Fine group gradings of the real forms of sl(4,\C), sp(4,\C), and o(4,\C)

We present an explicit description of the 'fine group gradings' (i.e. group gradings which cannot be further refined) of the real forms of the semisimple Lie algebras sl(4,\C), sp(4,\C), and o(4,\C). All together 12 real Lie algebras are considered, and the total of 44 of their fine group gradings are listed. The inclusions sl(4,\C)\supset sp(4,\C)\supset o(4,\C) are an important tool in our presentation. Systematic use is made of the faithful representations of the three Lie algebras by $4\times 4$ matrices.Comment: 19 page

Comparison of C═C bond hydrogenation in C-4 unsaturated nitriles over Pt/alumina

The hydrogenation of allyl cyanide (but-1-ene-4-nitrile, AC), trans- and cis-crotononitrile (E- and Z-but-2-ene nitrile, TCN and CCN), and methacrylonitrile (2-cyano-1-propene, MCN) were studied, both singly and competitively, over a Pt/alumina catalyst in the liquid phase. Each unsaturated nitrile only underwent C═C bond hydrogenation: no evidence was found for the formation of the saturated or unsaturated amine. The nonconjugated allyl cyanide was found to be the most reactive unsaturated nitrile. Activation energies for the hydrogenation of the C═C bond in AC and MCN were determined giving values of 64 ± 7 kJ mol–1 for AC and 37 ± 4 kJ mol–1 for MCN. The reaction was zero order for both nitriles. Competitive hydrogenations revealed that not only does allyl cyanide react preferentially over the other isomers but also it inhibits the hydrogenation of the other isomers. When all four nitriles were simultaneously hydrogenated, inhibition effects were easily seen suggesting that in terms of strength of bonding to the surface an order of AC > CCN > TCN ∼ MN can be generated

Inner Structure of Spin^{c}(4) Gauge Potential on 4-Dimensional Manifolds

The decomposition of $Spin^{c}(4)$ gauge potential in terms of the Dirac 4% -spinor is investigated, where an important characterizing equation $\Delta A_{\mu}=-\lambda A_{\mu}$ has been discovered. Here $\lambda$ is the vacuum expectation value of the spinor field, $\lambda =\Vert \Phi \Vert ^{2}$, and $A_{\mu}$ the twisting U(1) potential. It is found that when $\lambda$ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.Comment: 11 page

Equivariant Corks

For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on $\partial C$ whose associated pairs (C,g) for all $g \in G$ are distinct smoothings of the pair $(C,\partial C)$. Indeed C embeds in a 4-manifold so that cutting out C and regluing using distinct elements of G yield distinct smooth 4-manifolds.Comment: 9 pages, 3 figure

Characteristics of C-4 photosynthesis in stems and petioles of C-3 flowering plants

Most plants are known as C-3 plants because the first product of photosynthetic CO2 fixation is a three-carbon compound. C-4 plants, which use an alternative pathway in which the first product is a four-carbon compound, have evolved independently many times and are found in at least 18 families. In addition to differences in their biochemistry, photosynthetic organs of C-4 plants show alterations in their anatomy and ultrastructure. Little is known about whether the biochemical or anatomical characteristics of C-4 photosynthesis evolved first. Here we report that tobacco, a typical C-3 plant, shows characteristics of C-4 photosynthesis in cells of stems and petioles that surround the xylem and phloem, and that these cells are supplied with carbon for photosynthesis from the vascular system and not from stomata. These photosynthetic cells possess high activities of enzymes characteristic of C-4 photosynthesis, which allow the decarboxylation of four-carbon organic acids from the xylem and phloem, thus releasing CO2 for photosynthesis. These biochemical characteristics of C-4 photosynthesis in cells around the vascular bundles of stems of C-3 plants might explain why C-4 photosynthesis has evolved independently many times