Yasunari Shidama

Integral of Measurable Function 1

Integral of Measurable Function1 In this paper we construct integral of measurable function.

Partial Differentiation on Normed Linear Spaces R n

Partial Differentiation on Normed Linear Spaces Rn Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].

Using a neural network to make operational forecasts of ionospheric variations and storms at Kokubunji, Japan

An operational model was developed for forecasting ionospheric variations and storms at Kokubunji (35⊙N, 139⊙E), 24 hours in advance, by using a neural network. The ionospheric critical frequency (foF2) shows periodic variabilities from days to the solar cycle length and also shows sporadic changes known as ionospheric storms caused by geomagnetic storms (of solar disturbance origin). The neural network was trained for the target parameter of foF2 at each local time and input parameters of solar flux, sunspot number, day of the year, Kindex at Kakioka. The training was conducted using the data obtained for the period from 1960 to 1984. The method was validated for the period from 1985 to 2003. The trained network can be used for daily forecasting ionospheric variations including storms using prompt daily reports of K-index, sunspot number, and solar flux values available on-line.

Improved moving properties of an omnidirectional vehicle using stepping motor

Many kinds of omnidirectional vehicles driven by DC motors have been proposed and developed for application in robotics systems, but they have various problems like stability or operability in practical use, and have to be controlled by feedback system. This paper describes the improved moving properties of an omnidirectional vehicle driven by a stepping motor. An omnidirectional vehicle, which can move in all directions without changing the body direction of the vehicle, has been developed. This omnidirectional vehicle is used as the base of a calligraphy robot which is able to write Chinese characters using a brush. The movement and the control of this vehicle are evaluated, and the fields where this vehicle can be used are examined. Experimental results show that the proposed device is useful in achieving the desired performance.

Integral of Real-Valued Measurable Function 1

Integral of Real-Valued Measurable Function1 Based on [16], authors formalized the integral of an extended real valued measurable function in [12] before. However, the integral argued in [12] cannot be applied to real-valued functions unconditionally. Therefore, in this article we have formalized the integral of a real-value function.

The Lebesgue Monotone Convergence Theorem

The Lebesgue Monotone Convergence Theorem In this article we prove the Monotone Convergence Theorem [16]. MML identifier: MESFUNC9, version: 7.8.10 4.100.1011

Integral of Complex-Valued Measurable Function

Integral of Complex-Valued Measurable Function In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered. MML identifier: MESFUN6C, version: 7.9.01 4.101.1015

Banach Algebra of Bounded Functionals

Banach Algebra of Bounded Functionals In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded functionals. MML identifier: C0SP1, version: 7.8.10 4.99.1005

Differentiable Functions into Real Normed Spaces

Differentiable Functions into Real Normed Spaces In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers In this article, we extended properties of sequences of real numbers to sequences of extended real numbers. We also introduced basic properties of the inferior limit, superior limit and convergence of sequences of extended real numbers.