Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

On a construction of critical graphs which are not sensitive

Let ?(G) be theclosed-set lattice of a graphG. G issensitive if the following implication is always true for any graphG′: ?(G)??(G′)?(G)?G′G iscritical if ?(G)??(G-e) for anye inE(G) and ?(G)??(G+e) for anye in \(\left( {\bar G} \right)\) where \(\bar G\) is the complement ofG. Every sensitive graph is, a fortiori, critical. Is every critical graph sensitive? A negative answer to this question is given in this note.     

PHOTOCYCLOADDITION REACTION OF 5,7-DIMETHOXYCOUMARIN TO THYMIDINE

Abstract— The photocycloaddition reaction of 5,7-dimethoxycoumarin to thymidine on direct irradiation (λ > 300 nm) is studied as a model for photosensitization reaction of furocoumarins. The major photoadducts were isolated by silica gel column and gel permeation chromatography. Each component of the photoadducts was further separated by reverse phase, paired-ion high performance liquid chromatography. The structure of these photoproducts isolated is consistent with 1:1 C₄-cycloadducts in accordance with characteristics of their UV, IR, NMR and mass spectra and elemental analysis data. The stereochemistry of each isomer was studied by Fourier transform NMR, UV and IR spectra. The fraction C has the anti head-to-tail configuration and the fraction D has the configuration of anti head-to-head. The fractions A and B probably have the syn configuration.