• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.467-480
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• 2009

In 1859, Bernhard Riemann, in his epoch-making memoir, extended the Euler zeta function $\zeta$(s) (s > 1; $s{\in}\mathbb{R}$) to the Riemann zeta function $\zeta$(s) ($\Re$(s) > 1; $s{\in}\mathbb{C}$) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function $\zeta$(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of $\zeta$(2k) ($k {\in}\mathbb{N}$); Approximate functional equations for $\zeta$(s); Series involving the Riemann zeta function.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1193-1202
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• 2020

We consider the integral ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$ as a function of the positive integer n. We show that there exists an asymptotic series in ${\frac{1}{n}}$ and compute the first terms of this series together with an explicit error bound.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.401-403
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• 2011

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.485-494
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• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.157.6-157
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• 2001

We estimated various neuron functions to construct of engineering neurons, which are the combination of sigmoid, linear, sine, quadric, double/single bended, soft max/minimum functions. These combinations are estimated by the property on the potential surface between the learning points, calculation speed, and learning convergence; because the surface depends on the inference ability of a neuron system; and speed and convergence are depend on the efficiency on the points of engineering applications. After the evaluating discussions, we can select more appropriate combination than original sigmoid function´s, which is single bended function and linear one. The combination ...

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.763-766
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• 2002

This paper proposes design of new linear bipolar OTAs composed of an hyperbolic function circuit and a triple-tail cell. Two types of the OTAs are presented; one employs a hyperbolic sine circuit and the other contains a hyperbolic cosine circuit. The linear input voltage ranges of the proposed OTAs are wider than that of the conventional triple-tail cell, though the power dissipation is smaller. The results of SPICE simulation show that satisfactory characteristics are obtained.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.473-478
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• 2003

To detect motions of bodies, we have discussed them with two viewpoints; one is a detection algorithm, and another is the hardware implementation. The former is to find small terms expansions for sine/cosine functions. We researched Maclaurin and optimum expansions, and moreover to reduce hardware amounts, revised the expansions. The expansions don't include divide calculations, and the error is within 0.01%. As for the former problem, there is another approach also; that is the cordic method. The method is based on the rotation of a vector on the complex plain. It is simple iterations and don't require large logic. We examined the precision and convergence of the method on C-simulations, and implemented on HDL. The later problem is to make FPGA within small gates. We considered approaches to eliminate a divider and to reduce the bit number of arithmetic. We researched Newton-Raphson's method to get reciprocal numbers. The higher-order expression shows rapid convergence and doesn't be affected by the initial guess. It is an excellent algorithm. Using them, we wish to design a detector, and are developing it on a FPGA.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7C
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• pp.724-729
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• 2009

Binary offset carrier (BOC) signal synchronization is based on the correlation between the received and locally generated BOC signals. Thus, the multiple side-peaks in BOC autocorrelation are one of the main error sources in synchronizing BOC signals. Recently, new correlation functions with no side-peak were proposed for sine and cosine phased BOC signal synchronization, respectively, by the authors [3]. In this paper, we propose a new correlation function with no side-peak for composite BOC (CBOC) signals by using the similar approach to that in the previous work.

• Journal of Broadcast Engineering
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• v.9 no.4 s.25
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• pp.384-390
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• 2004

In this paper we compare the performance of 4 different algorithms for converting the sampling frequency of an audio from 44.1KHz to 48KHz. The algorithms considered here include the basic polyphase method. sine function based method. multi-stage method. and B-spline based method. For a fair comparison, the sampling rate converters using the 4 algorithms are redesigned under a high fidelity condition. Then, their H/W complexities are compared in terms of the computational complexity and the memory size. As a result, it is shown that the basic polyphase method and sine function based method outperform the other two in terms of the computational complexity, while the B-spline based method requires less memory than the others.