• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Journal of the Korean Chemical Society
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• v.35 no.6
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• pp.707-712
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• 1991

N'-phenyl-N-(2-chloroethyl)-N-aminourea has been prepared from N'-phenyl-N-(2-chloroethyl)-N-nitrosourea by means of the electrochemical reduction with the mercury pool electrolytic cell. In order to find out the optimum condition of the reaction, the voltammetric behaviors for N'-aryl-N-(2-chloroethyl)-N-nitrosourea derivatives have been investigated by the cyclic voltammetry and polarography. The peak potentials was shifted to the negative direction as the pH value of the solution decrease. The substituent effects of phenyl ring on the peak potential were not observed in this case. (5:3) EtOH/4 N-HCl mixed solution was employed for the electrolysis. The applied potential was -0.7 V vs. Ag/AgCl/4 N-HCl electrode. The number of electrons participated to the reduction process was 4, respectively. The product was identified by FT-IR, NMR, mass and/or elemental analysis data.

• Journal of the Korean Chemical Society
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• v.25 no.6
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• pp.383-389
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• 1981

Thianthrene cation radical perchlorate reacts with N-arylsulfonamides such as p-toluenesulfonanilide, benzenesulfonanilide, N-(2-methylphenyl)benzenesulfonamide, and N-phenyl-p-toluenesulfonanilide to give 5-(p-N-p-toluenesulfonamidophenyl)-(1a), 5-(p-N-benzenesulfonamidophenyl)-(1b), 5-(4-N-benzenesulfonamido-3-methylphenyl)-(1c), and 5-(p-N-phenyl-N-p-toluenesulfonamidophenyl thianthrenium perchlorate (1d), respectively. In the meantime, 1d reacts further with thiathrene cation ratical to form diperchlorate(1e). The structure of 1a~1e is very similar to 5-(p-acetamidophenyl) thianthrenium perchlorate which has been obtained from the reaction with acetanilide. However, the discrepancy in the stoichiometry between two reactions indicates that the reaction with sulfonamide appears not to proceed with a single mechanism.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.633-648
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• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

• Journal of the Institute of Convergence Signal Processing
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• v.11 no.1
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• pp.47-52
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• 2010

For cryptographic systems, nonlinearity is crucial since most linear systems are easily decipherable. C.Bracken, Z.Zhaetc., propose the APN(Almost Perfect Nonlinear) functions with the properties similar to those of the bent functions with perfect nonlinearity. We design two kinds of new code sequence generating algorithms using the above APN functions. And we find that the out of phase ${\tau}\;{\neq}\;0$, autocorrelation functions, $R_{ii}(\tau)$ and the crosscorrelation functions, $R_{ik}(\tau)$ of the binary code sequences generated by two new algorithms over GF(2), have three values of {-1, $-1-2^{n/2}$, $-1+2^{n/2}$}. We also find that the out of phase ${\tau}\;{\neq}\;0$, autocorrelation functions, $R_{p,ii}(\tau)$ and the crosscorrelation functions, $R_{p,ik}(\tau)$ of the nonbinary code sequences generated by the modified algorithms over GF(p), $p\;{\geq}\;3$, have also three values of {$-1+p^{n-1}$, $-1-p^{(n-1)/2}+p^{n-1}$, $-1+p^{(n-1)/2}p^{n-1}$}. We show that these code sequences have the characteristics of the correlation functions similar to those of Gold code sequences.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.427-431
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• 2014

In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{\geq}3$, are not simple and groups of order $2^npq^t$ for $t{\geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.

• Proceedings of the Materials Research Society of Korea Conference
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• 2010.05a
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• pp.56.2-56.2
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• 2010

An improvement in the optical and structural properties of p-GaN was obtained by using antimony (Sb) as a surfactant during p-GaN growth. Two different growth temperatures of p-GaN such as $1030^{\circ}C$ and $900^{\circ}C$ were considered. Keeping the growth conditions for p-GaN constant, Sb was introduced during p-GaN growth while varying the [Sb]/([Ga]+[Mg]) flow ratio. [Sb]/([Ga]+[Mg]) flow ratio will be denoted as SGM ratio for convenience. SGM ratio of 0, 0.015 and 0.03% were considered for high temperature p-GaN growth. SGM ratio of 0, 0.005, 0.01 and 0.02% were considered for low temperature p-GaN growth. The analysis results suggest that using the optimum SGM ratio during p-GaN growth greatly improves the optical and structural properties of the p-GaN.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.6
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• pp.221-228
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• 2013

It is impossible directly to find a prime number p,q of a large semiprime n = pq using Trial Division method. So the most of the factorization algorithms use the indirection method which finds a prime number of p = GCD(a-b, n), q=GCD(a+b, n); get with a congruence of squares of $a^2{\equiv}b^2$ (mod n). It is just known the fact which the area that selects p and q about n=pq is between $10{\cdots}00$ < p < $\sqrt{n}$ and $\sqrt{n}$ < q < $99{\cdots}9$ based on $\sqrt{n}$ in the range, [$10{\cdots}01$, $99{\cdots}9$] of $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$. This paper proposes the method that reduces the range of p using information obtained from n. The proposed method uses the method that sets to $p_{min}=n_{LR}$, $q_{min}=n_{RL}$; divide into $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$. The proposed method is more effective from minimum 17.79% to maxmimum 90.17% than the method that reduces using $\sqrt{n}$ information.

• Korean Journal of Crystallography
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• v.2 no.1
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• pp.12-16
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• 1991

C18H22N4OS, Mr=342.47, monoclinic, P2₁/c,a=11.802(2), b=31.962(2), c=9.829(2)A, β=100.12(1)˚, V=3694.8A3,F(000)=1472, Z=8, Dx=1.246 Mg m-3, Dm=1.17Mg m-3,λ=0.71073 A, μ=0.15mm-1, T=294 K. final R=0.0856 for 3718 observed reflection (Fo>3σ(Fo)) There are two molecules in an asymmetric unit and a major difference between these molecules is in the C(9)-N(1)-C(6)-C(7) torsion angles [58.8(8)˚and 1(1)˚]. Both molecules have intramolecular N(1)-H(10)'N(3) hydrogen bonds [ 2.613(7) and 2.566(7) A] and assume V-shaped conformation with N(2) atoms at the verices. The two independent molecules are linked by the two N(2)-H(11)'S' hydrogen bonds[3.367(5) A and 3.421(4)A] and the dimergen are held together by van der Waals forces.

• Development and Reproduction
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• v.15 no.3
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• pp.223-230
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• 2011

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental contaminants derived from incomplete combustion of carbons and crude oil. In this study, we investigated the effects of benzo[a]pyrene (B[a]P), a representative PAHs on in vitro sex steroid hormone production and germinal vesicle breakdown (GVBD) using isolated oocytes of longchin goby (Chasmichthys dolichognathus) and chameleon goby (Tridentiger trigonocephalus). Oocytes in diameters of 0.8-0.9 (end vitellogenic stage) and 0.9-1.0 mm (germinal vesicle migratory stage) from longchin goby and 0.5 mm (fully vitellogenic stage) from chameleon goby were used. In GVBD assay, B[a]P at 10 nM stimulated GVBD in the oocytes of 0.8-0.9 mm from longchin goby. B[a]P at 1 nM stimulated GVBD in the oocytes with diameter 0.5 mm from chameleon goby. In steroid production from oocytes of longchin goby, B[a]P at 100 nM decreased testosterone (T) production, B[a]P at 1,000 nM increased estraiol-17 (J (E2) production and 10 and 100 nM increased $17,20{\beta}$-dihydroxy-4-pregnen-3-one ($17{\alpha}20{\beta}P$) production in the oocytes with diameter 0.8-0.9 mm. B[a]P at 1,000 nM increased E2 production, 100 and 1,000 nM increased $17{\alpha}20{\beta}P$ production in the oocytes with diameter 0.9-1.0 mm. In steroid production of oocytes from chameleon goby, B[a]P at 1,000 nM increased $E_2$ production. B[a]P at 10 nM increased $17{\alpha}20{\beta}P$ production. In the ratio of $E_2$ to T ($E_2$/T), B[a]P at 100 and 1,000 nM increased $E_2$/T in the oocytes of longchin goby. B[a]P at 100 nM also increased $E_2$/T in the oocytes of chameleon goby. Taken together, these results suggest that B[a]P have not only weak estrogenic effects but progestogenic effects on oocyte maturation.