Excited-state proton transfer in N-methyl-6-hydroxyquinolinium salts: solvent and temperature effects

The excited-state proton transfer (ESPT) reaction of the "super"photoacid N-methyl-6-hydroxyquinolinium (MHQ) was studied using both fluorescence upconversion and time-correlated single photon counting (TCSPC) techniques. The ultrafast ESPT kinetics were investigated in various alcohols and water and determined to be solvent-controlled. The ESPT temperature dependence of MHQ was also studied in various alcohols and compared to that observed for another "super"photoacid, 5,8-dicyano-2-naphthol (DCN2). A full set of kinetic and thermodynamic parameters describing the ESPT was obtained. The protolytic photodissociation rate constant for MHQ was higher than that for DCN2, while the ESPT activation energies of MHQ were smaller. These findings are attributed to the approximately 3 orders of magnitude differences in excited-state acidities of MHQ and DCN2.     

Equiconsistencies at subcompact cardinals

We present equiconsistency results at the level of subcompact cardinals. Assuming SBH_δ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □(δ) and □_δ fail, then δ is subcompact in a class inner model. If in addition □(δ⁺) fails, we prove that δ is \({\Pi_1^2}\) subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. As a corollary we also see that assuming the existence of a Woodin cardinal δ so that SBH_δ holds, the Proper Forcing Axiom implies the existence of a class inner model with a \({\Pi_1^2}\) subcompact cardinal. Our methods generalize to higher levels of the large cardinal hierarchy, that involve long extenders, and large cardinal axioms up to δ is δ⁺⁽ⁿ⁾ supercompact for all n < ω. We state some results at this level, and indicate how they are proved.     

K-Theory for Triangulated Categories 3 1/2 (B): A Detailed Proof of the Theorem of Homological Functors Dedicated to Daniel Quillen and to the Memory of Robert Thomason

This article is a sequel to K-theory for triangulated categories 3 1/2 (A). In this article, we complete the proof of the main theorem of the previous article.     

A criterion for coarse iterability

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M ^* is a linear iterate of M as in (a), then M ^* is coarsely iterable with respect to iteration trees which do not use the top extender of M ^* and its images. Then M is coarsely iterable.     

A dependent theory with few indiscernibles

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ) _T,1 iff κ → (δ) _θ ^<ω . This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.     

Ultrafast proton transfer of three novel quinone cyanine photoacids

Steady-state and time-resolved emission techniques were used to study the photoprotolytic properties of three recently synthesized strong quinone cyanine photoacids (QCy7 and its sulfonated derivatives). The rate coefficient of the excited-state proton transfer (ESPT), k(PT), of the three dyes is roughly 1.5 × 10(12) s(-1), a high value that is comparable to the solvation dynamics rate of large polar organic molecules in H(2)O and D(2)O. It is twice as fast as the proton transfer rate between two adjacent water molecules in liquid water. We found that, as expected, two of the sulfonated photoacids geminately recombines with the proton at an elevated rate. The accelerated geminate recombination process of the sulfonated derivatives is different from a simple diffusion process of protons. The ESPT rate coefficient of these molecules is the highest recorded thus far.     

Unraveling Π 1 1 sets, revisited

We present a method of unraveling Π ₁ ¹ sets which greatly simplifies the construction in Neeman [6]. Apart from adding elegance, this method is also useful for proofs of determinacy involving long games; see Neeman [5]. This material is based upon work supported by the National Science Foundation under Grant No. DMS-0094174.