I am reading an article about these devices in Scientific American の特集. It seems that local behavior of squares which choose to replicate based on the surrounding squares can generate interesting global dynamics. A turing machine which …

自己開発のゲームの設計を記録して見ます。 Check Promotion部分1. Detecting all riddles for a level are clear. This is based on a comparison of two ScoreTracker data members: numRiddles and riddleNum. Analogous members are kept in the RiddleG…

Finally, getting to the definition of the integral: let g be a simple measurable function on an m-measurable set E, where E = UNION(Ei), and g(x)=ai if x element of Ei. Then define the integral of g over E: INTEGRAL(E)(g) = SIGMAsubi(ai*m(…

"次の定理の証明を読んで混乱しました。 Theorem: If a function f is Riemann integrable over E, then it is also Lebesgue integrable and the Riemann integral equals the Lebesgue integral. In addition, the function f is continuous almost everyw…

最近フーリエー級数を勉強する時にLebesgue積分の事を呼んでいます。 I found this somewhat confusing, as I had always believed that an integral, in two dimensions the area under the curve, had a single definition as explored by Newton and Leib…

以前にTorusの話を行いましたからその説明を済ませます。 Given that we have determined H0, H1, and H2, the homology groups on the torus, we now turn our attention to the Betti numbers h0, h1, and h2. The two groups isomorphic to C2, H0 and H2…

The next homology group and Betti number to be examined is the second homology group of the cube (H2(cube)). The only two 2-cycles on a cube are null and ABCDEF (where these are the six faces). These are not homologous, as the only two-bou…

以前に立方体のzeroth homology groupを計算しました。 今回はキューブのH1を考えます。 Points to consider when calculating H1(cube) are: 1. cycles are 1-boundaries (bound 2-chains) 2. There are 64 1-cycles on a cube. This point is a bit bemusi…