Essential countability of treeable equivalence relations

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E   is essentially countable if and only if there is no continuous embedding of _E1${\mathbb{E}}_1$ into E. Our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations, and allow us to show that up to continuous Kakutani embeddability, there is a minimum Borel function which is not essentially countable-to-one.     

Two Ways to Centralizers of Equivalence Relations

We investigate what is the common part of the action accessible and the fibrewise algebraically cartesian closed (facc) categories dealing with the existence of centralizers of equivalence relations. Doing this, we shall introduce some new aspects of the Beck-Chevalley commutation with respect to the fibration of points \(\P _{\mathbb C}\) and shall characterize the existence of those centralizers by a specific property of this same fibration.     

Tetrathiafulvalene hydrazone: efficient synthon for the synthesis of novel bidentate redox active ligands

The synthesis and the ability of TTF-hydrazone to act as a versatile precursor for the design of electroactive ligands are reported together with the chelating ability of these ligands through their M(CO)₄ complexes, (M = Mo, W).     

Deduction as Reduction, from a Categorical Point of View

Deduction systems and graph transformation systems are compared within a common categorical framework. This comparison results in a proposal for a new deduction method in diagrammatic logics, allowing the deletion of intermediate lemmas.     

Categorical (binary) difference terms and protomodularity

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.     

Synthesis of Protein Conjugates of 2-Carboxy-L-Arabinitol 5-Phosphate and 2-Carboxy-L-Ribitol 5-Phosphate

Abstract

The synthesis of 5-O-[5-(pentanoic acid)]-phosphono-L-erythro-pent-2-ulose 2 was successfully achieved by coupling benzyl 5-hydroxypentanoate 9b and 1-O-benzyl-L-erythro-pent-2-ulose ethane- 1,2-diyl dithioacetal 13 with the enediol pyrophosphate 18. Compound 2 was coupled to carrier proteins, porcine thyroglobuline and bovine serum albumin and the conjugates were treated with KCN to give conjugates of the hapten 1, designed to raise catalytic antibodies.     

Induced Chiroptical Changes of a Water‐Soluble Cryptophane by Encapsulation of Guest Molecules and Counterion Effects

We report the synthesis of the water‐soluble cryptophanol derivative 1 and the study of the chiroptical properties of its two enantiomers (>99 % ee) by polarimetry, electronic circular dichroism (ECD), and vibrational circular dichroism (VCD). We show that cryptophanol 1 exhibits unusual chiroptical properties in water under basic conditions (pH>12). For instance, the shapes of the ECD and VCD spectra of 1 in water were strongly dependent on the nature of the alkali metal ions (Li⁺, Na⁺, K⁺, Cs⁺) surrounding the cryptophane and whether or not a guest molecule is present inside the cavity of the host. To the best of our knowledge, this is the first example in which the nature of these counterions governs the chiroptical properties of a host molecule. Moreover, specific ECD spectra were obtained depending on the size of the guest molecules. This makes 1 a good sensor for small neutral molecules in aqueous solvent. Finally, VCD experiments associated with DFT calculations show that the chiroptical changes can be directly correlated to the presence of charges close to the aromatic rings and with a conformational change of the alkyl chains upon encapsulation.