(Diazoalkyl)Phosphoranes from [4 + 1]-cycloadditions of tetrahalo-orthobenzoquinones to (diazoalkyl)phosphanes [1]

The (diazoalkyl)phosphanes 4a–e undergo [4 + 1]-cycloaddition reactions with the tetrahalo-orthobenzoquinones 5a,b to furnish the previously unknown (diazoalkyl)phosphoranes 6a–h . The structure of product 6h has been investigated by X-ray crystallography.     

3,5-Bis(2-hydroxyphenyl)-1<Emphasis Type="Italic">H</Emphasis>-1,2,4-triazole based ligands — protonation and metal complex formation

3,5-Bis(2-hydroxyphenyl)-1H-1,2,4-triazole (H₂L^a) and 4-[3,5-bis(2-hydroxyphenyl)-1H-1,2,4-triazol-1-yl]benzoic acid (H₃L^b) have been prepared, and crystal structure of the intermediate 2-(2-hydroxyphenyl)-4H-1,3-benzoxazin-4-one has been determined. Temperature dependent ¹H NMR spectroscopic measurements of H₂L^a indicated dynamic behavior with the equilibrium between the two asymmetric tautomers. For H₃L^b, pD-dependent ¹H NMR spectroscopic measurements showed small but characteristic shifts in the range of 0 ≤ pD ≤ 1, indicative of a triazole nitrogen atom protonation; the corresponding pK _a of 0.98 ± 0.04 was determined by spectrophotometric titrations. (H₂O, 26°C, 1 M KCl/HCl). Formation of [Fe^III(L^a)]⁺ (pH 2.5) and [Fe^III(L^a)₂]⁻ (pH > 6) was verified by UV-Vis spectroscopy. Complex formation of H₃L^b with Al³⁺ and VO²⁺ was investigated by ¹H NMR spectroscopic titration and cyclic voltammetry, respectively. Single crystals of the phenoxo bridged [V^VO(HL^b)(EtO)]₂·2EtOH were characterized by X-ray structural analysis. Dedicated to Professor Milan Melník on the occasion of his 70th birthday     

From Plato to Frege: Paradigms of Predication in the History of Ideas

One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate.     

A computational approach to calculating frequency-dependent structural operators using the spectral finite element method and a wavenumber-based gridding technique

Spectral finite element methods are used to compute exact vibration solutions of structural models at specific frequencies. The applicability of these methods to certain areas of structural dynamics is limited by two major factors: the lack of separate structural operators (mass, damping, and stiffness matrices), and the subsequent difficulty in computing mode shapes via eigenvalue decomposition. In the work presented in this article, a method is investigated to accurately calculate spectral finite elements while overcoming these limitations. The approach incorporates a two-dimensional, discrete solution utilizing a wavenumber-based gridding technique to compute frequency-dependent local mass, damping, and stiffness matrices which can be assembled into the global structural operators. Computed models are able to be used for precise vibration analysis as well as modal analysis via eigenvalue decomposition of the structural operators.