Finite tchebycheff transformations of generalized functions

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.     

Integral representation in the theory of continuous trading

This paper deals with predictable representation in continuous trading. First of all we give a positive answer to a conjecture of Harrison and Pliska [2]. Then we prove the completeness of a model of mixed type (see[2]). A slight modificationof this example shows that the continuous and purely discontinuous parts of a local martingale depend on the filtration.     

Reversible and Stepwise Single-Crystal-to-Single-Crystal Transformation of a Platinum(II) Complex with Vapochromic Luminescence

The vapochromic single-crystal-to-single-crystal (SCSC) transformation of a highly luminescent Pt^II complex bearing an N-heterocyclic carbene [Pt(CN)₂(tBu-impy)] (tBu-impyH⁺=1-tert-butyl-3-(2-pyridyl)-1H-imidazolium) is reported. The trihydrate form of the complex, which exhibits blue ³MMLCT emission owing to weak Pt⋅⋅⋅Pt interactions, changed its luminescence color from blue to yellowish-green upon the desorption of water molecules while keeping the high emission quantum yield of more than 0.45. Variable-temperature and continuous in-situ tracking of single-crystal X-ray diffraction measurements revealed that the SCSC transformation proceeds reversibly by the release and reabsorption of water molecules, thereby changing the stacked structure slightly. As a result, the dynamics of vapor-induced SCSC transformation were elucidated: that the anhydrous form returned to the original trihydrate form in a two-step process under a water vapor atmosphere. In addition, the Pt^II complex exhibited a similar SCSC response accompanied by a luminescence color change in the presence of methanol vapor, while being inactive toward ethanol vapor.     

Phenyliodine(III) Diacetate/I2-Mediated Domino Approach for Pyrrolo[1,4]Thiazines and 1,4-Thiazines by a One-Pot Morin Rearrangement of N,S-Acetals

An efficient domino transformation using a phenyliodine(III) diacetate (PIDA)/I₂ combination towards Morin 1,4-thiazine compounds has been developed starting from N,S-acetals. The latter leads to “one-step” regioselective methylene insertion without the need for traditional sulfoxide intermediates in good yields. The reaction involves easily accessible N,S-acetals obtained from cost-effective basic ketones and cysteamine as starting materials. This process ultimately leads to 1,4-thiazines related to natural product and fused derivatives necessary for further QSAR study.     

Vapoluminescent Behavior and the Single-Crystal-to-Single-Crystal Transformations of Chloroform Solvates of [Au2(μ-1,2-bis(diphenylarsino)ethane)2](AsF6)2

The mono- and di-chloroform solvates of [Au₂(μ-1,2-bis(diphenylarsino)ethane)₂](AsF₆)₂ undergo single-crystal-to-single-crystal transformations that result in gain (over 12 hours) or slow loss (over five years) of only one chloroform molecule. The change in solvation results in changes in the structure and luminescence of the digold cation. The cation consists of a pair of slightly bent As-Au-As units that are connected through the two bridging dpae ligands and by aurophilic interactions with Au⋅⋅⋅Au contacts of 3.05152(15) Å in the disolvate or 2.9570(5) Å in the monosolvate.     

On the criteria for integrability of the Liénard equation

The Liénard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely answered yet. Here we provide a new criterion for integrability of the Liénard equation using an approach based on nonlocal transformations. We also obtain some of the previously known criteria for integrability of the Liénard equation as a straightforward consequence of our approach’s application. We illustrate our results by several new examples of integrable Liénard equations.     

The relation between structure changes and thermal expansion in liquid indium

The structure of liquid indium in a wide temperature range has been investigated by means of X-ray diffraction and reverse Monte Carlo methods. Analysis of temperature dependence of the interatomic distances and coordination numbers allowed us to determine the existence of structural transformation in a liquid state. Moreover, it was found that at a temperature of 640 K thermal expansion coefficients, estimated from temperature dependence of interatomic distances, change its sign from negative to positive confirming the transformations in structure of liquid indium which are observed by temperature variations.