점화식 a_n = a_(n-1) + a_(n-3), a_1 = a_2 = a_3 =1의 일반항에 대하여

노문기 ( Moon Chi Roh ),정재훈 ( Jae Hoon Jung ),강정기 ( Jeong Gi Kang ) 한국수학교육학회 2013 수학교육논문집 Vol.27 No.4

교사 위주의 수업보다 학생 중심의 탐구 활동이 지속적으로 강조되고 있지만, 이를 실행하기란 쉽지 않은 것이 현실이다. 학생들의 지적 호기심은 주관적이며, 지적 호기심을 충족해주는 것은 교육 과정에 충실한 교육 못지않게 중요하다. 본 연구는 문제를 해결하는 과정에서 얻은 수열로부터 시작되었다. 이 수열은 점화식 a_n = a_(n-1) + a_(n-3) (n≥ 4),a_1 = a_2 = a_3 =1으로 표현되었는데, 우리는 이 수열의 일반항을 찾아보고자 시도하였다. 주어진 문제의 점화식은 피보나치 수열의 점화식과 형태는 비슷해 보이지만 일반항을 구하는 과정은 결코 비슷하지 만은 않았다. 각고의 노력 끝에 우리는 같지만 서로 다르게 표현되는 두 개의 아름다운 일반항을 얻을 수 있었다. 본 연구와같은 탐구과정이 교육 현장에 활력을 불어 넣는 데 일조할 수 있기를 기대한다. It is important to make students do research for oneself. But the practice of inquiry activity is not easy in the mathematics education field. Intellectual curiosities of students are unpredictable. It is important to meet intellectual curiosities of students. We could get a sequence in the process solving a problem. This sequence was expressed in a form of the recurrence relation a_n = a_(n-1) + a_(n-3) (n≥ 4),a_1 = a_2 = a_3 =1. We tried to look for the general terms of this sequence. This sequence is similar to Fibonacci sequence, but the process finding the general terms is never similar to Fibonacci sequence. We can get two general terms expressed in different form after our a great deal of effort. We hope that this study will give the spot of education energy.

Synthesis and Antitumor Evaluation of cis-(1,2-Diaminoethane) dichloroplatinum (II) Complexes Linked to 5- and 6-Methyleneuracil and -uridine Analogues

Kim, Jack-C.,Lee, Min-Hwa,Choi, Soon-Kyu The Pharmaceutical Society of Korea 1998 Archives of Pharmacal Research Vol.21 No.4

The search for platinum (II)-based compounds with improved therapeutic properties was prompted to design and synthesize a new family of water-soluble, third generation cis-diaminedichloroplatinum (II) complexes linked to uracil and uridine. Six heretofore unreported uracil and uridine-platinum (II) complexes are; [N-(uracil-5-yl-methyl)ethane-1,2-di-amine]dichloroplatinum (II) (3a), [N-(uracil-6-yl-methyl)ethane-1,2-diaminel dichloroplatinum (II) (3b), t[N-($2^1$, $3^1$,$5^1$-tri-O-acetyl)uridine-5-yl-methyl] ethane-1,2-diamineldichloroplatinum (II) (6a), {[N-($2^1$,$3^1$, $5^1$-tri-O-acetyl) uridine-6-yl-methyl]ethane-1,2-diamine)dichloroplatinum (II) (6b),[N-(uridine- 5-yl-methyl)ethane-1,2-diamine]dichloroplatinum (II) (7a), [N-(uridine-6-yl- methyl)ethane-1,2-diamine]dichloroplatinum (II) (7b). These analogues were prepared from the key starting materials, 5-chloromethyluracil (1a) and 6-chloromethyluracil (1b) which were reacted with ethylenediamine to afford the respective 5-[(2-aminoethyl)aminol methyluracil (2a) and 6-[(2-aminoethyl)amino]methyluracil (2b). The cis-platin complexes 3a and 3b were obtained through the reaction of the respective 2a and 2b with potassium tetrachloroplatinate (II). The heterocyclic nucleic acid bases 1a and 1b were efficiently introduced on the .betha.-D-ribose ring via a Vorbruggen-type nucleoside coupling procedure with hexamethyldisilazane, trimethylchlorosilane and stannic chloride under anhydrous acetonitrile to yield the stereospecific .betha.-anomeric 5-chloromethyl- $2^1$,$3^1$,$5^1$-tri-O-acetyluridine (4a) and 6-chloromethyl-$2^1$,$3^1$,$5^1$-tri-O-acetyluridine (4b), respectively. The nucleosides 4a and 4b were coupled with ethylenediamine to provide the respective 5-[(amino-ethyl)aminolmethyl-$2^1$,$3^1$,$5^1$-tri-O-acetyluridine (5a) and 6-[(aminoethyl)amino] methyl-$2^1$,$3^1$,$5^1$-tri-O-acetyluridine (5b). The diamino-uridines 5a and 5b were reacted with potassium tetrachloroplatinate (II) to give the novel nucleoside complexes, 6a and 6b, respectively which were deacetylated into the free nucleosides, 7a and 7b by the treatment with CH$_{3}$ONa. The cytotoxic activities were evaluated against three cell lines (FM-3A, P-388 and J-82) and none of the synthesized compounds showed any significant activity.

N-Puzzle과 3n+1 문제의 행위적 유사성 분석

아흐마드이자즈,신석주 한국차세대컴퓨팅학회 2018 한국차세대컴퓨팅학회 논문지 Vol.14 No.1

3n+1 문제는 산술적으로는 단순하나 이에 대한 추정을 수학적으로는 증명하기 어려운 문제로 유명하다. 이 추정에대한 증명을 찾는 것이 어려운 이유는 다른 수학 분야들과 다소 동떨어진 분야이고, 수렴하는 순서에 있어서 특정패턴이 존재하지 않는다는 사실에 있다. N-puzzle은 초기 상태로부터 최종 목적 상태에 도달하기 위해 순서적으로타일을 움직이는 타일 게임 중 하나이다. 본 논문에서는 N-puzzle 에서의 타일 이동 패턴에 대한 3n+1 문제의 반복에 따른 수렴 패턴의 유사성을 연구하였다. 3n+1 문제에 대한 T-trajectory의 길이를 찾기 위하여 변형 시라쿠스(Modified Syracuse) 알고리즘을 구현하였고, N-puzzle에서 최적의 이동수를 도출하기 위해 맨하탄 디스턴스(Manhattan Distance)를 고려한 A* 알고리즘을 구현하였다. 연구로부터 N-puzzle의 초기 상태로부터 목적 상태까지의 Hamming distance와 Kendall tau distance에 기반하여 3n+1 문제의 반복 랜덤 특성이 N-puzzle 의 최적 이동 순서와 유사한 행위를 보임을 증명하였다. 3n+1 problem is well known in mathematics as arithmetically simplest to state yet hard to prove conjecture. The difficulty in finding a proof for the conjecture lies in its isolation from other mathematical areas and the fact that no pattern can be seen in the sequence. The N-puzzle is a tile game in which a sequence of moves is performed to reach goal state from any initial configuration. In this paper we present the study of 3n+1 problem’s iterations with respect to the moves of N-puzzle. We have implemented the Modified Syracuse algorithm to find length of T-trajectory of 3n+1 problem, and A* algorithm with Manhattan distance for finding optimal number of moves in N-puzzle. We have shown that in N-puzzle the sequence of optimal moves behaves similar to the random nature of 3n+1 problem iteration based on the Hamming distance and Kendall tau distance of N-puzzle initial configuration and goal state.

Interaction of Forskolin with the Effect of $N^6-Cyclopentyladenosine$ on $[^3H]-Acetylcholine$ Release in Rat Hippocampus

최봉규,박희만,강연욱,국영종,Choi, Bong-Kyu,Park, Hie-Man,Kang, Yeon-Wook,Kook, Young-Johng The Korean Society of Pharmacology 1992 대한약리학잡지 Vol.28 No.2

흰쥐 해마(hippocampus)에서 acetylcholine(Ach) 유리에 미치는 $A_1-adenosine$ 수용체의 역할과 post-receptor 기전에 있어서 adenylate cyclase 계의 관여여부에 관한 지견을 얻고자 하여 $[^3H]-choline$으로 평형시킨 해마 slice를 사용하여 $[^3H]-ACh$ 유리에 미치는 여러가지 약물들의 영향을 관찰하였다. $A_1-adenosine$ 수용체 흥분제인 $N^6-cyclopentyladenosine(CPA,\;0.1{\sim}10\;{\mu}M)$은 전기자극$(3Hz,\;5\;Vcm^{-1},\;2\;ms,\;rectangular\;pulses)$에 의한 $[^3H]-ACh$ 유리를 용량 의존적으로 감소시켰다. $A_1-adenosine$ 수용체 차단제인 8-cyclopentyl-1, 3-dipropylxanthine$(DPCPX,\;1{\sim}10\;{\mu}M)$은 용량 의존적으로 $[^3H]-ACh$ 유리를 증가시켰으며, 이때 기저(basal)유리 또한 증가됨을 관찰할 수 있었고, $2\;{\mu}M$ DPCPX 전처리는 CPA의 효과를 길항하여 CPA에 의한 용량반응곡선을 우측으로 이동시킴을 볼 수 있었다. G protein 억제제인 N-ethylmaleimide$(NEM,\;10\;&\;30\;{\mu}M)$는 그 자체에 의하여 자극에 의한 ACh 유리를 증가시켰으며, 기저유리 또한 증가함을 볼 수 있었다. NEM 전처리에 의하여 CPA의 효과는 완전히 소실되었다. 한편 adenylate cyclase 활성화제인 forskolin$(0.3{\sim}10\;{\mu}M)$은 기저유리에 변함없이 용량의존적인 $[^3H]-ACh$ 유리의 증가를 초래하였으며 $3\;{\mu}M$ forskolin 전처리는 대량$(10\;{\mu}M)$의 CPA의 효과를 제외하고는 CPA의 효과를 억제시킴을 관찰할 수 있었다. 이상의 실험 결과로 흰쥐 해마의 choline 작동성신경의 presynaptic $A_1-adenosine$ heteroreceptor는 ACh 유리에 중요한 역할을 하고 있으며, ACh 유리의 조절에 Gi-단백질을 통한 adenylate cyclase 계의 관여가 확실하다 하겠다. As it has been reported that the depolarization-induced acetylcholine (ACh) release is modulated by activation of presynaptic $A_1-adenosine$ heteroreceptor in hippocampus and various lines of evidence indicate the involvement of adenylate cyclase system in $A_1-adenosine$ post-receptor mechanism in hippocampus, it was attempted to delineate the role of adenylate cyclase system in the $A_1-receptor-mediated$ control of ACh release in this study. Slices from rat hippocampus were incubated with $[^3H]-choline$ and the release of the labelled products was evoked by electrical stimulation $(3\;Hz,\;5\;Vcm^{-1},\;2\;ms,\;rectangular\;pulses)$, and the influence of various agents on the evoked tritium-outflow was investigated. $N^6-cyclopentyladenosine$ (CPA), a specific $A_1-adenosine$ receptor agonist, in concentrations ranging from 0.1 to $10\;{\mu}M$, decreased the $[^3H]-ACh$ release in a dose-dependent manner without the changes of basal rate of release. 8-cyclopentyl-1,3-dipropylxanthine $(DPCPX,\;1{\sim}10\;{\mu}M)$, a selective $A_1-receptor$ antagonist, increased the $[^3H]-ACh$ release in a dose-related fashion with slight increase of basal tritium-release. And the CPA effects were significantly inhibited by DPCPX $(2\;{\mu}M)$ pretreatment and the dose-response curve produced by CPA was shifted to the right. The responses to N-ethylmaleimide $(NEM,\;10\;&\;30\;{\mu}M)$, a SH-alkylating agent of G-protein, were characterized by increments of the evoked ACh-release and the basal release, and the CPA effect were completely abolished by NEM pretreatment. Forskolin, a specific adenylate cyclase activator, in concentrations ranging from 0.3 to $10\;{\mu}M$, increased the evoked ACh-release in a dose-dependent manner and the CPA effects were inhibited by forskolin. These results indicate that the $A_1-adenosine$ heteroreceptor plays an important role in ACh-release via nucleotide-binding protein Gi in the rat hippocampus and that the adenylate cyclase system might be participated in this process.

최근 2년간 부산지역에서 급성호흡기 환자로부터 분리한 인플루엔자바이러스의 유행 양상

조경순,박선미,김성준,정명주,이주연,강춘,Cho, Kyung-Soon,Park, Sun-Mee,Kim, Seang-Joon,Jung, Myung-Ju,Lee, Joo-Yeon,Kang, Chun 한국미생물학회 2007 미생물학회지 Vol.43 No.3

2004년과 2005년 동안 부산지역에서 급성호흡기환자로부터 인플루엔자바이러스를 분리 동정하여 분식한 결과, 인플루엔자바이러스분리율은 2004년도는 1869건의 호흡기 검체 중 인플루엔자바이러스 154건 중, A/H3N2형은 77.3%에 해당하는 119건, B형의 경우 35건(22.7%)으로 나타났고 A/H1N1형은 검출되지 않았다. 분리된 인플루엔자바이러스의, 2005년의 경우 1579건의 호흡기 검체 중에서 분리된 인플루엔자바이러스 19건 중, A/H1N1형은 6건(31.6%) 검출되었으며, A/H3N2형은 52.6%에 해당하는 10건, B형의 경우는 3건(15.8%)으로 나타났다. 2005년의 경우 전체적인 인플루엔자바이러스 분리율은 2004년에 비해 떨어졌으나, A/H3N2의 경우 여전히 높은 분리율을 보였으며 2004년에는 전혀 검출되지 않았던 A/H1N1이 B형보다 많이 분리되었다. 부산지역에서 분리된 바이러스의 항원형을 분석한 결과 당해연도 백신주와 동일하거나 유사하였다. 연령별 발생 분포는 0-10세 이하에서 80-90%이상을 차지하였고, 남성에 비해 여성에서 약간 높은 분리율을 나타내었다. 월별 분리율은 2004년도는 4월, 2005년도는 2월이 가장 많이 분리되었다. 인플루엔자바이러스의 대유행 주기에 임박한 현 시점에서 지속적으로 인플루엔자유행예측조사로서 조기 분리한 인플루엔자바이러스 주를 유전자 염기서열을 분석함으로써 신종 인플루엔자바이러스가 출현되는지 적극적인 감시가 필요하다. The occurrence of acute respiratory infections caused by the influenza virus are particularly high during the winter season in Busan, Korea. In 2004 and 2005, a study of the rate of occurrences of the influenza virus was conducted. The results reveal that in 2004, of the 1,869 people with an acute respiratory infection that 154 (8.2%) people were infected by the influenza virus. In 2005, of the 1,579 people infected with an acute respiratory infection that 19 people (1.2%) were infected with the influenza virus. The study shows a decrease in the numbers of an influenza virus infection from 2004 to 2005. Data was collected by inspecting throat swabs and nasal discharge from those with an acute respiratory infection. Further inspection of the throat swab and nasal discharge from the infected individuals during 2004 and 2005 study show the occurrence of the different types of influenza virus in the population: 6 cases (3.5%) of influenza type A/H1N1, 129 cases (74.5%) of A/H3N2, and 38 cases (22.0%) of type B. The study conducted in 2004 and 2005 reveal that children between the ages of two and five were more likely to be infected than any other age group. In the study, about 62.2% of the infected individuals were between two and five years old. The detection rates between males and females are similar. However, it is notable that females are slightly more likely to develop an acute respiratory infection caused by the influence virus compared to their male counterparts.

2012년 부산 지역 인플루엔자바이러스의 월별 양상과 연령별 분포

전은미,허만규 한국자료분석학회 2015 Journal of the Korean Data Analysis Society Vol.17 No.2

Human influenza viruses in infants or young babies are important causes of upper respiratory tract illness and lower respiratory tract illness. A better understanding of influenza seasonality is useful to inform the timing and composition of vaccine recommendations and monitor the emergence of new virus variants. We tested influenza virus specimen in 2,421 hospitalized children of four hospitals in Busan to identify 3 kinds of respiratory viruses, influenza virus A (H1N1 and H3N2) and influenza virus B. Identification of viruses was used the indirect fluorescent test (IFA) with FITC-conjugated anti-mouse immunoglobulin and hemagglutination inhibition test (HI test). We analyzed the positive rate, annual frequencies according to the retrospective review of medical records. Of 1310 influenza virus A samples, 88 (7.0%) had positive. Of 88 positive influenza A virus samples, number of influenza H1N1 subtype was 31 (2.4%) and number of influenza H3N2 subtype was 57 (4.4%). The positive influenza virus B was 4.7% (52/1111). Positive respiratory viruses on January and February were detected 11.4% and 10.6%, respectively. The detection rates between males and females were similar pointing out each 1.3% out of specimens in 2012. As for the age distribution, the high detection rates were indicated in children at the age of two to five. 소아 및 유아에서 발병한 호흡기 인플루엔자바이러스 감염은 두통과 폐렴 등 여러 질병을 유발함으로 매우 중요하다. 인플루엔자의 계절별 동향과 세부 타입의 분류는 처방전에서 차이 등을 수반하므로 이들의 이해와 정보는 매우 유익하다. 부산 시내 2012년 4개 병원에서 수집한 2,421명의 소아 및 유아에서 발병한 호흡기 인플루엔자바이러스의 세부아형인 A형(H1N1, H3N2), B형을 동정하였다. 바이러스 동정은 FITC-접합한 항-마우스 면역글로블린을 이용한 간접면역형광법(IFA)과 헤마글루티네이션 억제법(HI test)으로 확인하였다. 의료기록에 근거한 연령별, 양성반응률, 연중 빈도를 분석하였다. 인플루엔자 바이러스 A형은 88건(7.0%)이 양성이었다. 88명의 환자에 대한 양성 인플루엔자 바이러스 A형 중 57건(4.4%)은 인플루엔자 H3N2세부아형이었다. 양성 인플루엔자B바이러스는 52건(4.7%)이었다. 양성 호흡기 바이러스에서 1월과 2월은 각각 11.4%, 10.6%였다. 한편, 부산지역의 4개 병원을 층(strata)으로 하여 각 병원 효과를 통제한 후 인플루엔자 유형과 감염비율이 연관성이 있는지 Cochran-Mantel-Haenzel 검정을 실시하였다. 먼저 Breslow-Day의 승산비 동질성 검정을 한 결과 각 병원의 오즈비가 동일하게 나왔으며(p=0.771) 병원 효과를 통제한 후 인플루엔자 유형과 양성반응 비율의 차이 검정을 종합적으로 분석한 결과 통계적으로 차이가 나타났다. 2011-2012년도 질병관리본부에서 3,785건의 분석결과와 비교시 인플루엔자 바이러스 A형과 B형의 빈도는 유사하였으나 A형 중 H1N1타입과 H3N2타입의 빈도는 유의한 차이가 있었다.

돼지 인플루엔자 바이러스의 혈청학적 역학조사 및 유전학적 분석

류영수,김로미,Lyoo, Young-soo,Kim, Lomi 대한수의학회 1998 大韓獸醫學會誌 Vol.38 No.1

Total of 1085 swine sera (1996-1997) from nation-wide were tested for the presence of antibodies to influenza A virus. Fifty nine percent of the tested sera showed seropositive by HI test. Positive sera consisted of 24--- of H3, 15--- of H1, and 20--- of the sample had both antibodies, respectively. Sera collected from various region represented 7~27--- seropositivity to H1N1, 15~25--- to H3N2, respectively. Swine influenza field isolate from nasal swab was characterized antigenically and genetically to elucidate its relatedness with other known strains of influenza A virus. The study was focused on the HA gene which is related to pathogenecity and antigenic variability of the influenza virus. By RT-PCR using influenza A/H1N1 specific primers, influenza virus H1N1 specific DNA fragment was amplified from A/Swine/Iowa/15/30(H1N1), US field isolate but not in H3N2 strain. PCR products were sequenced by dideoxy chain termination method to determine nucleotide homology with other strains of influenza A virus. The US field isolate and A/Swine/Indiana/1726/88 strain had 97--- of nucleotide homology and 98--- of amino acid homology. Based on the results obtained from this experiment, the field isolate was genetically related to A/Swine/Indiana/1726/88 and had higher homology with A/Swine/Indiana/1726/88 than with classical swine influenza virus, A/Swine/Iowa/15/30. The field isolate had no amino acid changes at the antigenic site compare to that of the A/Swine/Indiana/1726/88. The proteolytic enzyme cleavage site between HA1 and HA2 had no alteration and the amino acid arginine was intact. There is no evidence has been found that the field isolate has genetic shift or genetic drift which might altered antigenic determinant.

Study on (n, α) reactions for the production of 51Cr, 89Sr, 99Tc, 131I, 133Xe, 137Cs and 153Sm radioisotopes used in nuclear medicine

Abdullah Hallo M.,Ahmed Ali H. 한국원자력학회 2023 Nuclear Engineering and Technology Vol.55 No.9

Nuclear medicine seems to be a decent choice of medicine in the recent decade. The radioactive isotopes 51Cr, 89Sr, 99Tc, 131I, 133Xe, 137Cs and 153Sm are extremely essential in nuclear medicine. The excitation functions of the 54Fe (n, a) 51Cr, 92Zr (n, a) 89Sr, 102Rh (n, a) 99Tc, 134Cs (n, a) 131I, 136Ba (n, a) 133Xe, 140La (n, a) 137Cs and 156Gd (n, a) 153Sm reactions were calculated in this study using the EMPIRE 3.2.3 and TALYS 1.95 nuclear codes. Additionally, the cross sections at 14e15 MeV were calculated using empirical formulae and the experimental data. The computer codes were compared to the experimental data and Empirical formulas as well as the evaluated data (TENDL 2021, JENDL 3.3, JENDL 5, JEFF 3.3, EAF 2010, CENDL 3.1, CENDL 3.2, ROSFOND 2010, FENDL 3.2 b, and BROND 3.1).

Analysis on Behavioral Similarity of N-Puzzle with 3n+1 Problem

아흐마드 이자즈,신석주 한국차세대컴퓨팅학회 2018 한국차세대컴퓨팅학회 논문지 Vol.14 No.1

3n+1 problem is well known in mathematics as arithmetically simplest to state yet hard to prove conjecture. The difficulty in finding a proof for the conjecture lies in its isolation from other mathematical areas and the fact that no pattern can be seen in the sequence. The N-puzzle is a tile game in which a sequence of moves is performed to reach goal state from any initial configuration. In this paper we present the study of 3n+1 problem’s iterations with respect to the moves of N-puzzle. We have implemented the Modified Syracuse algorithm to find length of T-trajectory of 3n+1 problem, and A* algorithm with Manhattan distance for finding optimal number of moves in N-puzzle. We have shown that in N-puzzle the sequence of optimal moves behaves similar to the random nature of 3n+1 problem iteration based on the Hamming distance and Kendall tau distance of N-puzzle initial configuration and goal state.

생물안전 3등급(BSL3)시설의 생물재해 시나리오에 따른 실내 공기환경예측에 관한 연구

박현진(Hyun Jin Park),홍진관(Jin Kwan Hong) 대한설비공학회 2010 설비공학 논문집 Vol.22 No.11

Since the implementation of the LMO Law in Korea, the importance of the design qualification of BSL3 lab. is emphasizing. In this study, multizone simulation for three kind of biohazard scenarios using CONTAM is performed for design qualification of BSL3 lab. Also, in the case of unexpected spread of contaminants such as Influenza A virus(H1N1) in BL3 zone, the design qualification is carried out for diffusion and decontamination of contaminants according to differential pressure of BSL3 anteroom and door area of BSL3 lab. Also, in this study, appropriateness of laboratory room differential pressure and air flow rate to maintain pressure difference between laboratory rooms, and energy consumption due to air change rate variation according to door area in BL3 lab. Simulation results show that these approach methods are used as a tool for the design and verification of BL3 lab.