Countably compact topological group topologies on free Abelian groups from selective ultrafilters

Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c² using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom.     

QN-spaces, wQN-spaces and covering properties

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).     

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense.     

Shape transition from InAs quantum dash to quantum dot on InP(3 1 1)A

We report on the shape transition from InAs quantum dashes to quantum dots (QDs) on lattice-matched GaInAsP on InP(3 1 1)A substrates. InAs quantum dashes develop during chemical-beam epitaxy of 3.2 monolayers InAs, which transform into round InAs QDs by introducing a growth interruption without arsenic flux after InAs deposition. The shape transition is solely attributed to surface properties, i.e., increase of the surface energy and symmetry under arsenic deficient conditions. The round QD shape is maintained during subsequent GaInAsP overgrowth because the reversed shape transition from dot to dash is kinetically hindered by the decreased ad-atom diffusion under arsenic flux.     

Sansalvamide A固相合成新方法

报道了Pd催化丁基二乙基硅烷树脂与N-Boc-4-溴代苯丙氨酸甲酯直接反应形成Si—Ar键一步构建出硅基连接分子的新方法, 并采用Boc策略增长肽链, 以PyBOP (benzotriazole-1-yl-oxy-tris-pyrrolidino-phosphonium hexafluoro- phosphate)为环合剂固相合成了sansalvamide A.     

Microstructural evolution of decagonal quasicrystal in the undercooled Al72Ni12Co16 alloy melts

The microstructure evolution of decagonal quasicrystals in Al₇₂Ni₁₂Co₁₆ alloy was investigated by the electromagnetic melting and cyclic superheating method. Single-phase decagonal quasicrystals have been obtained when the undercoolings were larger than 60 K. The decagonal quasicrystals formed at various undercoolings show different microstructural morphologies. Furthermore, grain refinement was found near the undercooling of 120 K. Based on current thermodynamic and dendrite growth theories, a dimensionless superheating parameter was adopted to explain the effect of processing conditions on the microstructure of Al₇₂Ni₁₂Co₁₆ alloy. The result indicate that the fine equiaxied microstructure of decagonal quasicrystal (D-phase) formed near on undercooling of 120 K originates from the break-up of dendrites.     

Global existence of analytic solutions to the Cauchy problem in a complex domain

We present results on the global existence of analytic solutions to the Cauchy problem in starshaped or convex complex domains. No growth conditions are imposed. Our results rely on a notion of solution-tube that we introduce. à la mémoire de Jean Leray     

Chemical Constituents of Ligusticum sinensis Oliv.

The new phenylpropanoid diglycoside ligusinenoside A ( 1 ), and the two new 8,4′‐oxyneolignan(‘8‐O‐4′‐neolignan’) diglycosides ligusinenosides B ( 2 ) and C ( 3 ), together with nine known compounds, were isolated from the rhizomes of Ligusticum sinensis Oliv. The structures of 1 – 3 were elucidated on the basis of spectroscopic analyses.     

Unions of three starshaped sets in R2

LetS be a compact, simply connected set inR ². If every boundary point ofS is clearly visible viaS from at least one of the three pointsa, b, c, thenS is a union of three starshaped sets whose kernels containa, b, c, respectively. The result fails when the number three is replaced by four.As a partial converse, ifS is a union of three starshaped sets whose kernels containa, b, c, respectively, then the set of points in the boundary ofS clearly visible from at least one ofa, b, orc is dense in the boundary ofS.Supported in part by NSF grant DMS-8705336.     

Resolvability properties via independent families

The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable.