We prove that there is a unique way to construct a geometric scale of Hilbert spaces interpolating between two given spaces. We investigate what properties of operators, other than boundedness, are preserved by interpolation. We show that self-adjointness is, but subnormality and Krein subnormality are not. On the way to this last result, we establish a representation theorem for cyclic Krein subnormal operators.

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Japan’s lunar probe satellite “Kaguya”, China’s lunar probe satellite “Chang’ e-1 lunar probe” left the earth on September 14th, 2007 and October 24th, 2007, began the exploration to the moon. The launching of the China’s lunar satellite is the proud to the global Chinese. However, at the same time as we are proud of the event, we must admit that the pictures published which were sent back by Japanese are clearer and more beautiful than Chinese. While we are saying that the Japan has a better technology, maybe we also need to say that the Japanese can hold better chance than Chinese when taking the pictures. The following two pictures were sent back by the satellite. Picture one is sent back by Japan’s satellite, Picture two is sent back by China’s. It can be seen that there is a long way for China if we want to become stronger at science technology. We also hope that we can have some contribution in the prosperity of China now and in the future.

Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A∞-functor from the Fukaya category of X to the category of matrix factorizations of W. It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.

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