Hyperbolic Schwarz map for the hypergeometric differential equation

The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in a forthcoming paper.Comment: 16 pages, 8 figure

Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts

In the previous paper (math.CA/0609196) we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived Schwarz maps of the hypergeometric differential equation and, second, we construct a parallel family of flat fronts connecting the classical Schwarz map and the derived Schwarz map.Comment: 15 pages, 12 figure

Experimental Studies on the Elastic-Plastic Behavior of Braced Frames under Repeated Horizontal Loading. Part 1 Experiments of Braces with an H-shaped Cross Section in a Frame

An experimental study is conducted to obtain the hysteretic characteristics of the brace itself in a braced frame under repeated loading. Braces with an H-shaped cross section are tested in a single or a double bracing system. The effects of the slenderness ratio, the buckling plane and the local buckling are investigated. Furthermore, the fundamental properties of a brace for the formulation of the hysteretic characteristics under repeated loading are extracted

Implementation of High-Speed Pseudo-Random-Number Generator with Chaotic and Random Neural Networks

Chaotic and random time series generated from improved chaotic and random neural network (CRNN) afford statistically appropriate pseudo-random number series for information security. Randomness of outputs of CRNN is empirically validated in detail, and control methods of an appropriate ratio of chaotic character and randomness in the time series for PRNG is reported. The rate of random number generation has reached 2.8530×10^12 b/s. In future, the generator may play an important role on implementing applications for protecting personal information on the Internet

Conduction-Radiation Property of Ceramic and Graphite Fiber Thermal Insulation Mat

The thermal conductivities for four typical kinds of heat resisting fibrous thermal insulation mats were obtained by the steady state parallel plates method in a vacuum condition. These experimental results were correlated by a combined conduction and radiation heat transfer model to determine the conduction thermal conductivity and the extinction coefficient which govern the heat transfer in the layer of fibrous insulating material. On the basis of these values, a new simple method was proposed to estimate the thermal conductivities of the four materials as a function of the bulk density and the mean temperature in the insulation layer

FORCE AND POWER OUTPUTS OF TRUNK-TWIST DURING BAR TWIST EXERCISE -INFLUENCE OF LENGTH AND MASS OF BARS-

The purpose of this study was to investigate force and power outputs during bar twist exercises using barbell shafts, considering various moment of inertia (MOI), corresponding to changes in the bar length and mass. Twenty-one male college athletes performed the bar twist exercise using five barbell shafts: one normal barbell shaft, two long barbell shafts (with changes only in the length), and two heavy barbell shafts (with changes only in the mass). Kinematic and kinetic data were recorded using the Vicon system (250 Hz) and two force platforms (1,000 Hz). The results obtained in this study revealed that: (1) Peak angular velocity of bar and upper trunk for the long barbell shaft condition was higher than the heavy barbell shaft condition; (2) For higher MOI, the trunk-twist torque was higher; and (3) Even when the barbell shaft had equal MOI, the heavy bar showed higher trunk-twist torque prior to the bar rotation