• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.181-193
• /
• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.3
• /
• pp.133-137
• /
• 2008

We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.

• 한국해양학회지
• /
• v.14 no.1
• /
• pp.32-38
• /
• 1979

The original concept and theory of Shannon's function H=-$\Sigma$(i-1,n)Pi, log$\_$2/Pi and its applicable domains in ecology are discussed. The confusions exist in use and interpretation of this function are due to: 1. Mixing the idea of proper ecological diversity with that of Shannon's information theory. 2. Confusion of physical or thermodynamical systems with ecological systems. 3. Confusion of the system from which one had calculated function H with the system of which function H is interpreted. It's proposed to use function H for the comparison of community's structure and so, for the distinction of community's evolution (succession) steps.

• Korean Journal of Optics and Photonics
• /
• v.35 no.5
• /
• pp.210-217
• /
• 2024

We investigate the effects of mid-spatial frequency wavefront errors on the modulation transfer function (MTF) of optical imaging systems such as airborne cameras and astronomical telescopes. To reduce the prediction error of the MTF, an improved Shannon approximation is proposed. The Shannon approximation is useful for low-order wavefront errors, but it has limitations in predicting MTF with high-order wavefront errors, especially those caused by mid-spatial frequency errors from the manufacturing process of aspheric optical components. In this study, we analyze the impacts of concentric ring-shaped mid-spatial frequency wavefront errors on the MTF using MATLAB and Code V simulations and propose a method to improve the Shannon approximation, which has a new correction factor (K-factor).

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.513-520
• /
• 2022

The Jensen and Mercer inequalities are very important inequalities in information theory. The article provides the generalization of Mercer's inequality for convex functions on the line segments. This result contains Mercer's inequality as a particular case. Also, we investigate bounds for Shannon's entropy and give some new applications in zeta function and analysis.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.1
• /
• pp.59-68
• /
• 2017

The flower and woman are beautiful but Euler's theorem and the symmetry are the best. Shannon applied his theorem to information and communication based on Euler's theorem. His theorem is the root of wireless communication and information theory and the principle of today smart phone. Their meeting point is $e^{-SNR}$ of MIMO(multiple input and multiple output) multiple antenna diversity. In this paper, Euler, who discovered the most beautiful formula($e^{{\pi}i}+1=0$) in the world, briefly guided Shannon's formula ($C=Blog_2(1+{\frac{S}{N}})$) to discover the origin of wireless communication and information communication, and these two masters prove a meeting at the Shannon limit, It reveals something what this secret. And we find that it is symmetry and element-wise inverse are the hidden secret in algebraic coding theory and triangular function.

• Communications for Statistical Applications and Methods
• /
• v.16 no.5
• /
• pp.813-820
• /
• 2009

In this paper, we review the utility-based generalization of the Shannon entropy and Kullback-Leibler information measure as the U-entropy and the U-relative entropy that was introduced by Friedman et al. (2007). Then, we derive some relations between the U-relative entropy and other information measures based on a parametric family of utility functions.

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.379-385
• /
• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• Environmental Engineering Research
• /
• v.17 no.3
• /
• pp.167-174
• /
• 2012

In situ particle size spectra are obtained from two sequent cruises in order to evaluate the physical consequences of suspended particulate matters caused by episodic storm runoff from the Santa Ana River watershed, an urbanized coastal watershed. Suspended particles from various sources including surface runoff, near-bed resuspension, and phytoplankton are identified in empirical orthogonal function (EOF) analysis and an entropy-based parameterization (Shannon entropy). The first EOF mode is associated with high turbidity and fine particles as indicated by the elevated beam attenuation near the Santa Ana River and Newport Bay outlets, and the second EOF mode explains the suspended sediment dispersal and particle coarsening at the near-surface plume. Chlorophyll particles are also distinguished by negative magnitudes of the first EOF mode, which is supported by the relationship between fluorescence and beam attenuation. The integrated observation between the first EOF mode and the Shannon entropy index accentuates the characteristics of two different structures and/or sources of sediment particles; the near-surface plumes are originated from runoff water outflow, while the near-bottom particles are resuspended due to increased wave heights or mobilizing bottom turbidity currents. In a coastal pollution context, these methods may offer useful means of characterizing particle-associated pollutants for purposes of source tracking and environmental interpretation.

• Journal of IKEEE
• /
• v.3 no.2 s.5
• /
• pp.295-304
• /
• 1999

This paper presents a method of constructing the Multiple-Valued Logic Systems(MVLS) over Finite Fields(FF) using by Decision Diagram(DD) that is based on Graph Theory. The proposed method is as following. First, we derivate the Ordered Multiple-Valued Logic Decision Diagram(OMVLDD) based on the multiple-valued Shannon's expansion theorem and we execute function decomposition using by sub-graph. Next, we propose the variable selecting algorithm and simplification algorithm after apply the each isomorphism and reodering vertex. Also we propose MVLS design method.