Maxwell's Demon and detailed balancing

A particle of molecular dimensions which can exist in two states is associated with a membrane pore through which molecules of a gas can pass. The gas molecules from two identical phases on either side of the membrane may pass only when the particle is in one particular state. If certain restrictions are imposed on the system, then the particle appears to act like a Maxwell's Demon⁽¹⁾ which “handles” the gas molecules during their passage through the pore.     

Cauchy and the infinitely small

We consider Cauchy's use of the infinitely small in his textbooks. He never examined fully his concept of variables with limit zero, and he sometimes argued as if he were using actual infinitesimals. Occasionally he adopted an epsilon-delta approach. The author argues that historical evaluations of mathematical analysis may and should be made in the light of both standard and non-standard analysis. From this point of view, Cauchy's move toward founding analysis entirely on the standard real number system does not seem to have been inevitable. Some historical observations by the founder of non-standard analysis, Abraham Robinson, are extended, and in one case contested. It is shown that some of Cauchy's alleged errors are explained if he is admitted to have been thinking of actual infinitesimals and infinitely large integers. Cauchy's definitions of differential in his textbooks are examined, and the author shows that the earlier of his two definitions of total differential works well, but the later does not.     

On stationary baroclinic planetary dipole-vortices in a continuously-stratified fluid of finite depth

It is qualitatively known that the gravest mode associated with a vertical normal-mode decomposition of a stationary, baroclinic modon in a continuously-stratified fluid of finite depth on a -plane necessarily contains an exterior downstream Rossby wave field if the background zonal flow is eastward. An. exact solution is presented describing this situation which satisfies the correct upstream no-waves constraint.     

Actinophyllic acid, a potent indole alkaloid inhibitor of the coupled enzyme assay carboxypeptidase u/hippuricase from the leaves of Alstonia actinophylla (Apocynaceae)

Bioassay-guided fractionation of the aqueous extract of the leaves of Alstonia actinophylla with use of a coupled enzyme assay, CPU/hippuricase, to detect carboxypeptidase U inhibitors led to the isolation of a novel indole alkaloid, actinophyllic acid (1). The structure of 1 was determined from detailed 2D NMR studies. Actinophyllic acid was found to be a potent inhibitor of the coupled enzyme assay with an IC(50) of 0.84 microM. Actinophyllic acid possesses a unique 2,3,6,7,9,13c-hexahydro-1H-1,7,8-(methanetriyloxymethano)pyrrolo[1',2':1,2]azocino[4,3-b]indole-8(5H)-carboxylic acid skeleton.     

Nickel(II) and copper(II) complexes of 5-substituted-salicylaldehyde thiosemicarbazones

Binuclear nickel(II) and copper(II) complexes with four 5-methoxysalicylaldehyde N(3)-substituted thiosemicarbazones and nickel(II) complexes of four 5-nitro-salicylaldehyde N(3)-substituted thiosemicarbazones have been prepared and characterized. I.r., electronic, and e.s.r. spectra of the complexes, as well as i.r., electronic, and 1H- and 13C-n.m.r spectra of the thiosemicarbazones, have been obtained. None of these compounds show significant growth inhibitory activity against the fungi Aspergillus niger and Paecilomyces variotii.     

Above the surface multifragmentation of surface scattered fullerenes

C(60) (-) ions were scattered from a gold surface at impact energies of 80-900 eV. The C(n) (-) fragments abundance distribution (odd and even) and the sharp fragmentation threshold observed, point at a prompt shattering event. The measured angle and energy distributions of the C(n) (-) fragments (n=2-12) provide clear evidence for a multifragmentation process where the superheated fullerenes leave the surface "intact" and disintegrate away from the surface.     

Where does the planar-to-nonplanar turnover occur in small gold clusters?

Several levels of theory, including both Gaussian-based and plane wave density functional theory (DFT), second-order perturbation theory (MP2), and coupled cluster methods (CCSD(T)), are employed to study Au6 and Au8 clusters. All methods predict that the lowest energy isomer of Au6 is planar. For Au8, both DFT methods predict that the two lowest isomers are planar. In contrast, both MP2 and CCSD(T) predict the lowest Au8 isomers to be nonplanar.     

Multireference second-order perturbation theory: how size consistent is "almost size consistent"

A systematic study of the deviation from size consistency of the multireference second-order Moller-Plesset perturbation theory (MRMP2) method is presented. The size-consistency error is shown to depend on the number of monomers in a supermolecule calculation, size of basis set, number of correlated valence electrons, and size of active space. HF, F(2), and N(2) are used as test cases, with stretched bonds, to include simple, well-defined multireference character. This is essential in ensuring that MRMP2 is being tested as a multireference method. It is concluded that the MRMP2 and other multireference perturbation theory methods can exhibit significant size-consistency errors, and that the size of the error depends on the manner in which the perturbation theory is implemented.