Abstract:
Aim: To compare diets between obese and non-obese in children. Methods: Thirty-four obese and ten non-obese school children were recruited and their habitual factors of obesity were asked. Intakes of food in the obesity and non-obesity groups were checked using a model nutritional balance chart (MNBC). Results: Average intake ratio of food relative to ideal food intake was significantly higher in the non-obesity group than the obesity group. The relationship between obesity and exercise was significant but not significant for intake ratio of food, times watching TV and playing games. Conclusion: Food intake is not a primary factor of obesity but exercise is a key factor for obesity in school children. Since the effect of diet intervention in obese children was slight, exercise habit would be a more important strategy to reduce obesity than diet in school children.

In the integer and fractional quantum Hall effects, the electric
current flows through a thin layer under the strong magnetic field. The
diagonal resistance becomes very small at integer and specific fractional
filling factors where the electron scatterings are very few. Accordingly the
coherent length is large and therefore a tunneling effect of electrons may be
observed. We consider a new type of a quantum Hall device which has a narrow
potential barrier in the thin layer. Then the electrons flow with tunneling
effect through the potential barrier. When the oscillating magnetic field is applied
in addition to the constant field, the voltage steps may appear in the curve of
voltage V versus electric current I. If the voltage steps are
found in the experiment, it is confirmed that the 2D electron system yields the
same phenomenon as that of the ac-Josephson effect in a superconducting system.
Furthermore the step V is related to the transfer charge Q as V = (hf)/Q where f is the frequency of the
oscillating field and h is the Planck
constant. Then the detection of the step V determines the transfer charge Q. The
ratio Q/e (e is the
elementary charge) clarifies the

In this article, we study the string equation of type (2,5), which is
derived from 2D gravity theory or the string theory. We consider the equation
as a 4th order analogue of the first Painlevé equation, take the autonomous limit, and solve it
concretely by use of the Weierstrass’ elliptic function.

Abstract:
In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

This article concerns the quantum
superintegrable system obtained by Tremblay and Winternitz, which allows the separation
of variables in polar coordinates and possesses three conserved quantities with
the potential described by the sixth Painlevé equation. The degeneration procedure
from the sixth Painlvé equation to the fifth one yields another new
superintegrable system; however, the Hermitian nature is broken.

Abstract:
The spin polarization of a fractional quantum Hall state shows very
interesting properties. The curve of polarization versus magnetic field has
wide plateaus. The fractional quantum Hall effect is caused by the Coulomb
interaction because the 2D electron system without the Coulomb interaction yields
no energy gap at the fractional filling factor. Therefore, the wide plateau in
the polarization curve is also caused by the Coulomb interaction. When the
magnetic field is weak, some electrons have up-spins and the others down-spins.
Therein the spin-exchange transition occurs between two electrons with up and
down spins via the Coulomb interaction. Then the charge distribution before the
transition is the same as one after the transition. So these two states have
the same classical Coulomb energy. Accordingly, the partial Hamiltonian
composed of the spin exchange interaction should be treated exactly. We have
succeeded in diagonalizing the spin exchange interaction for the first and
second nearest electron pairs. The theoretical results reproduce the wide
plateaus very well. If the interval modulations between Landau orbitals are
taken into the Hamiltonian, the total energy has the Peierls instability. We
can diagonalize the Hamiltonian with the interval modulation. The results
reproduce wide plateaus and small shoulders which are in good agreement with
the experimental data.

Abstract:
We have investigated the Fractional Quantum Hall Effect (FQHE) on the fundamental Hamiltonian with the Coulomb interactions between normal electrons without any quasi particle. The electron pairs placed in the Landau orbitals can transfer to many empty orbitals. The number of the quantum transitions decreases discontinuously when the filling factor v deviates from the specific fractional number of v_{0}. The discontinuous decreasing produces the energy valley at the specific filling factors v_{0} = 2/3, 4/5, 3/5, 4/7, 3/7, 2/5, 1/3 and so on. The diagonal elements of the total Hamiltonian and the number of the quantum transitions give the total energy of the FQH states. The energy per electron has the discontinuous spectrum depending on the filling factor v. We obtain the function form of the energy per electron in the quantum Hall system. Then the theoretical Hall resistance curve is calculated near several filling factors. Therein the quantum Hall plateaus are derived from the energy valleys. The depths of the energy valleys are compared with the widths of the quantum Hall plateaus appearing in the experimental data of the Hall resistance. Our theoretical results are in good agreement with the experimental results.

Abstract:
Fractional quantum Hall effect (FQHE) is investigated by employing
normal electrons and the fundamental Hamiltonian without any quasi particle.
There are various kinds of electron configurations in the Landau orbitals.
Therein only one configuration has the minimum energy for the sum of the Landau
energy, classical Coulomb energy and Zeeman energy at any fractional filling
factor. When the strong magnetic field is applied to be upward, the Zeeman
energy of down-spin is lower than that of up-spin for electrons. So, all the
Landau orbitals in the lowest level are occupied by the electrons with
down-spin in a strong magnetic field at 1 < ν < 2. On the other hand, the Landau
orbitals are partially occupied by up-spins. Two electrons with up-spin placed
in the nearest orbitals can transfer to all the empty orbitals of up-spin at
the specific filling factors and so on. When the
filling factor ν deviates from ν_{0}, the number of allowed transitions
decreases abruptly in comparison with that at ν_{0}. This mechanism creates the energy
gaps at ν_{0}. These energy gaps yield the
fractional quantum Hall effect. We compare the present theory with the
composite fermion theory in the region of 2/3 < ν < 2.

The best constant of discrete Sobolev
inequality on the truncated tetrahedron with a weight which describes 2 kinds
of spring constants or bond distances. Main results coincides with the ones of
known results by Kametaka et al. under the assumption of uniformity of the
spring constants. Since the buckyball fullerene C60 has 2 kinds of edges,
destruction of uniformity makes us proceed the application to the chemistry of fullerenes.

In this article, we study the
string equation of type (2, 2n + 1), which is derived from 2D gravity theory or
the string theory. We consider the equation as a 2n-th order analogue of the
first Painlevéequation, take the autonomous limit, and solve it concretely by
use of the Weierstrass’ elliptic function.