Abstract:
Nitroaromatics are usually prepared using a mixed acid of nitric acid with strong acids. However, the use of strong acids caused dangerous work-up and the disposal of large amounts of acid-waste. Therefore, much effort has been made on the improvement of nitration process without strong acids. We examined solid-phase aromatic nitration with Mg(NO_{3})_{2} on silica gel in order to establish the nitration process without strong acids. The nitration of 1,2- and 1,3-, 1,4-dimethoxybenzenes and 4-methylanisole with Mg(NO_{3})_{2} proceeded by heating on silica gel at 150°C for 4 - 5 h to produce the nitroaromatics. The nitration of 1,3,5-trimethoxybenzene produced the nitrated dimer, 2,4,6,2’, 4’,6’-hexamethoxy-3-nitrobiphenyl, which was not isolated in other solid-phase nitration. In the cases of naphthalene derivatives, the α-nitrated compounds were obtained. In the cases of p-cresol and 2-naphthol, the esterification occurred at the hydroxyl group to give 4-tolyl nitrate and 2-naphthyl nitrate, respectively. It is synthetic interest to note that nitrate esters were isolated in solid phase. Thus Mg(NO_{3})_{2}-SiO_{2} composite was mild reagent for solid-phase nitration. Acidity of Mg(NO_{3})_{2}-SiO_{2} composite was determined to be pH 0.96 by the measurement of absorption spectra on a micro spectrophotometer using meso-tetra(p-cyanophenyl)porphyrin as a pH-indicator. Mg(NO_{3})_{2}-SiO_{2} composite made acidic conditions. Therefore, it was suggested that Mg(NO_{3})_{2} reacted with proton on silica gel to form the NO^{+}_{2}. Thus, electron-rich aromatic hydrocarbons led the efficient nitration through electrophilic attack of NO^{+}_{2}. After the nitration, acidic Mg(NO_{3})_{2}-SiO_{2} composite could be turned into neutrality by exposing wet conditions and disposed safely since the composite did not involve harmful elements. Thus the solid-phase nitration using Mg(NO_{3})_{2}-SiO_{2} composite will provide safety and environmentally conscious chemical process.

Abstract:
We study the stability of a non-rotating single-component jet using two-dimensional special relativistic hydrodynamic simulations. By assuming translational invariance along the jet axis, we exclude the destabilization effect by Kelvin-Helmholtz mode. The nonlinear evolution of the transverse structure of the jet with a normal jet velocity is highlighted. An intriguing finding in our study is that Rayleigh-Taylor and Richtmeier-Meshkov type instabilities can destroy cylindrical jet configuration as a result of spontaneously induced radial oscillating motion. This is powered by in-situ energy conversion between the thermal and bulk kinetic energies. The effective inertia ratio of the jet to the surrounding medium $\eta$ determines a threshold for the onset of instabilities. The condition $\eta < 1$ should be satisfied for the transverse structure of the jet being persisted.

Abstract:
The effect of rarefaction acceleration on the propagation dynamics and structure of relativistically hot jets is studied through relativistic hydrodynamic simulations. We emphasize the nonlinear interaction of rarefaction waves excited at the interface between a cylindrical jet and the surrounding medium. From simplified one-dimensional models with radial jet structure, we find that a decrease in the relativistic pressure due to the interacting rarefaction waves in the central zone of the jet transiently yields a more powerful boost of the bulk jet than that expected from single rarefaction acceleration. This leads to a cyclic in-situ energy conversion between thermal and bulk kinetic energies which induces radial oscillating motion of the jet. The oscillation timescale is characterized by the initial pressure ratio of the jet to the ambient medium, and follows a simple scaling relation $\tau_{\rm oscillation} \propto (P_{\rm jet,0}/P_{\rm amb,0})^{1/2}$. It is confirmed from extended two-dimensional simulations that this radial oscillating motion in the one-dimensional system manifests as modulation of the structure of the jet in a more realistic situation where a relativistically hot jet propagates through an ambient medium. It is found that when the ambient medium has a power law pressure distribution, the size of the reconfinement region along the propagation direction of the jet in the modulation structure $\lambda$ evolves according to a self-similar relation $\lambda \propto t^{\alpha/2}$ where $\alpha$ is the power-law index of the pressure distribution.

Abstract:
The number of university students’ dropouts is increasing rapidly these days in Japan. One of the possible causes is some kinds of problems relating to economic reasons. The other reason, there is a marked decline in the students’ scholastic performance. They are not able to keep up with class work at school. Our recent studies have focused on e-Learning support methods using the Gamification. It is one form of the above game-informed education. So far, we have seen that the student can use the Internet pleasantly and very interestingly. In this paper, we propose the flipped class- room design method using the Gamification. The flipped classroom is at the center of this discus- sion. It is an inverted version of the traditional learning model. It is a new pedagogical method. It is becoming increasingly well known around the University education in Japan. This concept has been put to use in several different fields, one such field being education. It is a type of blended learning. In order to discuss the pros and cons of gamification of education, the authors conducted an experiment and questionnaire using e-Learning with gamification elements for English as foreign language education. The results of this study particularly highlighted the importance of well-designed tutorial, task, interface and feedback for the effective game-based e-Learning. Therefore, “flipped classroom based on gamification” is helpful in improving learners’ understanding level and motivation.

Abstract:
There has recently been growing interest in the area of gamification, the application of game elements to non-game contexts. This concept has been put to use in several different fields, one such field being education. What is good about game-informed learning is that when conditions are satisfied, learners can enhance their intrinsic motivation towards goal achievement. For the purpose of the study, two types of discussion were utilized: gamification and flipped classroom. The flipped classroom used technology to access the lecture and other instructional resources outside the class- room. This paper proposes the flipped classroom support methods using the Gamification. In order to discuss the pros and cons of gamification of education, the authors conducted an experiment and questionnaire using flipped classroom with gamification elements for English as foreign language education. The results of this study particularly highlighted the importance of well-de- signed tutorial, task, interface and feedback for the effective game-based e-learning. It is an inverted version of the traditional learning model.

Abstract:
Relativistic Sweet-Parker type magnetic reconnection is investigated by relativistic resistive magnetohydrodynamic (RRMHD) simulations. As an initial setting, we assume anti-parallel magnetic fields and a spatially uniform resistivity. A perturbation imposed on the magnetic fields triggers magnetic reconnection around a current sheet, and the plasma inflows into the reconnection region. The inflows are then heated due to ohmic dissipation in the diffusion region, and finally become relativistically hot outflows. The outflows are not accelerated to ultra-relativistic speeds (i.e., Lorentz factor ~ 1), even when the magnetic energy dominates the thermal and rest mass energies in the inflow region. Most of the magnetic energy in the inflow region is converted into the thermal energy of the outflow during the reconnection process. The energy conversion from magnetic to thermal energy in the diffusion region results in an increase in the plasma inertia. This prevents the outflows from being accelerated to ultra-relativistic speeds. We find that the reconnection rate R obeys the scaling relation R S^{-0.5}, where S is the Lundquist number. This feature is the same as that of non-relativistic reconnection. Our results are consistent with the theoretical predictions of Lyubarsky (2005) for Sweet-Parker type magnetic reconnection.

Abstract:
The nonlinear dynamics of outflows driven by magnetic explosion on the surface of a compact star is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as the initial equilibrium state, a spherical stellar object embedded in hydrostatic plasma which has a density $\rho(r) \propto r^{- \alpha}$ and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of compact star breaks the equilibrium and triggers a two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly around the stellar surface, initiating a magnetically driven outflow. A strong forward shock driven outflow is then excited. The expansion velocity of the magnetically driven outflow is characterized by the Alfv\'en velocity on the stellar surface, and follows a simple scaling relation $v_{\rm mag} \propto {v_{\rm A}}^{1/2}$. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that it evolves according to a self-similar relation $\Gamma_{\rm sh} \propto r_{\rm sh}$, where $\Gamma_{\rm sh}$ is the Lorentz factor of the plasma measured at the shock surface $r_{\rm sh}$. Purely hydrodynamic process would be responsible for the acceleration mechanism of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, can provide a better understanding of the magnetic active phenomena on various magnetized compact stars.

Abstract:
A graph $G$ is \emph{uniquely k-colorable} if the chromatic number of $G$ is $k$ and $G$ has only one $k$-coloring up to permutation of the colors. For a plane graph $G$, two faces $f_1$ and $f_2$ of $G$ are \emph{adjacent $(i,j)$-faces} if $d(f_1)=i$, $d(f_2)=j$ and $f_1$ and $f_2$ have a common edge, where $d(f)$ is the degree of a face $f$. In this paper, we prove that every uniquely 3-colorable plane graph has adjacent $(3,k)$-faces, where $k\leq 5$. The bound 5 for $k$ is best possible. Furthermore, we prove that there exist a class of uniquely 3-colorable plane graphs having neither adjacent $(3,i)$-faces nor adjacent $(3,j)$-faces, where $i,j\in \{3,4,5\}$ and $i \neq j$. One of our constructions implies that there exist an infinite family of edge-critical uniquely 3-colorable plane graphs with $n$ vertices and $\frac{7}{3}n-\frac{14}{3}$ edges, where $n(\geq 11)$ is odd and $n\equiv 2\pmod{3}$.

This study analyses the
dynamics of nonlinear monopoly. To this end, the conventional assumptions in
the text-book monopoly are modified; first, the complete information on the
market is replaced with the partial information; second, the instantaneous
information is substituted by the delay information. As a result, since such a
monopoly is unable to jump, with one shot, to the optimal point for which the
profit is maximized, the monopoly has to search for it. In a continuoustime
framework, the delay destabilizes the otherwise stable monopoly model and
generates cyclic oscillations via a Hopf bifurcation. In a discrete-time
framework, the steady state bifurcates to a bounded oscillation via a
Neimark-Sacker bifurcation. Although this has been only an introduction of
delay into the traditional monopoly model, it is clear that the delay can be a
source of essentially different behavior from those of the nondelay model.

Abstract:
We explore the photospheric emission from a relativistic jet breaking out from a massive stellar envelope based on relativistic hydrodynamical simulations and post-process radiation transfer calculations in three dimensions. To investigate the impact of three-dimensional (3D) dynamics on the emission, two models of injection conditions are considered for the jet at the center of the progenitor star: one with periodic precession and another without precession. We show that structures developed within the jet due to the interaction with the stellar envelope, as well as due to the precession, have a significant imprint on the resulting emission. Particularly, we find that the signature of precession activity by the central engine is not smeared out and can be directly observed in the light curve as a periodic signal. We also show non-thermal features, which can account for observations of gamma-ray bursts, are produced in the resulting spectra, even though only thermal photons are injected initially and the effect of non-thermal particles is not considered.