• Title/Summary/Keyword: pN2

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PRECISE ASYMPTOTICS IN COMPLETE MOMENT CONVERGENCE FOR DEPENDENT RANDOM VARIABLE

  • Han, Kwang-Hee
    • Honam Mathematical Journal
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    • v.31 no.3
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    • pp.369-380
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    • 2009
  • Let $X,X_1,X_2,\;{\cdots}$ be identically distributed and negatively associated random variables with mean zeros and positive, finite variances. We prove that, if $E{\mid}X_1{\mid}^r$ < ${\infty}$, for 1 < p < 2 and r > $1+{\frac{p}{2}}$, and $lim_{n{\rightarrow}{\infty}}n^{-1}ES^2_n={\sigma}^2$ < ${\infty}$, then $lim_{{\epsilon}{\downarrow}0}{\epsilon}^{{2(r-p}/(2-p)-1}{\sum}^{\infty}_{n=1}n^{{\frac{r}{p}}-2-{\frac{1}{p}}}E\{{{\mid}S_n{\mid}}-{\epsilon}n^{\frac{1}{p}}\}+={\frac{p(2-p)}{(r-p)(2r-p-2)}}E{\mid}Z{\mid}^{\frac{2(r-p)}{2-p}}$, where $S_n\;=\;X_1\;+\;X_2\;+\;{\cdots}\;+\;X_n$ and Z has a normal distribution with mean 0 and variance ${\sigma}^2$.

Design of an Operator Architecture for Finite Fields in Constrained Environments (제약적인 환경에 적합한 유한체 연산기 구조 설계)

  • Jung, Seok-Won
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.18 no.3
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    • pp.45-50
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    • 2008
  • The choice of an irreducible polynomial and the representation of elements have influence on the efficiency of operators for finite fields. This paper suggests two serial multiplier for the extention field GF$(p^n)$ where p is odd prime. A serial multiplier using an irreducible binomial consists of (2n+5) resisters, 2 MUXs, 2 multipliers of GF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2+n$ clock cycles. A serial multiplier using an AOP consists of (2n+5) resisters, 1 MUX, 1 multiplier of CF(p), and 1 adder of GF(p). It obtains the mulitplication result after $n^2$+3n+2 clock cycles.

A Study on the Photo-Conductive Characteristics of (p)ZnTe/(n)Si Solar Cell and (n)CdS-(p)ZnTe/(n)Si Poly-Junction Thin Film ((p)ZnTe/(n)Si 태양전지와 (n)CdS-(p)ZnTe/(n)Si 복접합 박막의 광도전 특성에 관한 연구)

  • Jhoun, Choon-Saing;Kim, Wan-Tae;Huh, Chang-Su
    • Solar Energy
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    • v.11 no.3
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    • pp.74-83
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    • 1991
  • In this study, the (p)ZnTe/(n)Si solar cell and (n)CdS-(p)ZnTe/(n)Si poly-junction thin film are fabricated by vaccum deposition method at the substrate temperature of $200{\pm}1^{\circ}C$ and then their electrical properties are investigated and compared each other. The test results from the (p)ZnTe/(n)Si solar cell the (n)CdS-(p)ZnTe/(n)Si poly-junction thin fiim under the irradiation of solar energy $100[mW/cm^2]$ are as follows; Short circuit current$[mA/cm^2]$ (p)ZnTe/(n)Si:28 (n)CdS-(p)ZnTe/(n)Si:6.5 Open circuit voltage[mV] (p)ZnTe/(n)Si:450 (n)CdS-(p)ZnTe/(n)Si:250 Fill factor (p)ZnTe/(n)Si:0.65 (n)CdS-(p)ZnTe/(n)Si:0.27 Efficiency[%] (p)ZnTe/(n)Si:8.19 (n)CdS-(p)ZnTe/(n)Si:2.3 The thin film characteristics can be improved by annealing. But the (p)ZnTe/(n)Si solar cell are deteriorated at temperatures above $470^{\circ}C$ for annealing time longer than 15[min] and the (n)CdS-(p)ZnTe/(n)Si thin film are deteriorated at temperature about $580^{\circ}C$ for longer than 15[min]. It is found that the sheet resistance decreases with the increase of annealing temperature.

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The deformation space of real projective structures on the $(^*n_1n_2n_3n_4)$-orbifold

  • Lee, Jungkeun
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.549-560
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    • 1997
  • For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

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SOME RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P(α,β)n(x)

  • Choi, Junesang;Shine, Raj S.N.;Rathie, Arjun K.
    • East Asian mathematical journal
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    • v.31 no.1
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    • pp.103-107
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    • 2015
  • We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

EMBEDDING OF WEIGHTED $L^p$ SPACES AND THE $\bar{\partial}$-PROBLEM

  • Cho, Hong-Rae
    • East Asian mathematical journal
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    • v.19 no.1
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    • pp.73-80
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    • 2003
  • Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

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Cross-Correlation Distribution of a p-ary m-Sequence Family Constructed by Decimation (Decimation에 의해 생성된 p-진 m-시퀀스 군의 상호 상관 값의 분포)

  • Seo, Eun-Young;Kim, Young-Sik;No, Jong-Seon;Shin, Dong-Joon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.9C
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    • pp.669-675
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    • 2008
  • For an odd prime p, n=4k and $d=((p^2k+1)/2)^2$, there are $(p^{2k}+1)/2$ distinct decimated sequences, s(dt+1), $0{\leq}l<(p^{2k}+1)/2$, of a p-ary m-sequence, s(t) of period $p^n-1$. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l) takes the values in $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$ and their, cross-correlation distribution is also derived.

Key Recovery Algorithm from Randomly-Given Bits of Multi-Prime RSA and Prime Power RSA (비트 일부로부터 Multi-Prime RSA와 Prime Power RSA의 개인키를 복구하는 알고리즘)

  • Baek, Yoo-Jin
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.26 no.6
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    • pp.1401-1411
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    • 2016
  • The Multi-Prime RSA and the Prime Power RSA are the variants of the RSA cryptosystem, where the Multi-Prime RSA uses the modulus $N=p_1p_2{\cdots}p_r$ for distinct primes $p_1,p_2,{\cdots},p_r$ (r>2) and the Prime Power RSA uses the modulus $N=p^rq$ for two distinct primes p, q and a positive integer r(>1). This paper analyzes the security of these systems by using the technique given by Heninger and Shacham. More specifically, this paper shows that if the $2-2^{1/r}$ random portion of bits of $p_1,p_2,{\cdots},p_r$ is given, then $N=p_1p_2{\cdots}p_r$ can be factorized in the expected polynomial time and if the $2-{\sqrt{2}}$ random fraction of bits of p, q is given, then $N=p^rq$ can be factorized in the expected polynomial time. The analysis is then validated with experimental results for $N=p_1p_2p_3$, $N=p^2q$ and $N=p^3q$.

Effects of Different Extraction Extraction Media and Reaction Mixtures on Photosystem II Activity of Spinach Chloroplasts (시금치 엽록체의 광계의 활성에 미치는 추출용매와 반응용액의 영향)

  • 권병규
    • Journal of Plant Biology
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    • v.19 no.4
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    • pp.95-99
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    • 1976
  • This work deals with different extraction media and reaction mixtures on photosystem II activity of Spinach chloroplasts. The photoreduction rate of ferricyanide and DPIP by intact chloroplasts which extracted with four kinds of extraction media; S-Tris-N pH 7.2, 8.0, S-Tricine-N pH 7.2, 8.0, was measured in five kinds of reaction mixtures; S-Tris-N pH 7.2, 8.0, S-Tricine-N pH 7.2, 8.0, 0.05 M-Tris pH 7.2. The extraction medium which shows the highest photoreduction rate was S-Tris-N at pH 7.2 and S-Tricine-N at pH 8.0. As to the reaciton mixture, S-Tricine-N pH 8.0 showed the highest rate. On the complex effects of extraction media and reaction mixtures, the highest photordeuction rate of Hill oxidant by intact chloroplasts was obtained by S-Tris-N pH 7.2 extraction medium and S-Tricine-N pH 8.0 reaction mixture. The second highest activity was obtained by S-Tricine-N pH 8.0 extraction medium and reaction mixture.

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NON-TRIVIALITY OF TWO HOMOTOPY ELEMENTS IN π*S

  • Liu Xiugui
    • Journal of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.783-801
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    • 2006
  • Let A be the mod p Steenrod algebra for p an arbitrary odd prime and S the sphere spectrum localized at p. In this paper, some useful propositions about the May spectral sequence are first given, and then, two new nontrivial homotopy elements ${\alpha}_1{\jmath}{\xi}_n\;(p{\geq}5,n\;{\geq}\;3)\;and\;{\gamma}_s{\alpha}_1{\jmath}{\xi}_n\;(p\;{\geq}\;7,\;n\;{\geq}\;4)$ are detected in the stable homotopy groups of spheres, where ${\xi}_n\;{\in}\;{\pi}_{p^nq+pq-2}M$ is obtained in [2]. The new ones are of degree 2(p - 1)($p^n+p+1$) - 4 and 2(p - 1)($p^n+sp^2$ + sp + (s - 1)) - 7 and are represented up to nonzero scalar by $b_0h_0h_n,\;b_0h_0h_n\tilde{\gamma}_s\;{\neq}\;0\;{\in}\;Ext^{*,*}_A^(Z_p,\;Z_p)$ in the Adams spectral sequence respectively, where $3\;{\leq}\;s\;<\;p-2$.