Abstract:
Reports on physical functions during maintenance period of the elderly with cardiac and other serious diseases are limited. This study aims to clarify age and gender-related differences in their physical functions. Participants included 167 elderly individuals (males, 78; mean age, 76.5 years; SD = 6.0 years; females, 89; mean age, 75.5 years; SD = 4.5 years) who participated in a 1-year regular exercise therapy twice a week. The following eight physical function tests were selected: grip strength, 10-m obstacle walking time, one-legged balance with eyes open, sit-ups, sitting trunk flexion, 6-min walk, stepping by sitting position, and a timed up & go (TUG). Two-way analysis of variance was used to examine mean differences by gender and age: young elderly group (aged 65 - 74 years) and old elderly group (aged ≥ 75 years). In the grip strength, sit-ups, 6-min walk, 10-m obstacle walking time, stepping by sitting position, and sitting trunk flexion tests, males were superior in the former four tests, and females were superior in the latter two tests. The young elderly group was superior in all tests except for sit-ups compared with the old elderly group. The balance during one-legged with eyes open test was superior in males compared with females in the young elderly group, but decreased in males in the old elderly group. In conclusion, physical functions of the elderly during maintenance period are different between genders. Muscle strength, muscle endurance, whole-body endurance, and walking ability are superior in males, whereas flexibility and agility are superior in females. The old elderly group was inferior in all the elements of physical function except muscle endurance.

Abstract:
This research considered the effect of differences between instruction patterns in consecutive, selective reaction-time tests administered to early childhood participants. Participants included 62 young male children (mean age 5.3 ± 0.6 years, mean height 107.4？± 5.5 cm, mean mass 17.9 ± 2.2 kg). Starting from a standing position, each participant rapidly moved eight times on a sheet—either left, right, forward, backward, or diagonal—in accordance with the given target. Five different combinations were used;？each combination required participants to move in each of the eight possible directions once, including the four diagonal directions. On each pattern, the total times for all participants were added to yield a consecutive, selective reaction time for that pattern. Single-factor dispersion analysis results did not indicate a statistically significant difference in reaction times between the test patterns (the level of significance was determined as 0.05). Furthermore, a greater-than-medium correlation between the five patterns with regard to their total consecutive, selective reaction-times was observed. Consequently, while no large difference was demonstrated between patterns, a relatively high correlation was observed between patterns on consecutive, selective reaction-time tests administered to young children.

Abstract:
The objective of this study was to consider the gender differences in the monthly variation in throwing distances among kindergarten children using different balls. The subjects of this study were 111 healthy males and 109 healthy females. The subjects’ throwing distances of softballs and tennis balls were measured in June and November. By a gender-based two-way analysis of variance (difference by ball type × difference by month), we observed that the throwing distance of softballs was less than that of tennis balls for both males and females. Moreover, we note that the throwing distance of both ball types was shorter in June than in November. A second two-way analysis of variance (difference by gender × difference by ball type) determined that the throwing distance variation ratio ((November/June) × 100) was greater for softballs than for tennis balls among females only; however, this difference was not significant. The above results show that the throwing distance of softballs is less than that of tennis balls. However, we observe that the selection of ball type has no major effect on the monthly variation in throwing distances among children and that the trend does not vary greatly between males and females.

In this paper, we discuss
the theoretical validity of the observed partial likelihood (OPL) constructed
in a Coxtype model under
incomplete data with two class possibilities, such as missing binary
covariates, a cure-mixture model or doubly censored data. A main result is
establishing the asymptotic convergence of the OPL. To reach this result, as it
is difficult to apply some standard tools in the survival analysis, we develop
tools for weak convergence based on partial-sum processes. The result of the
asymptotic convergence shown here indicates that a suitable order of the number
of Monte Carlo trials is less than the square of the sample size. In addition,
using numerical examples, we investigate how the asymptotic properties
discussed here behave in a finite sample.

Abstract:
N. Katz introduced the notion of the middle convolution on local systems. This can be seen as a generalization of the Euler transform of Fuchsian differential equations. In this paper, we consider the generalization of the Euler transform, the twisted Euler transform, and apply this to differential equations with irregular singular points. In particular, for differential equations with an irregular singular point of irregular rank 2 at $x=\infty$, we describe explicitly changes of local datum caused by twisted Euler transforms. Also we attach these differential equations to Kac-Moody Lie algebras and show that twisted Euler transforms correspond to the action of Weyl groups of these Lie algebras.

Abstract:
In this paper, we study the Euler transform on linear ordinary differential operators on $\mathbb{P}^{1}$. The spectral type is the tuple of integers which count the multiplicities of local formal solutions with the same leading terms. We compute the changes of spectral types under the action of the Euler transform and show that the changes of spectral types generate a transformation group of a $\mathbb{Z}$-lattice which is isomorphic to a quotient lattice of a Kac-Moody root lattice with the Weyl group as the transformation group.

Abstract:
We give a characterization of a generalized Whittaker model of a degenerate principal series representation of $GL(n,\R)$ as the kernel of some differential operators. By this characterization, we investigate some examples on $GL(4,\R)$. We obtain the dimensions of the generalized Whittaker models and give their basis in terms of hypergeometric functions of one and two variables. We show the multiplicity one of the generalized Whittaker models by using the theory of hypergeometric functions.

Abstract:
Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend this problem to differential equations having an arbitrary number of unramified irregular singular points and determine the existence of solutions of the generalized additive Deligne-Simpson problems. Moreover we apply this result to the geometry of the moduli spaces of stable meromorphic connections of trivial bundles on the Riemann sphere. Namely, open embedding of the moduli spaces into quiver varieties is given and the non-emptiness condition of the moduli spaces is determined.

Abstract:
We consider a resolution of ramified irregular singularities of meromorphic connections on a formal disk via local Fourier transforms. A necessary and sufficient condition for an irreducible connection to have a resolution of the ramified singularity is determined as an analogy of the blowing up of plane curve singularities. We also relate the irregularity of Komatsu and Malgrange of connections to the intersection numbers and the Milnor numbers of plane curve germs. Finally, we shall define an analogue of Puiseux characteristics for connections and find an invariant of the family of connections with the fixed Puiseux characteristic by means of the structure of iterated torus knots of the plane curve germs.

Abstract:
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the study of the symmetries, a realization of the moduli spaces as quiver varieties is given and plays an essential role.