Report of the 9th Chubu-Area Colloquium

9th Month Thesis Report

environmental effects of gol-e-gohar iron ore mine on groundwater of the area

gol-e-gohar iron ore mine of sirjan in southern part of iran is a large open pit that operates below the groundwater table and during mining operation, dewatering is required to prevent operation processes from flooding. current operation is going on by digging wells in or out of the pit and pumping to prevent flooding. as a result of the former dewatering operation a vast deep cone of depressi...

Report on the 9th International Congress on Peritoneal Surface Malignancies

The 9 th International Congress on Per itoneal Sur face Malignancies, sponsored by the Peritoneal Surface Oncology Group International (PSOGI) and organized by the Netherlands Cancer Institute, was held in Amsterdam, the Netherlands, from October 9 to 11, 2014, with over 650 delegates from 66 countries attending the meeting. With the central theme to summarize the global progresses in peritonea...

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...

Solution of the 9th Homework

Proof. Let us first assume that c > 0. To prove that sup(cA) = c(sup A), we claim that sup(cA) ≤ c(sup A) and sup(cA) ≥ c(sup A). For the first inequality, let a′ ∈ cA be arbitrary. Then a′ = ca for some a ∈ A. But since a ≤ sup A, we have a′ = ca ≤ c(sup A). This shows that c(sup A) is an upper bound of cA, hence we have sup(cA) ≤ c(sup A). The reverse inequality also follows in a similar mann...