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      • Some notes on the separability of Lp and lp for 1≤P<∞

        안상기 全南大學校 1986 국내석사

        RANK : 248639

        여기서는 1≤P<∞에서 L^P공간과 l^P공간에 대한 可分性(separability)을 생각하였다. Let L^P be the class of all p^-th power summable function on A, where A is a measurable set, I. e L^p={f|∫_A|f|^p<∞}, and if f∈L^p, the non-negative finite number (∫_A|f|^p)^1/p is denoted ∥f∥_p. 다음에 a,b ∈ L^P에 대하여 ρ_p(a, b) = (∑^n_k=1|α_k-β_k|^p)^1/p으로 정의된 metric space를 l_n^p로 표시한다. 단 a=(α₁,α₂…), b=(β₁,β₂…)이고 <(α_i>, <β_i>는 Cauchy sequence 이다. 이를 고찰하는데 §2에서는 주정리를 돕기 위한 필요한 개념을 열거하였으며 §3과 §4 에서는 1≤P<∞ 위에서 L^P 공간과 l^P 공간의 성질 및 정리들을 설명하고 이를 기초로 하여 주정리 1, 2에 의하여 可分性을 증명하였다.

      • 압전 스피커 응용을 위한 PZT계 세라믹의 제조 및 특성 평가

        안상기 충주대학교 산업대학원 2010 국내석사

        RANK : 248639

        스피커는 휴대폰, PMP(휴대용 다매체 재생기)와 같은 여러 전자기기의 필수 구성 요소 중의 하나이다. 최근 휴대형 전자기기의 확산으로 소형경량화에 기술개발의 초점을 맞추고 있으며 MEMS(마이크로 전자기계 시스템) 기술로 실리콘 웨이퍼에 마이크로 스피커를 가공하여 사용한 스피커와 고분자 압전체를 이용한 필름형 압전 스피커가 만들어지고 있다. 그러나 음압(SPL)이 일정하지 않아 스피커로 사용하기에는 부적합하다. 본 연구에서는 필름 스피커의 낮은 음압을 개선하고자 압전체를 적용한 새로운 개념의 필름스피커 구조를 고안하였다. 이 새로운 개념의 압전 스피커에서는 압전 세라믹의 특성상 저음 영역이 약한 부분을 플라스틱과 같은 진동 매체를 부착하여 개선하고자 하였다. 압전체를 스피커에 적용하기 위해서는 높은 전기기계결합계수(k_(p))와 기계적품질계수(Q_(m))을 가져야 한다. 이러한 조건을 만족시키는 압전 세라믹스를 제조하기 위해 우수한 압전 특성을 갖는 PSN-PZT 계 조성을 선택하였다. 그리고 Q_(m) 값의 향상을 위해 MnO₂를 소량 첨가하여 실험을 진행하였다. 압전체 분말의 기본조성은 Pb(Sb₁/₂Nb_(1/2))_(x)(Zr_(0.51)Ti_(0.49))₁-(x)_O₃의 3성분계로 구성하였고, 일반적인 세라믹 분말의 제조공정을 통해 시료를 제작하였다. 혼합된 원료분말들을 에탄올, 지르코니아 볼과 함께 24 시간 동안 혼합 및 분쇄, 건조시킨 후 분말을 80 메시(mesh)의 체(sieve)를 이용하여 체가름 하였다. 체가름을 한 분말은 850℃에서 2 시간 동안 하소하였다. 하소한 분말은 24 시간 동안 재혼합, 분쇄한 후 1,250℃에서 2 시간 동안 소결하였다. 승온 속도는 3℃/min으로 일정하게 하였으며, 냉각은 노 내에서 속도 제어 없이 수행하였다. 시편의 미세구조 및 결정구조는 주사전자현미경(SEM)과 X-선 회절분석기(XRD)를 사용하여 관찰하였고, 압전 특성은 임피던스 분석기(HP4194)를 이용하여 측정하였다. 모든 시편은 XRD 분석 결과 2차 상이 없는 완전한 페로브스카이트 결정구조를 형성함을 확인할 수 있었다. PSN-PZT 압전체에서 PSN의 몰비가 0.7까지 증가하면 전기기계결합계수도 같이 증가하는 특성을 보였다. 그런데 PSN-PZT 압전체들은 기계적품질계수(Q_(m))가 100 이하로 낮게 측정되었다. 이러한 낮은 기계적품질계수 특성은 MnO₂를 소량(0.4 wt%) 첨가함으로서 해결하였다. 이렇게 MnO₂를 0.4 wt% 첨가하여 최적화시킨 Pb(Sb₁/₂Nb_(1/2))0.7(Zr_(0.51)Ti_(0.49))_(0.93)O₃ 압전체의 전기기계결합계수(k_(p))는 약 61%, 기계적품질계수는(Q_(m))는 198로 매우 우수한 특성을 나타내었다. 이상과 같이 최적화된 PSN-PZT 압전체를 이용하여 필름스피커를 제작하였고, 이 필름스피커의 특성을 평가하였다. PSN-PZT 압전체를 0.2 mm 정도로 얇게 제작하기 위해서 닥터블래이드 법을 적용하였다. 이렇게 제작된 얇은 압전체 필름을 0.2 mm 두께의 금속판(황동)에 양면으로 접합하였다(바이몰프 구조). 즉, 얇은 두께의 황동 판이 압전체의 안정성을 향상시키는데, 이러한 구조의 총 두께는 0.6 mm가 된다. 제작된 압전 진동판은 음압을 증가시키기 위해 가로 10 cm ×세로 10 cm ×두께 3 mm의 아크릴판에 접착시켰다. 이렇게 압전 진동판을 좀 더 큰 면적의 플라스틱 등에 부착하는 구조가 본 연구에서 새롭게 제안한 스피커 구조이다. 압전체의 모양과 크기는 스피커의 음압을 최대화하기 위해 다양하게 실험을 하였다. 제작된 압전 스피커의 음압은 스펙트럼 분석기와 연결된 기준 마이크로폰(microphone: B&K 4135)를 사용하여 측정하였다. 측정 시의 스피커와 마이크로폰 사이의 거리는 1 m를 유지하였고, 분석 주파수 범위는 300 Hz~10 kHz였다. 스피커의 구동 전압은 40 V_(rms)부터 10 V_(rms)까지 변화를 주었다. 음압은 전압이 상승함에 따라 100 V_(rms)에서 최대값을 나타내었고 압전체의 크기가 클수록 높게 나타났다. 100 V_(rms) 조건에서 50 mm ×50 mm 크기의 압전 스피커의 음압은 1 kHz에서 약 90 dB를 나타내었고, 300 Hz의 낮은 주파수 대역에서도 MEMS 스피커와 고분자 필름 스피커에 비해 매우 높은 값인 76 dB를 확보할 수 있었다. A speaker is one of the essential components for many electronic equipments such as mobile phone, portable multimedia player, and so on. And the size reduction of the instruments still remains the most prominent trends in the marketplace, which demands continual efforts for the size reduction of the speaker. Recently, MEMS (Micro-Electro-Mechanical Systems) technology has been used to fabricate a micro-speaker on a silicon wafer. The other efforts have also been performed for making a thin film speaker with a piezoelectric polymer film or with a composite of piezoelectric ceramic and polymer. But the sound pressure levels(SPL) of the speakers are not so good for commercial application. In this study, to overcome the low SPL issue of the film speakers, a noble thick film speaker was presented and fabricated with a piezoelectric ceramic material. The SPL of the speaker was greatly improved by attaching it on a vibration media such as plastic. Ferroelectric materials exhibit sensitive piezoelectric characteristics making them suitable for transducer applications. The most widely used ferroelectric material for transducer is the lead zirconate titanate system known as PZT. The interested material properties for the application of these materials as speaker are the electro-mechanical coupling factor(k_(p)) and the mechanical quality factor(Q_(m)). So, Pb(Sb₁/₂Nb_(1/2))(abbreviated as PSN) was added to the PZT ceramic for improving the k_(p) and a small amount of MnO₂ was doped to increase the Q_(m) value. The modified PZT powder of Pb(Sb₁/₂Nb_(1/2))_(x)(Zr_(0.51)Ti_(0.49))₁-(x)_O₃ with 0.4 wt% of MnO₂ dopant was synthesized by the conventional process of manufacturing ceramic powders. Raw materials of PbO, Sb2O₃, Nb2O5, ZrO₂, TiO₂ and MnO₂ were weighed and mixed with zirconia balls in ethyl-alcohol for 24 hours. The mixed powder was dried and sieved with 80-mesh sieve. And then, the powders were calcined at 850℃ for 2 hours. The calcined powders were again milled with zirconia balls and sintered at 1250℃/2h/air with the heating rate of 3℃/min. The microstructure of the composite films was analyzed by using X-ray diffraction method and scanning electron microscopy. The piezoelectric properties were measured with HP4194 Impedance/Gain Phase Analyzer. The crystal phases of all the sintered specimens were perovskite structure without a secondary phase. The electro-mechanical coupling factor was improved with increasing the PSN amount up to 0.7 wt%. And the mechanical quality factor could be increased by doping the MnO₂ of 0.4 wt%. From these results, the optimized composition of the modified PZT ceramic was Pb(Sb₁/₂Nb_(1/2))0.7(Zr_(0.51)Ti_(0.49))_(0.93)O₃ with 0.4 wt% of MnO₂ dopant. At the optimized composition, the k_(p) and Q_(m) was about 0.61 and 300, respectively. The performance of the film speaker fabricated by the modified PZT thick film was also reported in this paper for the first time. For fabricate the speaker, the modified PZT ceramic films having the thickness of 0.2 mm were made by using a doctor blade method. And the thick PZT films were glued to the brass foil(thickness: 0.2 mm) in both side, which is called bimorph structure. That is, the brass sheet was sandwiched between the two piezoelectric plates to increase the reliability of the vibration part, which had the total thickness of 0.6 mm. And then, the vibration part was fixed to a acrylic plate of 10 cm(width) ×10 cm(length) ×3 mm(thickness). The shape and size of the piezoelectric plates were varied to maximize the SPL of the speaker. The SPL of the fabricated piezoelectric speaker was tested by using a reference microphone(B&K 4135), which was connected to a spectrum analyzer. The SPL was measured at 1 m away from the speaker and the analyzed frequency range was 300 Hz ~ 10 kHz. The input voltage for driving the speaker was varied from 40 V_(rms) to 100 V_(rms). The SPL was increased with raising the driving voltage up to 100 V_(rms) and the value was also improved by enlarging the size of the piezoelectric plate. At the test condition of 100 V_(rms) driving voltage and the piezoelectric plate of 50 mm(width) ×50 mm(length), the SPL of the fabricated piezoelectric speaker was about 91 dB at 1 kHz and was about 76 dB even at the low frequency of 300 Hz, which was very high values in comparison with the competitive technologies such as MEMS speaker and polymer film speaker.

      • 마틴루터의 두 왕국론에 관한 연구

        안상기 강남대학교 신학대학원 1997 국내석사

        RANK : 248639

        In his theory of two kingdoms, Luther clarifies that one kingdom should not control or be subordinate to the other. He insist s the following: It is a big mistake to confuse the functions and the roles of church and state. It is wrong to reign the world with the gospel; it is also wrong to reign Christians with arms. These two organizations should be distinguished like the Law and the gospel. Luther also identifies the medieval times with the City of God and talks about the limitation of the supreme power of the secular world. He mentioned the limitation when Charles V and the feudal lords of Germany were hostile against his reformation. Here, he stressed the functions and the obiect s of the two kingdoms to such a great degree that he has been misunder stood as a segregator of the believers from the unbelievers. How do Christians under stand state power? In other words, where must Christians be placed in the context of church and state? To Luther, all people including Christians should obey the state authority that God established. If any injustice is found in the authority, Christians should fir st ask for it s correction, based on the witness of the Word, through a certain state office. Otherwise, they should willingly submit to the state injustice. In this respect, Luther's under standingof the state authority is that a state is God's interim, natural, and gracious care in the fallen world. Therefore, Luther defines state as 'God's left kingdom' as he distinguishes it from church as 'God's right kingdom.' In such context, separation of state and church, distinction of the two kingdoms, and the church's independent ecclesiastical authority which does not subordinate to state are revealed in the reformers. It is true that Luther evaluates state positively though not in a strong manner. He was critical on the state's threat at the time of reformation insisting that believer s had the right to disobey the state's supreme power. Luther justifies criticism of the state with the condition that revolution or resistance must be avoided. Believer s should live a clearly distinguished life between state and church. For Luther, believers, in one aspect, are under God's sovereign rule whether they are in church or in state. In another per spective, however, they are under the state's rule while they belong to the church. This thesis will make clear the position of the believers in the two kingdoms through a discussion that church and state exist for the glory of God, which is the reformative view on the state. This thesis will support the view that the believer s should obey state authority when it does not contradict the Bible, but ask for it s correction when it does violate the Bible. It will also make clear that love and justice must be realized in the world. The method and scope of this study will be written based on a survey of books related to the two kingdoms. Chapter 2 describes the historical and philosophical background of Luther's two kingdom theory. The historical background will include the following three event s occurred in Luther's time: the conflict between Boniface Ⅷ and Philip IV, and the rising of 'Guardian of Peace' by Mar silius and 'Monarchy' by Machiavelli; Nationalism; and the peasant war which directly motivated Luther to write on the two kingdoms. The philosophical background will cover the two city theory in De Civitate Dei, which deals with apocalyptical escatology and was written by Augustine, a spiritual teacher of Luther. It will also cover the philosophy and humanism of Thomas Aquinas, who represent s the school of Scholar in the medieval times. Chapter 3 of this thesis will analyze Luther's thought s on the two kingdoms and the relations between church and state in the books written by Luther at the beginning of his reformation. Also, based on his books, this books, this chapter will study how Luther's thought s on the church and state have developed since the peasant war, which occurred in 1525. Chapter 4 will cover the study of the premise of Luther's two kingdom theory, its Biblical base, and the relationship of the two kingdoms and the contents of his two kingdom theory. The conception of God's kingdom and the secular kingdom, as well as the distinctions and relations of the two kingdoms will also be studied. In chapter 5, the conclusion of the thesis, the two kingdom theory will be summarized, problems will be presented with critical evaluation, and the two kingdom theories of Calvin and Bonhoeffer will be considered. The purpose of criticizing Luther's thoughts is to search for a more positive relationship between church and state. The criticism will be made by pointing out the weadnesses and danger s of the two kingdom theory. The conclusion will include the important issue that the relationship between church and state must be a continual concern because they are the two foundations of Christian life.

      • 마르틴 루터의 갈라디아 주석 1519년판과 1535년판에 나타난 의인사상의 발전에 관한 연구

        안상기 호서대학교 대학원 2003 국내박사

        RANK : 248639

        The purpose of the study is to examine the idea of sanctification that has not been highlighted in the theology of Martin Luther, and to expose the formation and development of his view of justification. Since justification was known as the focal point of Luther's theology, his concept of sanctification has not been intensively studied. Moreover, people have even regarded him as one who rejected any idea of sanctification. But we know some of his writings in which show both justification and sanctification. Thus we need to reexamine why he is conceived as putting emphasis only on justification. This effort is to reinterpret the catch-word of the Reformation, which is "Justification by Grace through Faith only." Luther focuses on the view of justification which claims that humans are justified by God through faith only. There are two reasons why he did so. First, he stressed salvation centered on justification reacting against the idea of salvation centered on sanctification in the medieval church. Second, later Lutherans do not develop Luther's idea of sanctification because they are so obsessed with his thought of justification. Strictly put, the second reason belongs to the first. That is, it would be a distortion if we interpret his theology only in the view-point of justification at the expense of sanctification. In so doing, we may lose the theological balance found clearly in Luther. However, justification has to be emphasized since his idea of salvation revolves around justification. Accordingly, this study attempts to present the formation and development of his view of justification reviewing his first commentary on Galatians(1519), the second(1535), and other writings. 1. Luther discovers by studying Romans 1:17 the truth of the Reformation, which declares that humans are accepted as righteous not by their good-works or merits but only by God's grace and their faith in him. God imputes his righteousness into them and regards them as righteous even though they are totally corrupted and thus sinners. Only by faith can we experience the change of our status in relation to God after receiving his righteousness. Justification by faith is Luther's astounding theological discovery. 2. A relational change with God creates actual changes in us. They are expected to happen in believer's lives through participating in and uniting with God's imputed righteousness. We not only are accepted as righteous but become actually righteous. Our actual righteousness results from justification. Those whose nature have been changed and become actually righteous live a righteous life. The change of human nature brings forth a changed Christian life. This is what Luther's view of sanctification claims. The change makes justified humans actually righteous and appears as true to others. If a sinner is merely declared as righteous and still remains sinful, he or she cannot live a righteous life. Thus, justification should proceed to the process of sanctification through the change of nature. Of course, he did not do a systematic research to explain the process. However, Luther shows it fully in his writings in general, his commentaries on Romans and Galatians in particular. 3. The characteristics of his idea of sanctification can be explained in terms of simul justus et peccator, union with Christ, fight against sin and evil, progressiveness and practice of faith, and good work and law of Christian. These signify living a changed life, being accepted as righteous, and being actually righteous. For Luther, a righteous life comes naturally as the result of the change of human nature. But, it does not mean a passivity in our side. Rather, it calls us for an active participation and sanctification. 4. Justification and sanctification can be distinguished but not separated. The former is an one-time event while the latter is a long-time process. We are accepted as righteous in justification while we achieve an actual righteousness in sanctification. It will be a misjudgment that we think that Luther rejects the idea of sanctification and the progressive nature of salvation, which starts from justification. He clearly knew the difference between justification and sanctification. 5. Based on this discovery, we can find Luther's concern for ministry. His deep concern for those who live with the burden of sin and thus are frustrated and agonized surfaces frequently when he deals with the facts of life. Approaching existentially to the problems and facts of life, he attempts to give encouragement and strength to the stressed and provide a positive perspective on life. We can see his genius in his effort to relate the concerns of believers to Christ who grants them wisdom, righteousness, holiness, and redemption (1Cor. 1:30). This study presents that early Luther has an idea of subjective sanctification and that the idea is basically same as his later view of it. Thus, it may be argued that he as the progenitor of the Reformation establishes a firm theological basis and remains in it during his teaching days. In the last chapter, it contends that the heart of Luther as a pastor is always ready to meet the needs of believers. Their concerns have influence greatly on his theology and its methodology. This study corrects the claim that Luther does not emphasize sanctification, and shows that there are plenty of materials regarding it. This effort helps readers understand his intention and sanctification. His ideas of justification and sanctification find support in the Scripture. This does not mean that Luther's theology is perfect. His has minor defects when we reviews it in the eyes of modern evangelicals. We tend to and cannot but see the reformer of 16th century from the view-point of modernity. If we can overcome this tendency and consider Luther in the context of his situation, we will agree to that he makes contribution by stressing not only sola fide but sanctification which has tremendous implication for modern churches.

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