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Design of Serial-Parallel Multiplier for GF($2^n$) (GF($2^n$)에서의 직렬-병렬 곱셈기 구조)

  • 정석원;윤중철;이선옥
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.13 no.3
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    • pp.27-34
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    • 2003
  • Recently, an efficient hardware development for a cryptosystem is concerned. The efficiency of a multiplier for GF($2^n$)is directly related to the efficiency of some cryptosystem. This paper, considering the trade-off between time complexity andsize complexity, proposes a new multiplier architecture having n[n/2] AND gates and n([n/2]+1)- $$\Delta$_n$ = XOR gates, where $$\Delta$_n$=1 if n is even, $$\Delta$_n$=0 otherwise. This size complexity is less than that of existing ${multipliers}^{[5][12]}$which are $n^2$ AND gates and $n^2$-1 XOR gates. While a new multiplier is a serial-parallel multiplier to output a result of multiplication of two elements of GF($2^n$) after 2 clock cycles, the suggested multiplier is more suitable for some cryptographic device having space limitations.

Estimation of the Flash Point for n-Pentanol + n-Propanol and n-Pentanol + n-Heptanol Systems by Multiple Regression Analysis (다중회귀분석법을 이용한 n-Pentanol + n-Propanol계 및 n-Pentanol + n-Heptanol계의 인화점 예측)

  • Ha, Dong-Myeong;Lee, Sungjin
    • Fire Science and Engineering
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    • v.30 no.6
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    • pp.31-36
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    • 2016
  • The flash point is one of the most important properties for characterizing the fire and explosion hazard of liquid solutions. In this study, the flash points of two flammable binary mixtures, n-pentanol + n-propanol and n-pentanol + n-heptanol systems were measured using a Seta flash closed cup tester. The flash point was estimated using the methods based on Raoult's law and multiple regression analysis. The measured flash points were also compared with the predicted flash points. The absolute average errors (AAE) of the results calculated by Raout's law were $1.3^{\circ}C$ and $1.3^{\circ}C$ for the n-pentanol + n-propanol and n-pentanol + n-heptanol mixtures, respectively. The absolute average errors of the results calculated by multiple regression analysis were $0.4^{\circ}C$ and $0.3^{\circ}C$ for the n-pentanol + n-propanol and n-pentanol + n-heptanol mixtures, respectively. According to the AAE, the calculated values based on multiple regression analysis were better than those based on Raoult's law.

Hong Gil Ju(洪吉周)'s Algebra (홍길주(洪吉周)의 대수학(代數學))

  • Hong, Sung-Sa;Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.21 no.4
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    • pp.1-10
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    • 2008
  • In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

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Enhanced Mechanical Properties and Thermal Stability of CrAlN Coatings by Interlayer Deposition (중간층 증착에 의한 CrAlN 코팅의 기계적 물성 및 내열성 향상에 관한 연구)

  • Kim, Hoe-Geun;Ra, Jeong-Hyeon;Song, Myeon-Gyu;Lee, Sang-Yul
    • Proceedings of the Korean Institute of Surface Engineering Conference
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    • 2016.11a
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    • pp.100-100
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    • 2016
  • 물리기상증착방법 (Physical vapor deposition)에 의하여 합성된 천이금속 질화물 박막은 경도, 내마모성 등 절삭공구의 성능을 향상시키며, Ti-Al-N, Ti-Zr-N, Zr-Al-N, Cr-Si-N 등의 3원계 경질 박막에 대한 연구가 지속적으로 이루어지고 있다. 이중에서도 CrAlN 코팅은 높은 경도, 낮은 표면 조도 등의 우수한 기계적 특성 이외에 고온에서 안정한 합금상 형성으로 인하여 우수한 내열성을 보유하여 공구 코팅으로의 적용 가능성이 크다. 그러나 최근 공구사용 환경의 가혹화로 인하여 코팅의 내마모성 및 내열성 등의 물성 향상을 통한 공구의 수명 향상이 필요시 되고 있으며, 코팅에 적합한 중간층을 합성함으로써 공구 코팅으로의 적용 가능성을 높이는 연구들이 진행되고 있다. 본 연구에서는 CrAlN 코팅의 물성을 향상시키기 위해 CrAlN 코팅과 WC-Co 6wt.% 모재 사이에 CrN, CrZrN, CrN/CrZrSiN 등의 다양한 중간층을 합성하였으며, 중간층을 포함한 모든 코팅의 두께는 $3{\mu}m$ 로 제어하였다. 합성된 코팅의 미세조직, 경도 및 탄성계수, 내모성을 분석하기 위해 field emission scanning electron microscopy(FE-SEM), nano-indentation, ball-on-disk 마모시험기 및 ${\alpha}-step$을 사용하였다. 코팅의 내열성을 확인하기 위해 코팅을 furnace에 넣어 공기중에서 500, 600, 700, 800, 900, $1,000^{\circ}C$로 30분 동안 annealing 한 후에 nano-indentation을 사용하여 경도를 측정하였다. CrAlN 코팅을 나노 인덴테이션으로 분석한 결과, 모든 코팅의 경도(35.5-36.2 GPa)와 탄성계수(424.3-429.2 GPa)는 중간층의 종류에 상관없이 비슷한 값을 보인 것으로 확인됐다. 그러나, 코팅의 마찰계수는 중간층의 종류에 따라 다른 값을 보였으며, CrN/CrZrSiN 중간층을 증착한 CrAlN 코팅의 마찰계수는 0.34로 CrZrN 중간층을 증착한 CrAlN 코팅의 마찰계수(0.41)에 비해 낮은 값을 보였다. 또한, 코팅의 마모율 및 마모폭도 비슷한 경향을 보인 것으로 보아, CrN/CrZrSiN 중간층을 합성한 CrAlN 코팅의 내마모성이 상대적으로 우수한 것으로 판단된다. 이것은 중간층의 H/E ratio가 코팅의 내마모성에 미치는 영향에 의한 결과로 사료된다. H/E ratio는 파단시의 최대 탄성 변형율로써, 모재/중간층/코팅의 H/E ratio 구배에 따라 코팅 내의 응력의 완화 정도가 변하게 된다. WC 모재 (H/E=0.040)와 CrAlN 코팅(H/E=0.089) 사이에서 CrN, CrZrSiN 중간층의 H/E ratio 는 각각 0.076, 0.083 으로 모재/중간층/코팅의 H/E ratio 구배가 점차 증가함을 확인 할 수 있었고, 일정 응력이 지속적으로 가해지면서 진행되는 마모시험중에 CrN과 CrZrSiN 중간층이 WC와 CrAlN 코팅 사이에서 코팅 내부의 응력구배를 완화시키는 역할을 함으로써 CrAlN 코팅의 내마모성이 향상된 것으로 판단된다. 모든 코팅을 열처리 후 경도 분석결과, CrN/CrZrSiN 중간층을 증착한 CrAlN 코팅은 $1,000^{\circ}C$까지 약 28GPa의 높은 경도를 유지한 것으로 확인 되었고, 이는 CrZrSiN 중간층 내에 존재하는 $SiN_x$ 비정질상의 우수한 내산화성에 의한 결과로 판단된다.

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Effect of $NO_3-N$ : $NH_4-N$ Ratio in Nutrient Solution on Growth, Yield and Fruit Quality of Strawberry 'Akihime' in Hydroponic System (딸기 수경재배에서 $NO_3-N$$NH_4-N$의 비율이 '장희(章姬)'의 생육, 수량 및 과실의 품질에 미치는 영향)

  • Jun, Ha-Joon;Hwang, Jin-Gyu;Son, Mi-Ja;Yoon, Hae-Suk
    • Journal of Bio-Environment Control
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    • v.18 no.1
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    • pp.40-45
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    • 2009
  • The experiment has investigated the effects of growth, yield, fruit quality and cation absorption of strawberry 'Akihime' in different $NO_3-N:NH_4-N$ ratio in nutrient solution. $NO_3-N:NH_4-N$ ratios were 5.5:0, 4.0:1.5 and $3.0:2.5me{\cdot}L^{-1}$. As the ratio of $NH_4-N$ increased, pH was decreased by $5.0{\sim}6.0$ and EC sustained $0.8{\sim}1.0dS{\cdot}m^{-1}$ during experiment. Though in high $NH_4-N$ ratio of $3.0:2.5me{\cdot}L^{-1}$, the absorption of cations(K, Ca and Mg) was not inhibited. Treatment in contained $NH_4-N$ showed a tendency of increasing of petiole length and leaf width. The fruit length, fruit width, fruit weight and soluble solids were not significantly different. Yield per plant was lowest in $4.0:1.5\;me{\cdot}L^{-1}$, of $NO_3-N:NH_4-N$ ratio. Malformation fruit has not shown during the whole growth period.

Fabrication of Electroconductive $Si_3N_4$-TiN Ceramic Composites by In-Situ Reaction Sintering (In-Situ 반응소결에 의한 전도성 $Si_3N_4$-TiN 복합세라믹스 제조)

  • Lee, Byeong-Taek;Yun, Yeo-Ju;Park, Dong-Su;Kim, Hae-Du
    • Korean Journal of Materials Research
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    • v.9 no.6
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    • pp.577-582
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    • 1999
  • In order to make the electroconductive $Si_3N_4$-TiN composities, the Si-Ti(N) compacts were nitrided at $1450^{\circ}C$ for 20hours, and then they were post-sintered by a gas-pressure-sintering technique at 1TEX>$1950^{\circ}C$ for 3.5 hours. As starting powders, commercial si powder of about $10\mu\textrm{m}$, two types of Ti powders of 100 and 325 mesh, and fine-sized TiN of $2.5\mu\textrm{m}$ powders were used. In the $Si_3N_4$-TiN sintered bodies used Ti powders, the relative density and fracture strength and electrical conductivity are low due to the existence of large amounts of coarse pores. However, in the $Si_3N_4$-TiN composite used TiN powder, the fracture toughness, fracture strength and electrical resistivity were $5.0MPa{\cdot}m^{1/2}$, 624MPa and $1400{\omega}cm$, respectively. The dispersion of TiN particles in the composite inhibited the growth of $Si_3N_4$ in the shape of rod and made strong strain field contrasts at the $Si_3N_4$-TiNinterfaces. It was recognized that microstructural control is required to improve the electrical conductivity and mechanical properties of $Si_3N_4$-TiN composites by dispersing TiN particles homogeneously.

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GENERALIZED FIBONACCI AND LUCAS NUMBERS OF THE FORM wx2 AND wx2 ∓ 1

  • Keskin, Refik
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.1041-1054
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    • 2014
  • Let $P{\geq}3$ be an integer and let ($U_n$) and ($V_n$) denote generalized Fibonacci and Lucas sequences defined by $U_0=0$, $U_1=1$; $V_0= 2$, $V_1=P$, and $U_{n+1}=PU_n-U_{n-1}$, $V_{n+1}=PV_n-V_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equations $V_n=kx^2$ and $V_n=2kx^2$ with k | P and k > 1. Then, when k | P and k > 1, we solve some other equations such as $U_n=kx^2$, $U_n=2kx^2$, $U_n=3kx^2$, $V_n=kx^2{\mp}1$, $V_n=2kx^2{\mp}1$, and $U_n=kx^2{\mp}1$. Moreover, when P is odd, we solve the equations $V_n=wx^2+1$ and $V_n=wx^2-1$ for w = 2, 3, 6. After that, we solve some Diophantine equations.

STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS

  • Jung, Jong-Soo
    • Journal of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1151-1164
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    • 2009
  • Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.