Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.     

Synthetic thermally reversible gel systems. V

Differential thermal analysis has been used to study the fusion of aqueous thermally reversible gels of gelatin and polyacrylylglycinamide (PAG). In the case of gelatin gels, endotherms close to the melting point are readily observed and these are sometimes preceeded by a small exothermic heat of gel reorganization. Calculations are presented to show that breaking of the gelatin gel network requires only a small fraction of the observed endothermic heat of fusion and that most of the heat is required for melting larger crystallites within gelatin aggregates and for perhaps a helix → coil transition. Failure to observe endotherms by DTA over the known temperature range of fusion of PAG gels is consistent with prior measurements and conclusions. The noncrystallinity of PAG gels and soluble aggregates together with a heat of crosslinking of only ?5 to ?10 kcal/mole of crosslinks places the heat of fusion of PAG gels outside the lower limits of DTA sensitivity.     

Zwei neue pentacyclische dimere des cycloheptatriens

Titanium - catalyzed dimerization of cycloheptatriene affords pentacyclo[7.5.0.0^2,8.0^5,14.0^7,11]tetradeca-3,12-diene, $\text{3}$, and pentacyclo[8.4.0.0^3,7.0^4,14.0^6,11]tetradeca-8,12-diene, $\text{4}$. By heating, $\text{3}$ is converted quantitatively into $\text{4}$.     

Intramolecular cyclization of Z,E,E-1,5,9,-cyclododecatriene by the Cp2TiCl2?LiAlH4 system

The system Cp₂TiCl₂–LiAlH₄, in the absence of ethereal solvents, catalyzes the intramolecular cyclization of Z,E,E-1,5,9-cyclododecatriene, yielding a mixture of C₁₂ hydrocarbons consisting mainly of cis, anti, cis-and cis, syn, trans-tricyclo [7.3.0.0^2,6] dodec-7-ene and 5,6,7,8,9,10-hexahydrobenzocyclooctene.

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Cp₂TiCl₂–LiAlH₄, , Z,E,E,-1,5,9-, C₁₂, , , - , , - [7.3.0.0.^2,6] -7, 5,6,7,8,9,10-.