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W h e n an aqueous AgCI0,-sodium dodecylsulphate (SDS)-isopropyl alcohol (Pr' OH) solution was photolysed with 253.7 nm light, a sharp and intense absorption band of colloidal silver (A = 390-400 nm) appeared after a relatively long induction period. In contrast, t h e sharp colloidal absorption rapidly developed when an AgCI0,-SDS-acetone [(CH,),CO] solution was irradiated under t h e s a m e conditions. It has been shown by chemical analysis and TEM characterization of t h e reduced silver that some of t h e colloidal silver agglomerates formed as a result of photolysis were peptized to fine silver particles during irradiation. Acetone ketyl radical formed by excitation of (CH3),C0 with 253.7 nm light seems to have an ability to peptize colloidal agglomerate in t h e solution phase (peptizing action). A novel ' photo-acetone method' available for preparation of fine metal particles has been proposed and applied to obtain colloidal gold, copper and platinum.We have studied photochemical formation of metal particles and thin films under fairly mild condition^.'-^ In a previous paper,, we reported that colloidal silver, gold and platinum are formed by irradiation of AgClO, , HAuCl, and Na,PtCl,

Photochemical formation of colloidal silver, colloidal gold and silver-gold (Ag-Au) composite colloids under mild conditions has been studied. Irradiation of either aqueous AgCIO4 or HAuCI, solution in the presence of sodium alginate (SA) with 253.7 nm light yielded colloidal silver or gold, whose particle diameter was 10-30nm or 40-60 nm, respectively. The Ag-Au composite colloids consisting of mixtures of silver and gold domains (particle diameter 30-150 nm) have been prepared and their extinction spectra have been examined on the basis of a conventional Mie theory in combination with an effective medium theory to estimate the optical constants of these colloids. It has been shown that the extinction spectra of the Ag-Au composite colloids are completely different from those of Ag-Au alloy colloids, in that the former have two extinction maxima close to the colloidal extinction bands of pure silver and gold, in contrast to a single extinction maximum of the latter. The importance of natural, high-molecular carboxylic acids such as alginic acid in the photochemical formation of metal colloids and thin films has been stressed.

In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. In the present paper, we reconstruct their theory by using the "generalized Shestakov-Umirbaev inequality", which was recently given by the author. As a consequence, we obtain a more precise tameness criterion for polynomial automorphisms. In particular, we deduce that no tame automorphism of a polynomial ring admits a reduction of type IV.

We give a generalization of the Shestakov-Umirbaev inequality which plays an important role in their solution of the Tame Generators Problem on the automorphism group of a polynomial ring. As an application, we give a new necessary condition for endomorphisms of a polynomial ring to be invertible, which implies Jung's theorem in case of two variables.

In [4], Kuroda generalized Roberts' counterexample [5] to the fourteenth problem of Hilbert. The counterexample is given as the kernel of a locally nilpotent derivation on a polynomial ring. We replace his construction of the invariant elements by a more straightforward construction and give a more precise form of invariant elements.

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This paper presents a family of new counterexamples to Hilbert's Fourteenth Problem. They are realized as subfields of the rational function field of four variables over a field of characteristic zero of transcendence degree three. It was previously not known whether any counterexample could be found as a subfield of a rational function field of four variables, or whether counterexamples with minimal transcendence degree three could exist.