A counterexample to the fourteenth problem of Hilbert in dimension three

Analytical pyrolysis as a direct method to determine the lignin content in wood

“…Nevertheless several efforts were made to assign lignin-derived pyrolysis products using wood, lignin isolated from wood and/or lignin model compounds [17,57,58,63,[70][71][72][73][74] especially in the last years [75][76][77][78]. Model compound studies have shown that the b-O-4 linkage is cleaved extensively in pyrolysis, but only partial cleavage of carbon-carbon bonds are reported to take place [57,73], and that the phenolic forms are in general much more reactive than the non-phenolic forms [75,76]. Unfortunately nothing could be found about the lignin structure of larch wood.…”

Direct analysis of lignin and lignin-like components from softwood kraft pulp by Py-GC/MS techniques

“…Because not all the linkages between the lignin subunits are cleaved during pyrolysis, the standard used for external calibration needs to be structurally similar to the lignin to be quantified. Model compound studies have shown that the beta aryl ether bond is cleaved extensively in pyrolysis, but only partial cleavage of carbon-carbon bonds are reported to take place [4,5].…”

Algebra of bounded polynomials on a set Zariski closed at infinity cannot be finitely generated

“…outside any compact set) such that its algebra cannot be finitely generated. It is a geometric interpretation of a recent result of Shigeru Kuroda in [12] on the existence of counterexamples to Hilbert's XIVth Problem in low dimension and transcendence degree. More precisely, in [12] it is shown that there exist infinitely generated subalgebras of the ring of polynomials in four variables arising from intersections of this ring with a subfield L of the ring of fractions R(X) of transcendence degree three.…”

“…It is a geometric interpretation of a recent result of Shigeru Kuroda in [12] on the existence of counterexamples to Hilbert's XIVth Problem in low dimension and transcendence degree. More precisely, in [12] it is shown that there exist infinitely generated subalgebras of the ring of polynomials in four variables arising from intersections of this ring with a subfield L of the ring of fractions R(X) of transcendence degree three. The example of Krug can be a basic semialgebraic set and we feel that in context of attempts to generalise Schmüdgen's Positivstellensatz to a non-compact case it is an interesting question to ask whether infinitely generated algebras of bounded polynomials are really obstacles.…”