• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• The Mathematical Education
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• v.48 no.1
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• pp.81-91
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• 2009

This paper focuses on two problems in the 10th grade mathematics, the rational zero theorem and the content(the integer divisor) of a polynomial Among 138 students participated in the problem solving, 58 of them (42 %) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 %) consider the rational zero theorem is a mathematical fake(false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggests that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic(or primitive) polynomial as ail answer.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.41-49
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• 2009

Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

• Journal of Korea Foundry Society
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• v.25 no.5
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• pp.209-215
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• 2005

The design of the Metal mold casting should consider several variables such as the material properties and shape of the mold. In particular, the thermal stress generated by the thermal expansion and contraction depending on the thermal gradient of the mold causes partial plastic deformation on the mold, which causes damage or fracture of the cast. Consequently, the thermal deformation along with thermal stress leads to thermal deformation of the cast itself. In this study, the temperature analysis of the cast and mold is simulated by FDM to control the thermal deformation and stress as a result of the thermal gradient of mold. Using the results from FDM simulation, the thermal deformation and stress are analyzed by FEM and, the optimal mold design with minimum thermal deformation of the cast is suggested.

• Journal of Korea Foundry Society
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• v.26 no.4
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• pp.174-179
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• 2006

This study aims to investigate the microstructures and mechanical properties of DCI manufactured by sand and metal mold casting. To prohibit the formation of the chill, carbon, silicon and rare earth($0{\sim}0.2\;wt%$) were controlled and temperature of metal mold was constantly kept at $160^{\circ}C$. The sizes, counts and nodularity ratios of nodules were analyzed by image analysis device. Wear test using pin-on-disc wear tester was carried out under the conditions of load 47.2N, velocity 0.4 m/s and distance 2000 m. Tensile test using Instron type testing machine was performed with velocity of 0.1 mm/min according to the KS B 0802. The formation of the chill was not observed when percentage of the carbon and silicon were 3.8 and 2.5. Mechanical properties of GCD manufactured by metal mold were better than sand casting.

• Applied Chemistry for Engineering
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• v.30 no.3
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• pp.324-330
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• 2019

Petal-like nickel cobaltite ($NiCo_2O_4$)/reduced graphene oxide (rGO) composites with different $rGO-to-NiCo_2O_4$ weight ratios were synthesized using a simple hydrothermal method and subsequent thermal treatment. In the $NiCo_2O_4/rGO$ composite, the $NiCo_2O_4$ 3-dimensional nanomaterials contributed to the improvement of electrochemical properties of the final composite material by preventing the restacking of the rGO sheet and securing ion movement passages. The composite structure was examined by field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), and Fourier-transform infrared (FT-IR) spectroscopy. The FE-SEM and TEM images showed that petal-like $NiCo_2O_4$ was supported on the rGO surface. Cyclic voltammetry (CV), galvanostatic charge-discharge (GCD), and electrochemical impedance spectroscopy (EIS) were used for the electrochemical analysis of composites. Among the prepared composites, $0.075g\;rGO/NiCo_2O_4$ composite showed the highest specific capacitance of $1,755Fg^{-1}$ at a current density of $2Ag^{-1}$. The cycle performance and rate capability of the composite material were higher than those of using the single $NiCo_2O_4$ material. These nano-structured composites could be regarded as valuable electrode materials for supercapacitors that require superior performance.

• Advances in Energy Research
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• v.8 no.1
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• pp.41-57
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• 2022

Electrochemical double-layer capacitors (EDLCs) based on solid polymer electrolytes (SPEs) have gained an immense recognition in the present world due to their unique properties. This study is about preparing and characterizing EDLCs using a natural rubber (NR) based SPE with natural graphite (NG) electrodes. NR electrolyte was consisted with 49% methyl grafted natural rubber (MG49) and zinc trifluoromethanesulfonate ((Zn(CF₃SO₃)₂-ZnTF). It was characterized using electrochemical impedance spectroscopy (EIS) test, dc polarization test and linear sweep voltammetry (LSV) test. NG electrodes were made using a slurry of NG and acetone. EIS test, cyclic voltammetry (CV) test and galvanostatic charge discharge (GCD) test have been done to characterize the EDLC. Optimized electrolyte composition with NR: 0.6 ZnTF (weight basis) exhibited a conductivity of 0.6 x 10^-4 Scm^-1 at room temperature. Conductivity was predominantly due to ions. The electrochemical stability window was found to be from 0.25 V to 2.500 V. Electrolyte was sandwiched between two identical NG electrodes to fabricate an EDLC. Single electrode specific capacitance was about 2.26 Fg^-1 whereas the single electrode discharge capacitance was about 1.17 Fg^-1. The EDLC with this novel NR-ZnTF based SPE evidences its suitability to be used for different applications with further improvement.

• Journal of Sensor Science and Technology
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• v.8 no.1
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• pp.69-79
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• 1999

The research and implementation was preformed on high-resolution CCTV camera with CCD exclusive DSP conventional analog signal processor CCTV camera has its limit on auto exposure(AE), auto white balance(AWB), back light compensation(BLC) processing, severe distortion and noise of image, manual control parameter setting, etc. In our study, to resolve the problems in conventional CCTV camera, we made it possible to control AE, AWB, BLC automatically by the use of the DSP, which are used exclusively in the CCD camera produced domestically, and the microcontroller. And we utilized the function of screen display of microcontroller for the user-friendly interface to control CCD camera. And the electronic variable resister(EVR) was used to avoid setting parameters manually in the level of manufacturing process. As the result, It became possible to control parameters of the camera by program. And the cost-down effect was accomplished by improving the reliability of parameter values and reducing the efforts in setting parameters.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.7A
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• pp.547-556
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• 2003

This paper proposes a novel arithmetic unit over GF(2$^{m}$ ) for low-area elliptic curve cryptographic processor. The proposed arithmetic unit, which is linear feed back shift register (LFSR) architecture, is designed by using hardware sharing between the binary GCD algorithm and the most significant bit (MSB)-first multiplication scheme, and it can perform both division and multiplication in GF(2$^{m}$ ). In other word, the proposed architecture produce division results at a rate of one per 2m-1 clock cycles in division mode and multiplication results at a rate of one per m clock cycles in multiplication mode. Analysis shows that the computational delay time of the proposed architecture, for division, is less than previously proposed dividers with reduced transistor counts. In addition, since the proposed arithmetic unit does not restrict the choice of irreducible polynomials and has regularity and modularity, it provides a high flexibility and scalability with respect to the field size m. Therefore, the proposed novel architecture can be used for both division and multiplication circuit of elliptic curve cryptographic processor. Specially, it is well suited to low-area applications such as smart cards and hand held devices.

• The Journal of the Korea institute of electronic communication sciences
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• v.5 no.1
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• pp.66-73
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• 2010

The curriculum of programming education including algorithm has been recognized as a very important subject to many students majoring in natural sciences and engineering including electronic engineering and computer related departments. However, many students have had difficulties with it due to its characteristics; as a consequence, they have been in trouble taking upper-level subjects. Flow chart is a diagram that expresses logical stages necessary to solve certain problems and has been widely used to have an understanding of the flow of algorithm. The practice-oriented education of algorithm and programming would be very important to assist the understanding of operation processes. Furthermore, it has been desperately required to the necessity of auxiliary programs that could enhance an understanding of the concept of algorithm and program execution process. This study was aimed to design and embody the learning system of programming languages using basic algorithms so as for students to easily learn basic algorithm among the entire programming curriculum.