On certain indestructibility of strong cardinals and a question of Hajnal

A model in which strongness of is indestructible under ⁺ -weakly closed forcing notions satisfying the Prikry condition is constructed. This is applied to solve a question of Hajnal on the number of elements of { |2 <}.     

Some results on the nonstationary ideal

The strength of precipitousness, presaturatedness and saturatedness of NS_κ and NS _κ ^λ is studied. In particular, it is shown that:

1. The exact strength of “ $NS_{\mu ^ + }^\lambda $ for a regularμ > max(λ, ?₁)” is a (ω,μ)-repeat point.
2. The exact strength of “NS_κ is presaturated over inaccessible κ” is an up-repeat point.
3. “NS_κ is saturated over inaccessible κ” implies an inner model with ?αo(α) =α ⁺⁺.

     

On tall cardinals and some related generalizations

We continue the study of tall cardinals and related notions begun by Hamkins in 2009 and answer three of his questions posed in that paper.     

Aqueous enantioselective hydrogenation of methyl 2-acetamidoacrylate with Rh-MeDuPHOS occluded in PDMS

A new chiral heterogeneous catalytic system obtained by occlusion of the Rh-MeDuPHOS complex in a polydimethylsiloxane film was tested in the asymmetric hydrogenation of methyl 2-acetamidoacrylate in aqueous medium.     

The nonstationary ideal on ℵ2

We construct a model in which the filter of ω-closed unbounded subsets of ℵ₂ is precipitous and a model in which the filter of closed unbounded subsets of ℵ₂ is precipitous. For the first model we need a measurable cardinal, and for the second a measurable cardinal of order 2. Both results are equiconsistent.     

On some configurations related to the Shelah Weak Hypothesis

We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible. Received: 8 September 1999 / Published online: 3 October 2001     

Synthesis and electrical properties of (LiCo3/5Fe1/5Mn1/5)VO4 ceramics

(LiCo_3/5Fe_1/5Mn_1/5)VO₄ ceramic was synthesized via solution-based chemical method. X-ray diffraction analysis was carried out on the synthesized powder sample at room temperature, which confirms the orthorhombic structure with the lattice parameters of a = 10.3646 (20) Å, b = 3.7926 (20) Å, c = 9.2131 (20) Å. Field emission scanning electron microscopic analysis was carried out on the sintered pellet sample that indicates grains of unequal sizes (～0.1 to 2 μm) presents average grains size with polydisperse distribution on the surface of the ceramic. Complex impedance spectroscopy (CIS) technique is used for the study of electrical properties. CIS analysis identifies: (i) grain interior, grain boundary and electrode–material interface contributions to electrical response (ii) the presence of temperature dependent electrical relaxation phenomena in the ceramics. Detailed conductivity study indicates that electrical conduction in the material is a thermally activated process. The variation of A.C. conductivity with frequency at different temperatures obeys Jonscher's universal law.     

Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.     

Characterization of Powder Beds by Thermal Conductivity: Effect of Gas Pressure on the Thermal Resistance of Particle Contact Points

The thermal conductivity of ceramic powder packed beds was measured at temperatures below 100 °C for various powder sizes and compositions and under different gas atmospheres. Measurements at low pressures (down to 10 Pa) combined with a theoretical model allowed the elucidation of geometrical and thermal resistance parameters for the contact points between granules. The gap thickness and contact point size were found to be well correlated with the mean particle size. The thermal conductivities of all powders at low pressure were found to differ at most by a factor of two, whereas the solid‐phase conductivities of the powder materials differed by more than one order of magnitude. A theoretical model accounting for the size‐dependence of contact point conductivity is incorporated to rationalize this trend.     

A cardinal preserving extension making the set of points of countable V cofinality nonstationary

Assuming large cardinals we produce a forcing extension of V which preserves cardinals, does not add reals, and makes the set of points of countable V cofinality in κ⁺ nonstationary. Continuing to force further, we obtain an extension in which the set of points of countable V cofinality in ν is nonstationary for every regular ν ≥ κ⁺. Finally we show that our large cardinal assumption is optimal. This material is based upon work supported by the National Science Foundation under Grant no. DMS-0094174.