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Importance of light source in 3 dimensional virtual space where its division from real world becomes gradually vague contributes outstandingly to the results as much as compared to the importance of light in real world. Since the light tracking technique was announced in 1980, the study on 3 dimensional computer graphics to express property of light in a similar principle to actual phenomenon has realized gorgeous development as much as realizing the diffused reflection phenomenon of light by photon. Such development presents a possibility of realizing all the phenomena recognized by human's vision in 3 dimensional virtual space. This means that it becomes possible to express a lot of natural phenomena by light in the same principle, and its representative example is realization of caustic effects generated by a complicated phenomenon of reflection, refraction, scattering, diffraction, etc. of light.This study has deduced variables appearing in realizing light phenomenon at virtual space by performing comparison experiments on the basis of general physical phenomenon of light and principle of 3 dimensional computer graphics to express this, and has obtained a result that such variables can be minutely changed by various environments and secondary variables due to interaction between two variables can happen. However, natural phenomenon contains diverse variables that are still unpredictable, so quantitative evaluation of virtual space research for expressing this more exactly should be realized continuously.

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The interdisciplinary study addresses the G$\ddot{o}$del's ontology from the perspective of the mathematical maximality. We first investigate G$\ddot{o}$del's God having all the positive properties as the intersection of ultrafilters in his own ontological proof(1970). Regarding the axiom of choice and his compactness theorem(1930), the next part discusses the ontological meaning of the maximal rather than the maximum in terms of an episteme space. The results show that G$\ddot{o}$del's ontological arguments imply all the existence of the maximal reality, and all the human's epistemological boundedness as well.

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The notion of a compact topological space is an abstraction of certain important Properties of the set of real numbers. In this note we will introduce The Concept of Maximal Compactness, and Study Some Properties on a Space X having the maximal Compactness. We have the following results as main theorems £º (1) If (X,T) is Compact T©ü Space then (X.T) has the maximal Compactness. (2) A topological Space (X.T) has the maximal Compactness iff the closed sets in X Coincide with the Compact Sets in X. (3) If (X,T) has the maximal Compactness then (X,T) is Kc Space. (4) Let (X,T) be a topological Space which Satisfies the first axiom of Countability. Then (X,T) has the maximal Compactness iff (X,T) is Compact, T©ü Space. (5) Let X = Xi (i = 1,2,¡¦¡¦n). Then the product Spce ¡à Xi has the maximal Compactness iff the Space X is Compact, T©ü.

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In this study, the factors that have strong relationship with size effects on forging simulation are investigated and then a dimensionless concept is studied by implemented into the forging simulator. The approaches are applied to simulating a micro former forging process, a upsetting process of coupled analysis and a large-scaled crank shaft forging process . A micro former forging process involves a piercing process to make a hole of 0.7mm diameter of the product whose maximum diameter is 3mm. On the contrary the weight of crank shaft reaches more than the forged 900kg. A upsetting process is investigated changes of temperature by size effects. The former is small while the letter is large compared to a common forging for mechanical or automotive parts. The micro former forging process and the crank shaft forging process are simulated isothermal assumption. The upsetting process is simulated non-isothermal assumption.

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The terminology of bioenergy means the biomass. The urge to make biomass more Quantitative has led to the wide spread Inclusion of plants, grains and all organic substances. Biomass for nonelectrical uses In the our country accounts for approximately 2¡­3% of the total energy consumption In 1999. Biomass also generally produces lower gas pollutant omission than fossil energies and to attractive because It's a renewable energy source .

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