Cyclic Group Actions on 4-Manifolds

Let X be a closed, oriented Riemannian 4-manifold. Suppose that a cyclic group Z( _p (p is prime) acts on X by an orientation preserving isometry with an embedded Riemann surface as fixed point set. We study the representation of Z _p on the Spin^c-bundles and the Z _p-invariant moduli space of the solutions of the Seiberg–Witten equations for a Spin^c-structure X. When the Z _p action on the determinant bundle det L acts non-trivially on the restriction L| over the fixed point set , we consider -twisted solutions of the Seiberg-Witten equations over a Spin^c-structure ' on the quotient manifold X/Z _p X', (0,1). We relate the Z _p -invariant moduli space for the Spin^c-structure on X and the -twisted moduli space for the Spin^c-structure on X'. From this we induce a one-to-one correspondence between these moduli spaces and calculate the dimension of the -twisted moduli space. When Z _p acts trivially on L|, we prove that there is a one-to-one correspondence between the Z _p -invariant moduli space M( ^Zp and the moduli space M (") where ' is a Spin^c-structure on X' associated to the quotient bundle L/Z _p X'. vskip0pt When p = 2, we apply the above constructions to a Kahler surface X with b ₂ ⁺ (X) > 3 and H ₂(X;Z) has no 2-torsion on which an anti-holomorphic involution acts with fixed point set , a Lagrangian surface with genus greater than 0 and []2H ₂(H ;Z). If _K ^X 2 > 0 or K _X ² = 0 and the genus g()> 1, we have a vanishing theorem for Seiberg–Witten invariant of the quotient manifold X'. When K _X ² = 0 and the genus g()= 1, if there is a Z ²-equivariant Spin^c-structure on X whose virtual dimension of the Seiberg–Witten moduli space is zero then there is a Spin^c-structure " on X' such that the Seiberg-Witten invariant is ±1.     

Surface Measures and Tightness of (r,p)-Capacities on Poisson Space

We prove tightness of (r,p)-Sobolev capacities on configuration spaces equipped with Poisson measure. By using this result we construct surface measures on configuration spaces in the spirit of the Malliavin calculus. A related Gauss-Ostrogradskii formula is obtained.     

Decompositions of Fundamental Groups of Closed Surfaces into Free Constructions

Let T be a closed surface. It is proven that any decomposition of ₁(T,x) into an amalgamated product (or, more generally, into the fundamental group of a finite graph of groups) with f.g. edge group(s) is almost geometric. A problem of H. Zieschang is solved and the edge rigidity property is investigated.     

Birational automorphisms of quartic Hessian surfaces

We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice of rank 26 and signature . The generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of Kondo. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface.

     

Finite-Size Effects for the Potts Model with Weak Boundary Conditions

Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L ^–d , the same as for periodic boundary conditions, the shift is much larger, of order L ^–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust.     

Relationship between coffee husk caffeine degradation and respiration of Aspergillus sp. LPBx in solid-state fermentation

Studies were carried out in a packed-bed column fermentor using coffee husk as substrate in order to verify a relationship between caffeine degradation and the respiration of Aspergillus sp. LPBx. Fermentation conditions were optimized by using factorial design experiments. The kinetic study showed that the caffeine degradation was related to the development of mold and its respiration and also with the consumption of reducing sugars present in coffee husk. From the values obtained experimentally for oxygen uptake rate and CO₂ evolved, we determined a biomass yield of 3.811 g of biomass/g of consumed O₂ and a maintenance coefficient of 0.0031 g of consumed O₂/(g of biomass·h). The maximum caffeine degradation achieved was 90%.     

The Surface Energy of MgO: Multiscale Reconstruction from Thermal Groove Geometry

The surface energy of MgO is determined using experimental data collected from equilibrated thermal grooves circumscribing island grains. Local equilibrium assumptions at each groove require that the Herring equations be satisfied at each data site, thereby yielding a large and overdetermined system of equations involving the surface energy . This inverse problem is then solved using a new technique that is statistical in nature and multiscale in implementation. The resulting discrete solution represents a statistically significant representation of the surface energy of MgO as a function of surface orientation. Comparisons to results derived from a more traditional approach, along with suggested further applications, are discussed.     

Unusual Behavior of Nanocrystalline Strontium Oxide Toward Hydrogen Sulfide

The thermodynamically favored reaction of solid strontium oxide with gaseous hydrogen sulfide is kinetically enhanced to a large degree by the use of higher surface area nanocrystalline SrO in the form of brush-like collections of metal oxide fibers. An unusual feature is that the reaction SrO + H₂S SrS + H₂O proceeds stoichiometrically at room temperature, but at higher temperatures the reaction efficiency goes down, apparently due to rapid temperature induced crystal growth of the nanocrystalline SrO. The samples studied vary in crystallite size from 20 to 27nm, while average particle size (nanocrystal aggregates) varies in the following order; aerogel prepared SrO (100nm) 相似文献   

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate