Subalgebras of FA-presentable algebras

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.     

Categorical Geometry and Integration Without Points

The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article (Segal, Bull Am Math Soc 71:419–489, 1965). In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology. First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical σ-algebra). Second (and here we have a major difference from the classical theory), we prove that every finite-additive function μ with values in [0,1] can be extended to a measure on an abstract σ-algebra; this correspondence is functorial and yields uniqueness. As an example we show that the Segal space can be characterized by completely canonical data. Furthermore, from our results it follows that a satisfactory point-free integration arises everywhere where we have a finite-additive probability function on a Boolean algebra.     

Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian Motions

In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity holds for arbitrary unbounded open sets. Then we introduce the notion of κ-fatness at infinity for open sets and show that the Martin boundary at infinity of any such open set consists of exactly one point and that point is a minimal Martin boundary point.     

Dimerisation Process of Silybin‐Type Flavonolignans: Insights from Theory

Natural polyphenols are known to be oxidized by free radicals, which partially explains the antioxidant properties of a number of these compounds. This oxidation may also be used to synthesise new compounds of biological interest, for example, dimers. The present theoretical study describes the existing experimental evidence showing that silybin and dehydrosilybin [natural polyphenols isolated from milk thistle (Silybum marianum)] form dimers regioselectively. Based on DFT calculations, thermodynamic and kinetic values were computed in order to better understand the physicochemical behaviour of these dimerisation processes. Calculations showed that after H‐atom transfer (from polyphenol to radical), dimerisation could proceed in two steps: 1) bond formation and, when possible, 2) tautomerisation reorganisation. The former step is the limiting step, while the latter is crucial for the process to be thermodynamically favourable (ΔG<0). If this rearrangement is impossible then dimerisation is not feasible, or at least becomes a minor process (e.g., dehydrosilybin dimerisation after H‐atom abstraction from the 3‐OH group). This explains the regioselectivity of polyphenol dimerisation.     

Diastereoselective ortho-lithiation of [5]ferrocenophanes

Planarly chiral ferrocene derivatives with bridged cyclopentadienyl rings are interesting ligands in asymmetric catalysis. A planar stereogenic unit is conveniently introduced by diastereoselective ortho-lithiation. The directed lithiation of several [5]ferrocenophane derivatives followed by quenching with chlorodiphenylphosphane led to planarly chiral ligands. The sense of diastereoselection was studied by computational methods. Absolute configuration of methoxy phosphane was determined by single crystal X-ray diffraction study.     

Preserving the activity of cellulase in a batch foam fractionation process

Foam fractionation isone of the low operating-cost techniques for removing proteins from a dilute solution. The initial bulk solution pH and air superficial velocity play an importantrole in the foam-fractionation process. Denaturation of proteins (enzymes) can occur, however, during the foamfractionation process from the shear forces resulting from bursting air bubbles. At the extreme bulk solution pHs (lower than 3.0 and higher than 10.0), the en zymatic activity of cellulase in the foamate phase drops significantly. Within these two pH boundsan increase in the air superficial velocity, V_o, and a decrease in the bulk solution pH leads to a decrease in the separation ratio (SR), defined as theratio of the protein concentration in the foamate to the protein concentration in the residue. On the other hand, an increase in V_o provides a higher foamate-protein recovery. The process efficiency is defined as the product of foamate-protein recovery times the SR times the cellulase activity. The optimal operating condition of the cellulase foamfractionation process is taken into account at the maximum value of the processefficiency. In this study, that optimal condition is atan air superficial velocity of 32 cm/min and a bulk-solution pH of 10.0. At this condition, the recovered foamate is about 80% of the original protein mass, the SR is about 12, and the en zymatic activity is about 60% of the original cellulase activity.