Charge-density-waves (CDW) and the related properties of group Vb transition- metal trichalcogetiides are reviewed. These compounds have the common structural unit of the triangular column of the formula MX₃, which is the origin of their low-dimensionality.
The unique structure of NbS₃ is explained by a property of the Peierls state with the wave vector q=0.5b*. The commensurate periodic lattice distortion observed in TaS₃ below 218K is explained in terms of the Fermi surface nesting and the importance of the commensurability energy is stressed. The electrical conductivity below the transition temperature is presented. The conductivity below 100 K is much larger than that extrapolated from above. The contribution of the kinks of CDW (phase solitons) is suggested.
Two kinds of CDW are observed in NbSe₃. Both wave vectors are incommensurate to the host lattice. A possible model of discommensuration is presented. The conductivity of NbSe₃ remains metallic even below the transition temperature, but it is highly non-Ohmic. The field dependence of the conductivity, the effect of impurities and the high frequency noise in the non-Ohmic region reflecting the motion of CDW. Finally, the relation ship between CDW and the superconductivity is discussed.

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The molecular replacement method consists of the three consecutive stages : (1) determination of the orientation of the molecule in the crystal, (2) determination of the position of the molecule and (3) solution of the phase problem.
The problem in the first stage was solved almost satisfactorily by using the rotation function first developed by Rossmann and Blow and recently improved by Crowther.
In the second stage, the problem was not always solved satisfactorily because of several theoretical and/or computational drawbacks inherent to the translation function.
Lack of efficient translation functions of universal applicability prevented the po-tentially much more powerful molecular replacement method from being popular in the structure determinations of macromolecules.
A case of a known model structure is discussed, considering the origins of inefficacy of the translation functions proposed so far, and a new powerful translation function which is highly efficient in computation is proposed.

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