• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.777-787
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• 2009

In this paper we investigate the upper bound on the Castelnuovo-Mumford regularity of a graded module with linear free presentation. Let M be a finitely generated graded module over a polynomial ring R with zero dimensional support. We prove that if M is generated by elements of degree $d{\geq}0$ with a linear free presentation $$\bigoplus^p{R}(-d-1)\longrightarrow^{\phi}\bigoplus^q{R}(-d){\longrightarrow}M{\longrightarrow}0$$, then the Castelnuovo-Mumford regularity of M is at most d+q-1. As an important application, we can prove vector bundle technique, which was used in [11], [13], [17] as a tool for obtaining several remarkable results.

• Journal of Electrical Engineering and Technology
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• v.9 no.3
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• pp.970-977
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• 2014

In this paper, the artificial neural network is used to predict the junction temperature of the IGBT power module, by measuring the temperature sensitive electrical parameters (TSEP) of the module. An experiment circuit is built to measure saturation voltage drop and collector current under different temperature. In order to solve the nonlinear problem of TSEP approach as a junction temperature evaluation method, a Back Propagation (BP) neural network prediction model is established by using the Matlab. With the advantages of non-contact, high sensitivity, and without package open, the proposed method is also potentially promising for on-line junction temperature measurement. The Matlab simulation results show that BP neural network gives a more accuracy results, compared with the method of polynomial fitting.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.267-280
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• 2022

Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bidirectional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro- and microscale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.399-406
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• 2009

In this study, Polynomial Radial Basis Function Neural Network(pRBFNN) based on Fuzzy Inference System is designed and its parameters such as learning rate, momentum coefficient, and distributed weight (width of RBF) are optimized by means of Particle Swarm Optimization. The proposed model can be expressed as three functional module that consists of condition part, conclusion part, and inference part in the viewpoint of fuzzy rule formed in 'If-then'. In the condition part of pRBFNN as a fuzzy rule, input space is partitioned by defining kernel functions (RBFs). Here, the structure of kernel functions, namely, RBF is generated from HCM clustering algorithm. We use Gaussian type and Inverse multiquadratic type as a RBF. Besides these types of RBF, Conic RBF is also proposed and used as a kernel function. Also, in order to reflect the characteristic of dataset when partitioning input space, we consider the width of RBF defined by standard deviation of dataset. In the conclusion part, the connection weights of pRBFNN are represented as a polynomial which is the extended structure of the general RBF neural network with constant as a connection weights. Finally, the output of model is decided by the fuzzy inference of the inference part of pRBFNN. In order to evaluate the proposed model, nonlinear function with 2 inputs, waster water dataset and gas furnace time series dataset are used and the results of pRBFNN are compared with some previous models. Approximation as well as generalization abilities are discussed with these results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.5
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• pp.744-752
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• 2012

In this study, the Polynomial-based Radial Basis Function Neural Networks is proposed as an one of the recognition part of overall face recognition system that consists of two parts such as the preprocessing part and recognition part. The design methodology and procedure of the proposed pRBFNNs are presented to obtain the solution to high-dimensional pattern recognition problems. In data preprocessing part, Principal Component Analysis(PCA) which is generally used in face recognition, which is useful to express some classes using reduction, since it is effective to maintain the rate of recognition and to reduce the amount of data at the same time. However, because of there of the whole face image, it can not guarantee the detection rate about the change of viewpoint and whole image. Thus, to compensate for the defects, Linear Discriminant Analysis(LDA) is used to enhance the separation of different classes. In this paper, we combine the PCA&LDA algorithm and design the optimized pRBFNNs for recognition module. The proposed pRBFNNs architecture consists of three functional modules such as the condition part, the conclusion part, and the inference part as fuzzy rules formed in 'If-then' format. In the condition part of fuzzy rules, input space is partitioned with Fuzzy C-Means clustering. In the conclusion part of rules, the connection weight of pRBFNNs is represented as two kinds of polynomials such as constant, and linear. The coefficients of connection weight identified with back-propagation using gradient descent method. The output of the pRBFNNs model is obtained by fuzzy inference method in the inference part of fuzzy rules. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient) of the networks are optimized by means of Differential Evolution. The proposed pRBFNNs are applied to face image(ex Yale, AT&T) datasets and then demonstrated from the viewpoint of the output performance and recognition rate.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.5
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• pp.676-682
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• 2014

In this paper, precipitation echo(PRE) and non-precipitaion echo(N-PRE)(including ground echo and clear echo) through weather radar data are identified with the aid of neuro-fuzzy algorithm. The accuracy of the radar information is lowered because meteorological radar data is mixed with the PRE and N-PRE. So this problem is resolved by using RBFNN and judgement module. Structure expression of weather radar data are analyzed in order to classify PRE and N-PRE. Input variables such as Standard deviation of reflectivity(SDZ), Vertical gradient of reflectivity(VGZ), Spin change(SPN), Frequency(FR), cumulation reflectivity during 1 hour(1hDZ), and cumulation reflectivity during 2 hour(2hDZ) are made by using weather radar data and then each characteristic of input variable is analyzed. Input data is built up from the selected input variables among these input variables, which have a critical effect on the classification between PRE and N-PRE. Echo judgment module is developed to do echo classification between PRE and N-PRE by using testing dataset. Polynomial-based radial basis function neural networks(RBFNNs) are used as neuro-fuzzy algorithm, and the proposed neuro-fuzzy echo pattern classifier is designed by combining RBFNN with echo judgement module. Finally, the results of the proposed classifier are compared with both CZ and DZ, as well as QC data, and analyzed from the view point of output performance.

• The Journal of the Korea institute of electronic communication sciences
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• v.14 no.1
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• pp.69-80
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• 2019

This paper proposes a multimodal sensor platform which supports plug and play (PnP) technology. PnP technology automatically recognizes a connected sensor module and an application program easily controls a sensor. To verify a multimodal platform for PnP technology, we build up a firmware and have the experiment on a sensor system. When a sensor module is connected to the platform, a firmware recognizes the sensor module and reads sensor data. As a result, it provides PnP technology to simply plug sensors without any software configuration. Measured sensor raw data suffer from various distortions such as gain, offset, and non-linearity errors. Therefore, we introduce a polynomial calculation to compensate for sensor distortions. To find the optimal coefficients for sensor calibration, we apply a genetic algorithm which reduces the calibration time. It achieves reasonable performance using only a few data points with reducing 97% error in the worst case. The platform supports various protocols for multimodal sensors, i.e., UART, I2C, I2S, SPI, and GPIO.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.519-530
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• 2014

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. For an integer s > -1, we say that M is Cohen-Macaulay in dimension > s if every system of parameters of M is an M-sequence in dimension > s introduced by Brodmann-Nhan [1]. In this paper, we give some characterizations for Cohen-Macaulay modules in dimension > s in terms of the Noetherian dimension of the local cohomology modules $H^i_m(M)$, the polynomial type of M introduced by Cuong [5] and the multiplicity e($\underline{x}$;M) of M with respect to a system of parameters $\underline{x}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1851-1861
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• 2014

We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.