• Title/Summary/Keyword: Plateau's problem

Search Result 11, Processing Time 0.02 seconds

THE SECOND DERIVATIVE OF THE ENERGY FUNCTIONAL

  • Kim, Hwa-Jeong
    • Honam Mathematical Journal
    • /
    • v.34 no.2
    • /
    • pp.191-198
    • /
    • 2012
  • Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.

변분법과 최대.최소 : 역사적 고찰

  • 한찬욱
    • Journal for History of Mathematics
    • /
    • v.17 no.1
    • /
    • pp.43-52
    • /
    • 2004
  • In this paper we investigate the origin of the variational calculus with respect to the extremal principle. We also study the role the extremal principle has played in the development of the calculus of variations. We deal with Dido's isoperimetric problem, Maupertius's least action principle, brachistochrone problem, geodesics, Johann Bernoulli's principle of virtual work, Plateau's minimal surface and Dirichlet principle.

  • PDF

Channel Electrode Voltammetric and In Situ Electrochemical ESR Studies of Comproportionation of Methyl Viologen in Acetonitrile

  • Lee, Ji U;John C. Eklund;Robert A. W. Dryfe;Richard G. Compton
    • Bulletin of the Korean Chemical Society
    • /
    • v.17 no.2
    • /
    • pp.162-167
    • /
    • 1996
  • Two redox processes of methyl viologen (+2/+, +/0) in acetonitrile were investigated by using channel electrode voltammetric and in situ electrochemical ESR methods. Two separated unequal plateau currents of the first (+2/+) and second (+/0) redox processes of the viologen were observed in the channel electrode voltammograms and showed a cube-root depedndence on the electrolyte flow rate, respectively. The simple Levich analysis resulted in two different diffusion coefficients of $D_{+2}=2.2{\times}10^{-5}\;cm^2/s$ and $D_+=3.0{\times}10^{-5}cm^2/s$ from the limiting currents. In situ electrochemical ESR studies were performed for the monocation radicals generated at the potentials of the two plateau currents in the electrolyte flow range $1.3{\times}10^{-1}{\geq}v_f{\geq}2.7{\times}10^{-3}\;cm^3/s$. Backward implicitfinite difference method was employed to simulate the electrochemical kinetic problem of two sequential electron transfers ($MV^{+2}+e{\leftrightarrows}MV^+,\;MV^{+}+e{\leftrightarrows}MV^0$) coupled with reversible comproportionation ($MV^{2+}+MV^0{{\leftrightarrows}^{k_f}_{k_b}}2MV^+$). $k_f$ was found to be greater than ($10^6M^{-1}s^{-1}.

Optimal Poultry Litter Management through GIS-based Transportation Analysis System

  • Kang, M.S.;Srivastava, P.;Fulton, J.P.;Tyson, T.;Owsley, W.F.;Yoo, K.H.
    • Journal of The Korean Society of Agricultural Engineers
    • /
    • v.48 no.7
    • /
    • pp.73-86
    • /
    • 2006
  • Concentrated poultry production in the State of Alabama, U.S.A. results in excessive poultry litter. Application of poultry litter to pastures and row crops serves as a cheap alternative to commercial fertilizer. However, over the years, poultry litter application to perennial forage crops in the Appalachian Plateau region of North Alabama has resulted in phosphorus (P) buildup in soils. Phosphorus index (P-index) and comprehensive nutrient management plans (CNMP) are often used as a best management practice (BMP) for proper land application of litter. Because nutrient management planning is often not done for small animal feeding operations (AFOs), and also because, in case of excess litter, litter transportation infrastructure has not been developed, over application of poultry litter to near by area is a common practice. To alleviate this problem, optimal poultry litter management and transportation infrastructure needs to be developed. This paper presents a methodology to optimize poultry litter application and transportation through efficient nutrient management planning and transportation network analysis. The goal was accomplished through implementation of three important modules, a P-Index module, a CNMP module, and a transportation network analysis module within ArcGIS, a Geographic Information System (GIS). The CNMP and P-Index modules assist with land application of poultry litter at a rate that is protective of water quality, while the transportation network analysis module helps transport excess litter to areas requiring litter in the Appalachian Plateau and Black Belt (a nutrient-deficient area) regions. Once fully developed and implemented, such a system will help alleviate water quality problems in the Appalachian Plateau region and poor soil fertility problems in the Black Belt region by optimizing land application and transportation. The utility of the methodology is illustrated through a hypothetical case study.

Burqanism from the Origin of the Pastoral Nomadic Koryo Region and the Vision of Korean Livestock Farming (고려의 원시영역 유목초지, 그 부르칸(불함)이즘과 한국축산의 비전)

  • Chu Chae Hyok
    • Journal of The Korean Society of Grassland and Forage Science
    • /
    • v.25 no.1
    • /
    • pp.71-82
    • /
    • 2005
  • Khori(高麗) refers to the Chaabog(reindeer) that live on lichens(蘚) on Mt. Soyon(鮮) in which pastures are the cold and dry plateau of North Eurasia. Thus, the origin region of the Khori or Koguryo that are the ancestors of the reindeer-herding pastoral nomads(馴鹿 遊牧民) can be said to be the Steppe-Taiga-Tundra pastoral areas of North Eurasia and North America. When the pastoral nomads moved on to the great mountain(大山) zone of the Jangbaek(長白) to the Baekdu(白頭) Mountains, they could have been in contact with pastoral farmers or agricultural farmers living there and they became the farmers remaining on agricultural farms. They were the Koryo people, the ancestors of Korea. Staying in one place, they gradually forgot the origin of their reindeer-herding pastoral nomadic history in the Northwest area of Mt. Soyon, the small mountain(小山) zone of the Steppe-Taiga-Tundra pastoral areas. In other words, they lost their identity as reindeer-herding pastoral nomads when they entered the agricultural area after leaving the pastoral area. However, since their basic genes had already formed when they lived on the cold and dry plateau of North Eurasia, it is possible to study their pastoral nomadic history focusing on 'the minority living in the broad area(廣域少數)', by utilizing highly advanced biotechnological science and focusing on genes and information technology innovation, and removing various past hindrances in research. Therefore, it is not so difficult to restore the reindeerherding pastoral nomadic history of the Koguryo(高句麗) people and secure their pastoral nomadic identity, of which the first steps have already been taken into their historical stages. The Eurasian continent and the Korean peninsula, especially the cold and dry plateau of North Eurasia and the Korean peninsula have been closely related to each other ecologically and historically. They can never be a separate space at all. The Eurasian continent lies horizontally east to west and thus, the continent forms an isothermal zone. Also, since the time of producing their own foods, it was relatively easy for people with their technology to move to other places owing to the pastoral nomadic characteristic of mobility. Unlike the Chungyen(中原) region, western Asia and the regions covering the Siberia-Manchu-Korean peninsula where food production revolution was first made were connected to the Mongolian lichens route(蘚苔之路: Ni, ukinii jam) and steppe roads. Although the ecological conditions of nature have changed a bit throughout a long history, it was natural for the many tribes in North Asia living on the largest Steppe-Taiga-Tundra area in the world to have believed 'the legends related to animals in relation to their founders and ancestors(獸祖傳說)'. Assuming that Siberian tigers and the tigers living on Mt. Baekdu were connected ecologically and genetically because of the ecological characteristics of the animals, and their migration from plateau to plateau, we would suspect that the Chosun(朝鮮) tribe living on Mt. Baekdu were ethnically and culturally more closely connected to the farther removed Ural-Altai tribes that lived on the cold and dry plateau region than to the Han(i14;) tribe who lived in Chungyen(中原) that was close to Mt. Baekdu. More evidence is the structure of the Korean language which has the form of 'Subject + Object + Verb', which is assumed to have originated from the speedy lifestyle of the reindeer-herding pastoral nomads. The structure is quite different from that of the Han(漢) language, which is based on agricultural life. Also, it is natural for reindeer riding reindeerherding pastoral nomads or horse-riding sheep-herding pastoral nomads(騎馬, 羊遊牧民) to have held military and political power over the region and eventually to have established an ancient pastoral nomadic empire in the process of their conquest of agricultural regions. The stages for founding global empires in the history of mankind maybe largely divided into two, in terms of ecological conditions and occupations. They are the steppes and the oceans. Of course, the steppe-based empires were established based on the skills to deal with horses and the ability to shoot arrows while riding horses, along with the use of iron ware in the 8th century BC. The steppe-based empires became the foundation for an oceanic empire, which could have been established by the use of warships and warship guns since the 15th Century. Based on those facts, we know that Chosun, Puyo(夫餘), and Koguryo are the products of a developmental process of pastoral nomadic empires on the steppes. Maybe we can easily find the pastoral nomadic identity of the Koguryo more than we expected when we trace the origins and history of the Korean tribe living in the pastures located in the northwest area of Mt. Jangbaek by focusing on pastoral nomadic mobility and organization just as we have investigated the historic origins of Anglo-Saxons in America by focusing on the times before the 15th Century. In the process, we should keep in mind that English culture originated from the Industrial Revolution and was directly delivered to the American continent, although America was far from England and was not an intermediate point on long sojourns either. Further, American culture came back to England in a more advanced form later. The most important thing currently to be resolved is to cause Koreans to look back on their own history in a freer way of thinking and with diverse, profound, and sharp insight, taking away the old and existing conventional recognition that is entangled with complicated interests with Korean people and other countries. The meanings of Chosun, Khori, and Solongos have been interpreted arbitrarily without any historic evidence by the scholars who followed conventional tradition of fixed-minded aristocrats in an agricultural society. If the Siberian cultural properties of the stone age, the earthenware age, the bronze age, and the iron age are analyzed in such a way, archaeological discovery will never be able to contribute to the restoration of the Koguryo's pastoral nomadic identity. One should transcend the errors that tend to interpret the cultural properties discovered in the pastoral nomadic regions as not being differentiated from those of agricultural regions and just interpret them altogether from the agricultural point of view. A more careful intention is required in the interpretation of cultural properties of ancient Korean empires that seem to have been formed due to mutual interactions of pastoral nomadic and agricultural cultures. Also, it is required that the conventional recognition chain of 'reverse-genes' be severed, which has placed more weight on agricultural properties than pastoral nomadic ones, since their settlement on agricultural farms was made after the establishment of their ancient pastoral nomadic empires. There is no reason at all to place priority on stoneware, earthenware, bronze ware, and iron ware than on wooden ware(木器) and other ware which were made of animal skins(皮器), bones and horns(骨角器), in analyzing the history in the regions of reindeer or sheep pastures. Reading ancient Korean history from the perspective of pastoral nomadic history, one feels strongly the instinctive emotions to return to the natural 'mother place'. The reindeer-herding pastoral nomadic identity of the Koguryo people that has been accumulated in volumes in their genes and hidden deep inside and have interacted organically could be reborn with Burqanism(Burqan refers to 不咸 in Chinese), which was their religion by birth and symbolized as the red willow(紅柳=不咸). The mother place of the Koguryo's people is the endless vast green pastures of North Eurasia and North America, where we anticipated the development of Korean livestock farming following the inherent properties in the genes of the reindeer-herding pastoral nomads with Korean ancestors. We anticipate that the place would be the core resource that could contribute to the development of life of living creatures following the inherent properties of their genes and biotechnological factors. In other words, biotechnology used for a search for clues on the well-being of humans could be the fruit brought by Burqanism of the Koguryo people and the fruit of the globalization of Korean livestock farming. It is the Chosun farmer in China come from the vast nomadic reindeer pastures of North Eurasia that resolved the food problem of a billion Chinese people with lowland paddy rice seeds (水稻) by transforming Heilongjiang Province(黑龍江省) into an oceanic lowland paddy rice field(水田). Even Mao Tse-tung(毛擇東) could not resolve the food problem by his revolution campaigns for tens of years. Today is the very time that requires the development of special livestock farming following the inherent properties of the ancient Korean reindeer-herding pastoral nomads that respected the dignity of life on the cold and dry plateau of North Eurasia and the America continent. I suggest that research should be started from the pastures of the Dariganga Steppe in East Mongolia that was the homeland of Hanwoo(韓牛) and the central horse-herding steppe place(牧馬場) of Chingis Khan's Mongolia. The Dariganga Steppe is awash with an affluent natural environment for pastoral nomadic living however, the quality of life of the pastoral nomads there is still low. I suggest we Koreans, the descendents of the Koguryo, should take our first steps for our livestock farming business project and develop the Northern nomadic pastures, here at the pastures of the Dariganga Steppe, which is the Mongolian core place of state-of-the-art technology for military weapons.

The effect of low temperature aging on the mechanical property & phase stability of Y-TZP ceramics

  • Kim, Hyung-Tae;Han, Jung-Suk;Yang, Jae-Ho;Lee, Jai-Bong;Kim, Sung-Hun
    • The Journal of Advanced Prosthodontics
    • /
    • v.1 no.3
    • /
    • pp.113-117
    • /
    • 2009
  • STATEMENT OF PROBLEM. Recently Yttrium-stabilized tetragonal zirconia polycrystal (Y-TZP) has been introduced due to superior flexural strength and fracture toughness compared to other dental ceramic systems. Although zirconia has outstanding mechanical properties, the phenomenon of decrease in the life-time of zirconia resulted from degradation in flexural strength after low temperature aging has been reported. PURPOSE. The objective of this study was to investigate degradation of flexural strength of Y-TZP ceramics after various low temperature aging treatments and to evaluate the phase stability and micro-structural change after aging by using X-ray diffraction analysis and a scanning electron microscope (SEM). MATERIAL AND METHODS. Y-TZP blocks of Vita In-Ceram YZ (Vita Zahnfabrik, Bad $S\ddot{a}ckingen$, Germany) were prepared in 40 mm (length) $\times$ 4 mm (width) $\times$ 3 mm (height) samples. Specimens were artificially aged in distilled water by heat-treatment at a temperature of 75, 100, 125, 150, 175, 200, and $225^{\circ}C$ for 10 hours, in order to induce the phase transformation at the surface. To measure the mechanical property, the specimens were subjected to a four-point bending test using a universal testing machine (Instron model 3365; Instron, Canton, Mass, USA). In addition, X-ray diffraction analysis (DMAX 2500; Rigaku, Tokyo, Japan) and SEM (Hitachi s4700; Jeol Ltd, Tokyo, Japan) were performed to estimate the phase transformation. The statistical analysis was done using SAS 9.1.3 (SAS institute, USA). The flexural strength data of the experimental groups were analyzed by one-way analysis of variance and to detect statistically significant differences ($\alpha$= .05). RESULTS. The mean flexural strength of sintered Vita In-Ceram YZ without autoclaving was 798 MPa. When applied aging temperature at below $125^{\circ}C$ for 10 hours, the flexural strength of Vita In-Ceram YZ increased up to 1,161 MPa. However, at above $150^{\circ}C$, the flexural strength started to decrease. Although low temperature aging caused the tetragonal-to-monoclinic phase transformation related to temperature, the minimum flexural strength was above 700 MPa. CONCLUSION. The monoclinic phase started to appear after aging treatment above $100^{\circ}C$. With the higher aging temperature, the fraction of monoclinic phase increased. The ratio of monoclinic/tetragonal + monoclinic phase reached a plateau value, circa 75% above $175^{\circ}C$. The point of monoclinic concentration at which the flexural strength begins to decrease was between 12% and 54%.