• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.211-225
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• 2014

A new class of smoothing functions is introduced in this paper, which includes some important smoothing complementarity functions as its special cases. Based on this new smoothing function, we proposed a smoothing Newton method. Our algorithm needs only to solve one linear system of equations. Without requiring the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Numerical results indicate that the smoothing Newton method based on the new proposed class of smoothing functions with ${\theta}{\in}(0,1)$ seems to have better numerical performance than those based on some other important smoothing functions, which also demonstrate that our algorithm is promising.

• 호남수학학술지
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• 제35권3호
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• pp.351-372
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• 2013

In this paper, we study a distinction the two generating functions : ${\varphi}^k(q)=\sum_{n=0}^{\infty}r_k(n)q^n$ and ${\varphi}^{*,k}(q)={\varphi}^k(q)-{\varphi}^k(q^2)$ ($k$ = 2, 4, 6, 8, 10, 12, 16), where $r_k(n)$ is the number of representations of $n$ as the sum of $k$ squares. We also obtain some congruences of representation numbers and divisor function.

• 대한수학회보
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• 제49권4호
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• pp.693-704
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• 2012

We consider Weierstrass functions and divisor functions arising from $q$-series. Using these we can obtain new identities for divisor functions. Farkas [3] provided a relation between the sums of divisors satisfying congruence conditions and the sums of numbers of divisors satisfying congruence conditions. In the proof he took logarithmic derivative to theta functions and used the heat equation. In this note, however, we obtain a similar result by differentiating further. For any $n{\geq}1$, we have $$k{\cdot}{\tau}_{2;k,l}(n)=2n{\cdot}E_{\frac{k-l}{2}}(n;k)+l{\cdot}{\tau}_{1;k,l}(n)+2k{\cdot}{\sum_{j=1}^{n-1}}E_{\frac{k-1}{2}(j;k){\tau}_{1;k,l}(n-j)$$. Finally, we shall give a table for $E_1(N;3)$, ${\sigma}(N)$, ${\tau}_{1;3,1}(N)$ and ${\tau}_{2;3,1}(N)$ ($1{\leq}N{\leq}50$) and state simulation results for them.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.67-70
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• 1998

Let ${\eta}(\tau)=q^{1/24}\prod_{n=1}^{\infty}(1-q^n)$, where $q=e^{2{\pi}i{\tau}}$ and ${\tau}{\in}\mathbb{C}$. Then the transformation $$g(\tau)={\rho}\frac{\{\eta(\frac{\tau+1}{2})\eta(\frac{\tau+2}{2})\}^{16}}{\eta(\tau)^{24}}({\bar{{\rho}}{\eta}}(\frac{\tau+1}{2})^8+{\eta}(\frac{\tau+2}{2})^8)^2$$ is holomorphic for Im ${\tau}$ > 0, and has the property $$g(\tau+1)=g(\tau),\;g(-\frac{1}{\tau})={\tau}^{12}g(\tau)$$. (Theorem)

• 한국주조공학회지
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• 제15권4호
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• pp.408-415
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• 1995

Polycrystalline Al-Cu ribbons were produced by planar flow casting(PFC). Solidification behavior and microstructual changes of the ribbons have been investigated as a function of ribbon thickness and processing parameters. The solidification front velocity, V varies within the ribbon, decreasing with increasing the distance, S from the wheel-contact surface, as $V=17.6S^{-1}$. In Al-4.5wt%Cu alloy, rapid decrease in solidification velocity toward the free surface causes a change in solidification morphology from planar to cellular, and finally, to dendritic. The length and inclination of columnar grains solidified with planar front were related to the wheel velocity. The transition from particulate degenerate eutectic structure to regular lamellar eutectic structure was observed to be caused by a difference of the relative growth velocites of ${\alpha}-Al$ and ${\theta}$ during solidification in the Al-Cu eutectic alloy.

• 한국전기전자재료학회논문지
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• 제15권7호
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• pp.591-596
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• 2002

In this work, epitaxial GaN is grown on sapphire substrate in AlGaN/GaN heterostructures. Deliberate oxygen doping of GaN grown by MOVPE has been studied. The electron concentration increased as a function of the square root of the oxygen partial Pressure. Oxygen is a shallow donor with a thermal ionization energy of $27\pm2 meV$ measured by temperature dependent Hall effects. A compensation ratio of $\theta$=0.3~0.4 was determined from Hall effect measurements. The formation energy of $O_N$ of $E^F$ =1.3eV determined from the experimental data, is lower than the theoretically predicted vague.

• 한국전기전자재료학회논문지
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• 제15권8호
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• pp.671-677
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• 2002

In this study, the high frequency SMD ceramic resonators with the size of $3.7{\times}3.1{\times}0.385\textrm{mm}^3$ were fabricated using $Pb_{0.88}(La_{0.6}Nd_{0.4})_{0.08}(Mn_{1/3}Sb_{2/3})_{0.02}Ti_{0.98}O_3$ ceramics with the variations of electrode radius size. With increasing the electrode radius size, resonant resistance in third overtone mode was decreased and electromechanical coupling factor($k_{t3}$) in third overtone mode was showed constant values. Taking into consideration mechanical quality factor($Qm_{t3}$) of 5,552 and dynamic range(D.R) of 60.72dB in third overtone mode, the ceramic resonator with the electrode radius size of $\theta$1.13mm was suitable for 20MHz resonator application.

• 전자공학회논문지C
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• 제34C권11호
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• pp.95-103
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• 1997

A robust center estimation tecnique of n-fold engineering parts is presented, which use self-organizing neural networks with generating and merging learning for training neural units. To estimate the center of the n-fold engineering parts using neural networks, the segmented boundaries of the interested part are approximated to strainght lines, and the temporal estimated centers by thecosine theorem which formed between the approximaged straight line and the reference point, , are indexed as (.sigma.-.theta.) parameteric vecstors. Then the entries of parametric vectors are fed into self-organizing nerual network. Finally, the center of the n-fold part is extracted by mean of generating and merging learning of the neurons. To accelerate the learning process, neural network uses an adaptive learning rate function to the merging process and a self-adjusting activation to generating process. Simulation results show that the centers of n-fold engineering parts are effectively estimated by proposed technique, though not knowing the error distribution of estimated centers and having less information of boundaries.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2003년도 추계학술대회
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• pp.283-288
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• 2003

The object of this study is to investigate a fracture characteristics of static tensile test as a function of acoustic emission according to the fiber orientation $\theta=0^{\circ}C$ in carbon/epoxy composites, CFRP. On tensile loading, it was recognized that the fracture characteristics of CFRP in a unidirectional composites. Using the results of the AE analysis(a=2mm), it was found that the amplitude distributions of AE signals corresponding the matrix cracking, fiber debonding or delamination, and fiber breaking are 55~70dB(<200sec), 100dB(200~600sec), and 80dB(>600sec).

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.492-496
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• 1987

The testing philosophy and control schemes are investigated and applied to construct the Automatic Microwave Leakage Inspection System (AMLIS) . AMLIS is consists of three major parts such as Material Handling Mechanism, Fine Positioning Mechanism and Scanning Mechanism. The material Handling unit is designed to perform loading and unloading microwave oven onto the testing point by pneumatic cylinder and vacuum pump. The Fine positioning part includes X-Y-.THETA. table and distance sensing equipment. The scanning part is composed of five SCARA robots, which traverse X-Y-Z catesian coordinates respectively. The leakage testing probes are placed at the end of this each robot then the path and speed are both controlled via microprocessors. A performance test of this system combined with electric parts and software is done and the basic major function of system are accomplished.