacities in
this study. The initial Na^{+} intercalation-deintercalation capacities
of the Li_{2}Ti_{5}O_{11} were 120 mAh/g and
100 mAh/g; the amounts of Na^{+} correspond to 1.9 and 1.6 of the
formula unit, respectively. The titanates are nontoxic, inexpensive and environmentally benign.

Abstract:
Cathode materials for rechargeable batteries have been extensively investigated. Sodium-ion batteries are emerging as alternatives to lithium-ion batteries. In this study, a novel cathode material for both lithium- and sodium-ion batteries has been derived from a layered crystal. Layer-structured titanate Cs_{x}Ti_{2}_{-}_{x}/_{2}Mg_{x}/_{2}O_{4} (x = 0.70) with lepidocrocite (γ-FeOOH)-type structure has been prepared in a solid-state reaction from Cs_{2}CO_{3}, anatase-type TiO_{2}, and MgO at 800°C. Ion-exchange reactions of Cs^{+} in the interlayer space were studied in aqueous solutions. The single phases of Li^{+}, Na^{+}, and H^{+} exchange products were obtained, and these were found to contain interlayer water. The interlayer water in the lithium ion-exchange product was removed by heating at 180°C in vacuum. The resulting titanate Li_{0.53}H_{0.13}Cs_{0.14}Ti_{1.65}Mg_{0.30}O_{4} was evaluated for use as cathodes in both rechargeable lithium and sodium batteries. The Li^{+} intercalation-deintercalation capacities were found to be 151 mAh/g and 114 mAh/g, respectively, for the first cycle in the voltage range 1.0 - 3.5 V. The amounts of Li^{+} corresponded to 0.98 and 0.74 of the formula unit, respectively. The Na^{+} intercalation-deintercalation capacities were 91 mAh/g and 77 mAh/g, respectively, for the first cycle in the voltage range 0.70 - 3.5 V. The amounts of Na^{+} corresponded to 0.59 and 0.50 of the formula unit, respectively. The new cathode material derived from the layer-structured titanate is non-toxic, inexpensive, and environmentally benign.

Abstract:
We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.

Abstract:
B. Friedman found in his 1946 paper that the set of analytic univalent functions on the unit disk in the complex plane with integral Taylor coefficients consists of nine functions. In the present paper, we prove that the similar set obtained by replacing "integral" by "half-integral" consists of another twelve functions in addition to the nine. We also observe geometric properties of the twelve functions.

Abstract:
In this note, we discuss the coefficient regions of analytic self-maps of the unit disk with a prescribed fixed point. As an application, we solve the Fekete-Szeg\H{o} problem for normalized concave functions with a prescribed pole in the unit disk.

Abstract:
In the present paper, we will discuss the Hankel determinants $H(f) =a_2a_4-a_3^2$ of order 2 for normalized concave functions $f(z)=z+a_2z^2+a_3z^3+\dots$ with a pole at $p\in(0,1).$ Here, a meromorphic function is called concave if it maps the unit disk conformally onto a domain whose complement is convex. To this end, we will characterize the coefficient body of order 2 for the class of analytic functions $\varphi(z)$ on $|z|<1$ with $|\varphi|<1$ and $\varphi(p)=p.$ We believe that this is helpful for other extremal problems concerning $a_2, a_3, a_4$ for normalized concave functions with a pole at $p.$