Reduction of ketimine with trichlorosilane was carried out using bisformamide catalyst1a derived from cyclohexanediamine to give the corresponding product in 81% yield with 39% ee. Deprotection of the formyl groups of the catalysts 1 gave the corresponding diamines 2 which were utilized in aldol reaction of acetone with 4-nitrobenzaldehyde. The reaction using 2b in brine afforded the aldol adduct in 81% yield with 29% ee.

Abstract:
Mannich-type reactions of aldimines with silyl enolates and hetero Diels-Alder reactions of aldehydes with Danishef-sky’s diene in the presence of anion catalysts derived from proline were performed to afford the corresponding products in high yields.

Abstract:
The microscopic physical properties of Hardened Cement Paste (HCP) surfaces were evaluated by using Scanning Probe Microscopy (SPM). The cement pastes were cured under a hydrostatic pressure of 400 MPa and the contacting surfaces with a slide glass during the curing were studied. Scanning Electron Microscope (SEM) observation at a magnification of 7000 revealed smooth surfaces with no holes. The surface roughness calculated from the SPM measurement was 4 nm. The surface potential and the frictional force measured by SPM were uniform throughout the measured area 24 h after the curing. However, spots of low surface potential and stains of low frictional force and low viscoelasticity were observed one month after curing. This change was attributed to the carbonation of hydrates.

Abstract:
Contact angle of ethylene glycol and formamide on (100) faces of NaCl, KCl, and KBr single crystal was measured, and the specific surface free energy (SSFE) was calculated. Dispersion component of the SSFE was 90.57, 93.78, and 99.52 mN·m^{-1} for NaCl, KCl, and KBr, respectively. Polar component of the SSFE was 1.05, 0.65, and 0.45 mN·m^{-1} for NaCl, KCl, and KBr. Such a large ratio of dispersion component of SSFE results from the neutrality of the crystal surface of alkali halide. Lattice component of alkali halide is 780, 717 and 689 kJ·mol^{-1} for NaCl, KCl, and KBr. The larger lattice enthalpy decreases dispersion component, and increases polar component of the SSFE. The larger lattice enthalpy is considered to enhance the rumpling of the crystal surface more strongly, and such rumpling is considered to decrease the neutrality of the crystal surface.

Abstract:
The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field $ \phi : S^1 \to S^1 $. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has an infinite number of inequivalent quantizations. It is also shown that when a central extension is introduced into the algebra, the winding operator and the momenta operators satisfy anomalous commutators.

Abstract:
Target space duality is reconsidered from the viewpoint of quantization in a space with nontrivial topology. An algebra of operators for the toroidal bosonic string is defined and its representations are constructed. It is shown that there exist an infinite number of inequivalent quantizations, which are parametrized by two parameters $ 0 \le s, t < 1 $. The spectrum exhibits the duality only when $ s = t $ or $ -t $ (mod 1). A deformation of the algebra by a central extension is also introduced. It leads to a kind of twisted relation between the zero mode quantum number and the topological winding number.

Abstract:
We consider the $ U(1) $ sigma model in the two dimensional space-time which is a field-theoretical model possessing a nontrivial topology. It is pointed out that its topological structure is characterized by the zero-mode and the winding number. A new type of commutation relations is proposed to quantize the model respecting the topological nature. Hilbert spaces are constructed to be representation spaces of quantum operators. It is shown that there are an infinite number of inequivalent representations as a consequence of the nontrivial topology. The algebra generated by quantum operators is deformed by the central extension. When the central extension is introduced, it is shown that the zero-mode variables and the winding variables obey a new commutation relation, which we call twist relation. In addition, it is shown that the central extension makes momenta operators obey anomalous commutators. We demonstrate that topology enriches the structure of quantum field theories.

Abstract:
R.P. Feynman showed F.J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We formulate both a special relativistic and a general relativistic versions of Feynman's derivation. Especially in the general relativistic version we prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge and gravitational fields. We also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context.

Abstract:
We consider the uncertainty relation between position and momentum of a particle on $ S^1 $ (a circle). Since $ S^1 $ is compact, the uncertainty of position must be bounded. Consideration on the uncertainty of position demands delicate treatment. Recently Ohnuki and Kitakado have formulated quantum mechanics on $ S^D $ (a $D$-dimensional sphere). Armed with their formulation, we examine this subject. We also consider parity and find a phenomenon similar to the spontaneous symmetry breaking. We discuss problems which we encounter when we attempt to formulate quantum mechanics on a general manifold.

Abstract:
A definition of quantum mechanics on a manifold $ M $ is proposed and a method to realize the definition is presented. This scheme is applicable to a homogeneous space $ M = G / H $. The realization is a unitary representation of the transformation group $ G $ on the space of vector bundle-valued functions. When $ H \ne \{ e \} $, there exist a number of inequivalent realizations. As examples, quantum mechanics on a sphere $ S^n $, a torus $ T^n $ and a projective space $ \RP $ are studied. In any case, it is shown that there are an infinite number of inequivalent realizations.