• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.129-164
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• 2023

The aim of this work is to present some interesting results on weighted ergodic functions and prove the existence and uniqueness of Stepanov-like pseudo almost automorphic solutions using the spectral decomposition of the phase space developed by Adimy and co-authors. We also give the next challenge of this work.

• Korean Journal of Acupuncture
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• v.30 no.4
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• pp.305-318
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• 2013

Objectives : The aim of this study was to examine the effect of electroacupuncture(EA) at an acupoint, HT8(Sobu), on normal humans by using power spectral analysis. We examined the effect on the Heart Rate Variability(HRV), and the balance of the autonomic nervous system. Methods : Thirty-two healthy volunteers participated in this study. EEG(Electroencephalogram) power spectrum exhibits site-specific and state-related differences in specific frequency bands. A thirty-two channel EEG study was carried out on thirty-two subjects(14 males; mean age=23.5 years old, 18 females; mean age=21.5 years old). HRV and EEG were simultaneously recorded before and after acupuncture. Results : In the ${\alpha}$(alpha) band, during the HT8-acupoint treatment, the power values in the ${\alpha}$(alpha) band significantly decreased(p<0.05) at 28 channels. In the ${\beta}$(beta) band significantly decreased(p<0.05) at 26 channels. In ${\delta}$(delta) band significantly decreased(p<0.05) at 18 channels. In ${\theta}$(theta) band significantly decreased(p<0.05) at 20 channels. ${\alpha}/{\beta}$ values were increased at 6 channels and decreased at 10 channels.${\beta}/{\theta}$ values were increased at 10 channels and decreased at 19 channels. Mean-RR(RR-interval), Complexity, RMSSD(Root mean square of successive differences), SDSD(Standard deviations differences between adjacent normal R-R intervals), norm HF showed a significantly increased and mean-HRV, norm LF, LHR(LF/HF Ratio) showed a significantly decreased after HT8-acupoint treatment(p<0.05). Conclusions : These results suggest that EA at the HT8 mostly causes significant changes on alpha(28 channels), beta(26 channels), delta(18 channels), theta(20 channels) bands and mean-HRV, mean-RR, complexity, RMSSD, SDSD, norm LF, norm HF and LHR. If practicing EA at the HT8, it will regulate the function of the cerebral cortex, decrease activity of the sympathetic and increase parasympathetic nervous activity.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• Korean Journal of Remote Sensing
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• v.33 no.5_1
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• pp.455-467
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• 2017

When performing target detection using hyperspectral imagery, a feature extraction process is necessary to solve the problem of redundancy of adjacent spectral bands and the problem of a large amount of calculation due to high dimensional data. This study proposes a new band selection method using the $L_{2,1}$-norm regression model to apply the feature selection technique in the machine learning field to the hyperspectral band selection. In order to analyze the performance of the proposed band selection technique, we collected the hyperspectral imagery and these were used to analyze the performance of target detection with band selection. The Adaptive Cosine Estimator (ACE) detection performance is maintained or improved when the number of bands is reduced from 164 to about 30 to 40 bands in the 350 nm to 2500 nm wavelength band. Experimental results show that the proposed band selection technique extracts bands that are effective for detection in hyperspectral images and can reduce the size of the data without reducing the performance, which can help improve the processing speed of real-time target detection system in the future.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1041-1041
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• 2001

Removal of variability in spectra data before the application of chemometric modeling will generally result in simpler (and presumably more robust) models. Particularly for sparsely sampled data, such as typically encountered in diode array instruments, the use of Savitzky-Golay (S-G) derivatives offers an effective method to remove effects of shifting baselines and sloping or curving apparent baselines often observed with scattering samples. The application of these convolution functions is equivalent to fitting a selected polynomial to a number of points in the spectrum, usually 5 to 25 points. The value of the polynomial evaluated at its mid-point, or its derivative, is taken as the (smoothed) spectrum or its derivative at the mid-point of the wavelength window. The process is continued for successive windows along the spectrum. The original paper, published in 1964 [1] presented these convolution functions as integers to be used as multipliers for the spectral values at equal intervals in the window, with a normalization integer to divide the sum of the products, to determine the result for each point. Steinier et al. [2] published corrections to errors in the original presentation [1], and a vector formulation for obtaining the coefficients. The actual selection of the degree of polynomial and number of points in the window determines whether closely situated bands and shoulders are resolved in the derivatives. Furthermore, the actual noise reduction in the derivatives may be estimated from the square root of the sums of the coefficients, divided by the NORM value. A simple technique to evaluate the actual convolution factors employed in the calculation by the software will be presented. It has been found that some software packages do not properly account for the sampling interval of the spectral data (Equation Ⅶ in [1]). While this is not a problem in the construction and implementation of chemometric models, it may be noticed in comparing models at differing spectral resolutions. Also, the effects on parameters of PLS models of choosing various polynomials and numbers of points in the window will be presented.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.

• Korean Journal of Remote Sensing
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• v.36 no.5_2
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• pp.961-973
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• 2020

In this manuscript, a new pansharpening model based on Convolutional Neural Network (CNN) was developed. Dilated convolution, which is one of the representative convolution technologies in CNN, was applied to the model by making it deep and complex to improve the performance of the deep learning architecture. Based on the dilated convolution, the residual network is used to enhance the efficiency of training process. In addition, we consider the spatial correlation coefficient in the loss function with traditional L1 norm. We experimented with Dilated Residual Networks (DRNet), which is applied to the structure using only a panchromatic (PAN) image and using both a PAN and multispectral (MS) image. In the experiments using KOMPSAT-3A, DRNet using both a PAN and MS image tended to overfit the spectral characteristics, and DRNet using only a PAN image showed a spatial resolution improvement over existing CNN-based models.

• Current Optics and Photonics
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• v.5 no.3
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• pp.270-277
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• 2021

The adaptive sparse representation (ASR) can effectively combine the structure information of a sample dictionary and the sparsity of coding coefficients. This algorithm can effectively consider the correlation between training samples and convert between sparse representation-based classifier (SRC) and collaborative representation classification (CRC) under different training samples. Unlike SRC and CRC which use fixed norm constraints, ASR can adaptively adjust the constraints based on the correlation between different training samples, seeking a balance between l₁ and l₂ norm, greatly strengthening the robustness and adaptability of the classification algorithm. The correlation coefficients (CC) can better identify the pixels with strong correlation. Therefore, this article proposes a hyperspectral image classification method called correlation coefficients and adaptive sparse representation (CCASR), based on ASR and CC. This method is divided into three steps. In the first step, we determine the pixel to be measured and calculate the CC value between the pixel to be tested and various training samples. Then we represent the pixel using ASR and calculate the reconstruction error corresponding to each category. Finally, the target pixels are classified according to the reconstruction error and the CC value. In this article, a new hyperspectral image classification method is proposed by fusing CC and ASR. The method in this paper is verified through two sets of experimental data. In the hyperspectral image (Indian Pines), the overall accuracy of CCASR has reached 0.9596. In the hyperspectral images taken by HIS-300, the classification results show that the classification accuracy of the proposed method achieves 0.9354, which is better than other commonly used methods.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.213-218
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• 1991

A new model which contains the dynamics of the motor system and the kinematics of the timing belt system is derived for an inverted pendulum system in FAPA Lab. Generalized standard compensator configuration(SCC) which contains the variable design parameters Kl, K2, .., K5 is proposed so that any desired design specification can be achieved. The robust controller which has robust property against the influence of sensor noise, system parameter variation and model uncertainty is designed minimizing the H$_{\infty}$-norm of transfer function from exogenous input to controlled output. The method of solving the two Riccati equations in state space and determining the controller uses on iteration method where the unique stabilizing solution to two algebraic Riccati equation must be positive definite and the spectral radius of their product less than .gamma.$^{2}$. Some cases are derived by varying the design parameter for simulation on a digital computer and experimenting the H$_{\infty}$- controller on an analog computer. The design parameters of controller which satisfies the desired control specification is selected on the basis of the simulation result and experimenting. The reasonableness and validity of the simulation and the robustness of the controller is established.d.

• Journal of Biomedical Engineering Research
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• v.39 no.3
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• pp.124-133
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• 2018

We tried to investigate the changes in cortical activities according to emotional valence states during watching video clips. We examined the neural basis of two emotional states (positive and negative) using spectral power analysis and brain functional connectivity analysis of cortical current density time-series reconstructed from high-density electroencephalograms (EEGs). Fifteen healthy participants viewed a series of thirty-two 2 min emotional video clips. Sixty-four channel EEGs were recorded. Distributed cortical sources were reconstructed using weighted minimum norm estimation. The temporal and spatial characteristics of spectral source powers showing significant differences between positive and negative emotion were examined. Also, correlations between gamma-band activities and affective valence ratings were determined. We observed the changes of cortical current density time-series according to emotional states modulated by video clip. Gamma-band activities showed significant difference between emotional states for thirty seconds at the middle and the latter half of the video clip, mainly in prefrontal area. It was also significantly anti-correlated with the self-ratings of emotional valence. In addition, the gamma-band activities in frontal and temporal areas were strongly phase-synchronized, more strongly for negative emotional states. Cortical activities in frontal and temporal areas showed high spectral power and inter-regional phase synchronization in gamma-band during negative emotional states. It is inferred that the higher amygdala activation induced by negative stimuli resulted in strong emotional effects and caused strong local and global synchronization of neural activities in gamma-band in frontal and temporal areas.