How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrolysis of HNSO2: A potential route for atmospheric production of H2SO4 and NH3

The hydrolysis of sulfonylamine (HNSO₂) results in the formation of sulfuric acid along with ammonia, and is of significant interest due to their negative impact on environment and life on Earth. The formation of H₂SO₄ through the reaction of HNSO₂ with (H₂O)_2-4 has been studied using high level electronic structure calculations. This hydrolysis reaction is a step-wise process, in the first step a H-atom from H₂O is transferred to the N-atom of HNSO₂ which results in the formation of NH₂, and in the next step, H₂SO₄, NH₃ and water molecule(s) are formed. The results show that the energy barrier associated with the formation of intermediates and product complexes is reduced by 7 to 10 kcal/mol when the number of water molecules is increased from 2 to 4. The rate constant was calculated using canonical variational transition state theory with small curvature tunneling correction over the temperature range of 200 to 1000 K. At 298 K, the calculated rate constant for the formation of intermediate in the first step is 2.24 × 10⁻¹⁶, 1.03 × 10⁻¹², and 2.10 × 10⁻¹¹ cm³ mol⁻¹ s⁻¹, respectively, for the reaction with water dimer, trimer and tetramer. The calculated enthalpy and free energy show that the reaction corresponding to the formation of H₂SO₄ is highly exothermic and exoergic in nature.     

Topological density of ccc Boolean algebras--Every cardinality occurs

For every uncountable cardinal there is a ccc Boolean algebra whose topological density is .

     

The Necessary Maximality Principle for c. c. c. forcing is equiconsistent with a weakly compact cardinal

The Necessary Maximality Principle for c. c. c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dilation equations and Markov operators

Using the theory of Markov operators, we give a new proof of the known fact saying that for every positive integers N and k>1, and for every nonnegative reals c₀,…,cN satisfying the first sum rule the dilation equation

     

Iterative approximation of a zero of accretive operator in Banach space

This paper introduces an iteration scheme for viscosity approximation of a zero of accretive operator in a reflexive Banach space with weakly continuous duality mapping. A new iterative sequence is introduced and strong convergence of the algorithm {x_n} is proved. The results improve and extend the results of Su [Xiaolong Qin, Yongfu Su, Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 320 (2007) 415-424] and some others.     

First countable pseudocompactifications

A general construction for creating first countable pseudo-compact extensions of certain spaces is given. We show that there exists a first countable σ-compact space with no first countable pseudocompactification. We construct a new Suslinean example, namely, a first countable, pseudocompact, ccc, non-separable space. Assuming Martin's Axiom, we can further achieve a point-countable base. A second application is to unify and clarify examples of Scott and Watson of pseudocompact, metaLindelöf and point-countable base non-compact spaces.     

Universal forcing notions and ideals

Our main result states that a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give some results concerning cardinal characteristics of the σ-ideals determined by those universality parameters. Both authors acknowledge support from the United States-Israel Binational Science Foundation (Grant no. 2002323). Also, we would like to thank the referee for valuable comments and suggestions concerning the exposition of the paper. This is publication 845 of the second author     

Local regularity theorems for the stationary thermistor problem with oscillating degeneracy

In this paper we present some regularity results for solutions to the system −Δu=σ(u)²|∇φ|, div(σ(u)∇φ)=0 in the case where σ(u) is allowed to oscillate between 0 and a positive number as u→∞. In particular, we show that u is locally bounded if σ(u) is bounded below by a suitable exponential function.     

Low-regularity solutions of the periodic general Degasperis-Procesi equation

This paper studies low-regularity solutions of the periodic general Degasperis-Procesi equation with an initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic general Degasperis-Procesi equation.