• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1133-1143
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• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1697-1708
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• 2017

This paper proposes an algorithm for the differential protection of an Indirect Symmetrical Phase Shift Transformer (ISPST) by considering the different behaviors of the compensated differential current under internal fault and magnetizing inrush conditions. In this algorithm, a criterion function is defined which is based on the difference of amplitude of the wavelet transformation over a specific frequency band. The function has been used for the discrimination between three phase magnetizing inrush and internal fault condition and requires less than a quarter cycle after disturbance. This method is independent of any coefficient or threshold values of wavelet transformation. The merit of this algorithm is demonstrated by the simulation of different faults in series and excitation unit and magnetizing inrush with varying switching conditions on ISPST using PSCAD/EMTDC. Due to unavailability of in-field large interconnected transformers for such a large number of destructive tests, the results are further verified by Real Time Digital Simulator (RSCAD/RTDS). The proposed algorithm has been compared with the conventional harmonic restraint based method that justifies the application of wavelet transform for differential protection of ISPST. The proposed algorithm has also been verified for different rating of ISPSTs and satisfactory results were obtained.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.223-233
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• 2010

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.205-211
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• 2002

Unknown inputs observer(UIO) which is achieved by the coordinate transformation method has the differential of system outputs in the observer and the equation for unknown inputs estimation. Generally, the differential of system outputs in the observer can be eliminated by defining a new variable. But it brings about the partition of the observer into two subsystems and need of an additional differential of system outputs still remained to estimate the unknown inputs. Therefore, the block pulse function expansions and its differential operation which is a newly derived in this paper are presented to alleviate such problems from an algebraic form.

• Journal of the Korean Society of Safety
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• v.20 no.3 s.71
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• pp.27-33
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• 2005

The shape memory effect in Ti-50.4at.%Ni alloy after solution treatment at 1273K for 2h and aged at 350, 450, $550^{\circ}C$ for 0.5, 1, 1.5, 2, 4, 10hrs had been investigated by differential scanning calorimetry measurement. It was found that ageing in the temperature range of $350^{\circ}C{\sim}550^{\cric}C$ induced complex transformation behavior, involving the R-phase and multiple-stage martensitic transformation. Usually aged Ni-rich NiTi alloys undergo martensitic transformation on cooling from high temperatures in two step : Austenite to R-phase and then R-phase to Martensite (normal behavior). In sample aged at $350^{\circ}C$ two distinct DSC peaks arised giving evidence of intermediate stages of martensite transformation. This results in the nucleation and growth of coherent $Ni_4Ti_3$-precipitate. These explain all features of the evolution of DSC charts during ageing including the number of distinct DS peaks and their positions.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1845-1847
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• 1991

In general, it is not easy to find the linearizing coordinate transformation map for a class of systems which are state equivalent to linear systems, because it is required to solve a set of partial differential equations. It is possible to construct an arbitrary nonlinear function with a backpropagation(BP) net. Utilizing this property of BP neural net, we construct a desired linearizing coordinate transformation map. That is, we implement a unknown coordinate transformation map through the training of neural weights. We have shown an example which supports this idea.

• Journal of Navigation and Port Research
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• v.30 no.2
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• pp.167-172
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• 2006

In this paper, the issue of blind detection of Alamouti-type differential space-time (ST) ${\pi}/2$-shifted BPSK modulation in static Rayleigh fading channels is considered. We introduce a novel transformation to the received signal from each receiver antenna such that this binary ST modulation, which has a second-order transmit-diversity, is equivalent to QPSK modulation with second-order receive-diversity. The pre-detection combining of the result of transformation allows us to apply a low complexity detection technique specifically designed for receive-diversity, namely, scalar multiple-symbol differential detection (MSDD). With receiver complexity proportional to the observation window length, our receiver can achieve the performance 1.5dB better than that of conventional differential detection ST and 0.5dB worse than that qf a coherent maximum ratio combining receiver (with differential decoding) approximately.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.5
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• pp.323-329
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• 2002

This paper presents the application of the technique of differential transformation to the post-buckling problem of non-uniform cantilever column subjected to a combined load. Numerical calculations are carried out and compared with previously published results to validate the results of the present method. The results obtained by this method agree very well with those reported in the previous works. The results obtained by the present method are presented for both various non-uniform columns and loads.

• Journal of the Korean Chemical Society
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• v.15 no.5
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• pp.241-245
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• 1971

Endothermic peak of transformation of ${\gamma}-MnO_2$ was obviously shown by differential heating curve in the present study, and the transformation temperature was different from other modification. ${\gamma}-MnO_2$ carried out to analyze exclusively, by means of the half area method in corresponding endothermic peak of differential heating curve. ${\alpha}-\;and\;{$beta}-MnO_2$ (Pyrolusite) containing in sample about 75% is interfered about ${\pm}$10% of the relative error, and while those of below 50% is interfered about ${\pm}$5%.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.11
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• pp.1058-1063
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• 2010

The vibration analysis of a rotating cantilever beam with tip mass was studied by using DTM(differential transformation method). DTM is one of the numerical methods, for finding series solutions by transforming differential equations to algebraic ones similar with Laplace transform. The advantages of the DTM are that it is easy to understand and is effective in finding numerical solutions. Applying DTM, the natural frequencies of a rotating cantilever beam were obtained taking into consideration the effects of tip mass. Also, convergence study of DTM was performed to decide the number of terms used in eigenvalue problems. Numerical results obtained by DTM show good agreement with those by other methods. As a result, it is expected that DTM can be a useful method in vibration analysis such as that of a rotating cantilever beam with tip mass.