Search

Inspired by a Japanese sangaku problem, we examine six equal circles problems from a view point of sphere packing theory. The original problem was to find the size of the rectangular tablet within which nonoverlapping six circles of the same radius are arranged in a particularly nice configuration. Knowing its solution for the rectangle size, we formulate an optimization problem to ask conversely if we can reconfigure the six circles to maximize the area that they cover within the rectangle. This optimization problem is to maximize a quadratic convex function subject to nonconvex constraints. An attempt to find locally optimal solutions for the optimization problems has numerically demonstrated that the original sangaku configuration is indeed a local optimum and that there is another local optimum which covers a larger area. We formulate a new optimal control problem based on sangaku problem. [ABSTRACT FROM AUTHOR]

A semi-coloring is a fractional-type edge coloring of graphs. Daniely and Linial (J Graph Theory 69:426-440, ) conjectured that every graph has a semi-coloring. In this paper, we give an affirmative answer to this conjecture by considering a $$2$$ -factor in almost regular graphs. [ABSTRACT FROM AUTHOR]

With application to the impulse radio communications in mind, a time-limited and zero-mean pulse which is orthogonal to its shifts by integers is sought among the exponential splines having the knot interval 12. For the existence of real or complex-valued pulses, a necessary and sufficient condition is given in terms of the parameters of the dynamical system that shapes the exponential splines. The one for the existence of real-valued pulses is left as an open problem. Nonetheless, a real-valued example pulse is obtained that complies with the regulation imposed by the US Federal Communications Commission. This pulse will potentially enable an impulse radio communications system as fast as 6 giga pulses per second. [ABSTRACT FROM AUTHOR]

With application to the impulse radio communications in mind, a time-limited and zero-mean pulse which is orthogonal to its shifts by integers is sought among the exponential splines having the knot interval ½. For 2 the existence of real or complex-valued pulses, a necessary and sufficient condition is given in terms of the parameters of the dynamical system that shapes the exponential splines. The one for the existence of real-valued pulses is left as an open problem. Nonetheless, a real-valued example pulse is obtained that complies with the regulation imposed by the US Federal Communications Commission. This pulse will potentially enable an impulse radio communications system as fast as 6 giga pulses per second. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors proposed a design method for representing the window function by the C-spline function, which is a linear combination of the B- spline functions. By using that design method, a window function is obtained which has the same mainlobe bandwidth and the highest sidelobe level as the Hanning window or Blackman window, but a faster sidelobe fall-off. However, the design method for the new window function is not practical due to the fact that the description of the design specification is premature and the optimal dimension is not specified. This paper aims at the realization of a practical design method by improving those points. A design method is proposed in which the specification for the high-frequency range is given in terms of the sidelobe fall-off, and the specification for the low-frequency range is given in terms of the desired frequency characteristics in the logarithmic scale, together with the tolerable approximation error, represented by the mean-square error. The optimal dimension is determined, in the iterative approximation increasing the dimension to reduce the error in regard to the desired frequency characteristics, as the minimum dimension that reduces the err- or to the tolerable value. The usefulness of the proposed design method is demonstrated by a design example for the window function, which has a better characteristic than those of Kaiser-Bessel, Gauss and Hanning windows. [ABSTRACT FROM AUTHOR]

If the signal space matched to the representation is selected according to the properties of the signal to be handled, the signal processing can be made efficient. this paper is a step toward the structuralization of the signal spaces for systematic selection of the signal space. As a particular problem, the relation is analyzed between the signal spaces composed of spline functions, which have the feature that the smoothness as the continuous differentiability varies according to the degree, and the band-limited signal spaces, which is fundamental in the signal processing. As a result of analysis, it. is shown that the signal spaces composed of spline functions agree with the band-limited signal spaces in the limit of infinite order. This implies that the signal spaces composed of spline functions and the band-limited signal spaces can be structured as a sequence with the degree as the parameter. The result in this paper provides a view that the continuous differentiability can be used as an index in the systematic selection of the signal spaces. [ABSTRACT FROM AUTHOR]

The spline interpolation using the sampling bases has a feature of real-time computation which is not observed in other methods since the result of interpolation is derived directly from the sampled value sequence. Then it is necessary that the sampling function should be truncated in a finite interval. This paper aims to clarify the relation in this method between the error in the result of interpolation due to the truncation and the length of the truncation interval. The result is summarizes in a correspondence table for the truncation interval length and the error. In the proposed interpolation method, the truncation interval length to ensure the given tolerable range of error can be determined using the correspondence table. [ABSTRACT FROM AUTHOR]

The signal space composed of spline functions, which are smooth piecewise polynomials and almost free from oscillation, has attracted attention in the problems of interpolation and signal approximation. To make full use of such a signal space, there must be available a clear description of its properties. As a general approach to this problem, it is effective to derive the sampling basis in the signal space. Previously, the authors discussed the signal space composed of spline functions, and derived the sampling basis for the case where the degree is restricted to two. This paper extends the result to the arbitrary degree. Examples of sampling bases are shown for the practical cases of the second and the third degrees. The sampling basis derived in this paper provides the basic characterization of the signal space composed of spline functions of arbitrary degree. [ABSTRACT FROM AUTHOR]

In our previous paper, it was shown that the rectangular, triangular and Parzen windows can be generalized as a 6-spline function according to its order. That series of window functions has a merit in that a fast fall-off of the sidelobe is realized by increasing the parameter, I.e., the order, while it has a demerit in that the bandwidth of the nainlobe is increased. This paper aims at the improvement of this point, and proposes a design method whereby the window function is represented by a linear combination of Bespline functions. As an example of the window function obtained by the proposed method, a window function is presented which has the same mainlobe bandwidth and highest sidelobe level as Hanning or Blackman window, and still has a faster fall-off. Almost the same quality of approximation as the Hanning or Blackman window is also demonstrated, [ABSTRACT FROM AUTHOR]

Identification and classification of voltage and current disturbances in power systems are important tasks in the monitoring and protection of power system. Most power quality disturbances are non-stationary and transitory and the detection and classification have proved to be very demanding. The concept of discrete wavelet transform for feature extraction of power disturbance signal combined with artificial neural network and fuzzy logic incorporated as a powerful tool for detecting and classifying power quality problems. This paper employes a different type of univariate randomly optimized neural network combined with discrete wavelet transform and fuzzy logic to have a better power quality disturbance classification accuracy. The disturbances of interest include sag, swell, transient, fluctuation, and interruption. The system is modeled using VHSIC Hardware Description Language (VHDL), a hardware description language, followed by extensive testing and simulation to verify the functionality of the system that allows efficient hardware implementation of the same. This proposed method classifies, and achieves 98.19% classification accuracy for the application of this system on software-generated signals and utility sampled disturbance events. [ABSTRACT FROM AUTHOR]

A tabletop system can facilitate multi-user collaboration in a variety of settings, including small meetings, group work, and education and training exercises. The ability to identify the users touching the table and their positions can promote collaborative work among participants, so methods have been studied that involve attaching sensors to the table, chairs, or to the users themselves. An effective method of recognizing user actions without placing a burden on the user would be some type of visual process, so the development of a method that processes multi-touch gestures by visual means is desired. This paper describes the development of a multi-touch tabletop system using infrared image recognition for user position identification and presents the results of touch-gesture recognition experiments and a system-usability evaluation. Using an inexpensive FTIR touch panel and infrared light, this system picks up the touch areas and the shadow area of the user’s hand by an infrared camera to establish an association between the hand and table touch points and estimate the position of the user touching the table. The multi-touch gestures prepared for this system include an operation to change the direction of an object to face the user and a copy operation in which two users generate duplicates of an object. The system-usability evaluation revealed that prior learning was easy and that system operations could be easily performed. [ABSTRACT FROM AUTHOR]