Phosphorylation of imidazo[2,1‐b]thiazoles with phosphorus(III) halides in the presence of bases

The reaction of phosphorus(III) halides with 6‐substituted imidazo[2,1‐b]thiazoles in the presence of bases proceeds regioselectively and affords 5‐phosphinoimidazo[2,1‐b]thiazoles, useful synthons for the preparation of various P(III) and P(V) derivatives. 5‐Phosphinoimidazo[2,1‐b]thiazoles are selectively alkylated at the phosphorus or heterocyclic nitrogen atom, depending on the alkylating agent. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:648–655, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20166     

On linearizations of the quadratic two-parameter eigenvalue problem

We present several transformations that can be used to solve the quadratic two-parameter eigenvalue problem (QMEP), by formulating an associated linear multiparameter eigenvalue problem. Two of these transformations are generalizations of the well-known linearization of the quadratic eigenvalue problem and linearize the QMEP as a singular two-parameter eigenvalue problem. The third replaces all nonlinear terms by new variables and adds new equations for their relations. The QMEP is thus transformed into a nonsingular five-parameter eigenvalue problem. The advantage of these transformations is that they enable one to solve the QMEP using existing numerical methods for multiparameter eigenvalue problems. We also consider several special cases of the QMEP, where some matrix coefficients are zero     

The structure of monomeric unsolvated and weakly solvated (Me<Subscript>2</Subscript>Cu)Li and (Me<Subscript>2</Subscript>Cu)Cu

Density functional theory was used to study the structure of various isomers of (Me₂Cu)Li (1), (Me₂Cu)Cu (2), (Me₂Cu)Li · 2Me₂O (3), and (Me₂Cu)Cu · 2Me₂S (4) in the gas phase. Isomers of 1 and 3 were shown to be typical cuprates, whereas isomers of 2 and 4 should rather be treated as unsolvated and solvated methylcopper dimers, respectively. The reasons for the difference between structures 2, 4 and 1, 3 were considered. The energies of solvation of 1 by two dimethyl ether molecules (∼34 kcal/mol) and of 2 by two dimethyl sulfide molecules (∼36 kcal/mol) and the dissociation energies of all the compounds to the dimethylcuprate anion and the corresponding cation were calculated. The energies of solvation of 1 and 2 being almost equal, the transformation of 2 into 4 decreased the dissociation energy much more substantially than the transformation of 1 into 3.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Molecular structure of the boron(III) oxide molecule in the SCF approximation

The potential surface for the boron(III) oxide (B₂O₃) ground state has been calculated in restricted HF approximation with a minimal STO—3G basis set. The equilibrium geometry has C_2v symmetry; the corresponding structural parameters are as follows: r(O_i—B₁)= 1.241 Å; r(B_i—O)= 1.341 Å ; ∠B₁QB₂ = 142° and ǒO₁B₁O = 177°. Calculations were also carried out using the SCF-Xα approach for two configurations of B₂O₃ with C_2v and D_∞h symmetry.     

Scepticism,context and modal reasoning

I analyze some classical solutions of the skeptical argument and some of their week points (especially the contextualist solution). First I have proposed some possible improvement of the contextualist solution (the introduction of the explicit-implicit belief and knowledge distinction beside the differences in the relevance of some counter-factual alternatives). However, this solution does not block too fast jumps of the everyday context (where empirical knowledge is possible) into skeptical context (where empirical knowledge is impossible). Then I analyze some formal analogies between some modal arguments on the contingency of empirical facts (and the world as whole) and the skeptical arguments against empirical knowledge. I try to show that the skeptical conclusion “Empirical knowledge does not exist” is logically coherent with the thesis that they are empirical facts and that we have true belief on them. In order to do that without contradictions I have to accept a non-classical definition of knowledge: S knows that p:= S is not justified to allow that non-p. Knowledge and justified allowance function here as some pseudo-theoretical concepts which allow only some partial and conditional definitions by some “empirical” terms and logical conditions.     

Reagents for Detection of Carboxylate Anion Ligands after Chromatographic Separation of Zinc Carboxylato Complexes

JPC – Journal of Planar Chromatography – Modern TLC - Reagents for detection of carboxylate anions as components of zinc carboxylato mixed-ligand complexes, after chromatographic...     

Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors

We formulate coordinate-free conditions for identifying all the symmetry classes of the elasticity tensor and prove that these conditions are both necessary and sufficient. Also, we construct a natural coordinate system of this tensor without the a priory knowledge of the symmetry axes.