Monogenic functions in the biharmonic boundary value problem

We consider a commutative algebra over the field of complex numbers with a basis {e₁,e₂} satisfying the conditions , . Let D be a bounded domain in the Cartesian plane xOy and D_ζ={xe₁+ye₂:(x,y)∈D}. Components of every monogenic function Φ(xe₁+ye₂) = U₁(x,y)e₁+U₂(x,y)ie₁+U₃(x,y)e₂+U₄(x,y)ie₂ having the classic derivative in D_ζ are biharmonic functions in D, that is, Δ²U_j(x,y) = 0 for j = 1,2,3,4. We consider a Schwarz‐type boundary value problem for monogenic functions in a simply connected domain D_ζ. This problem is associated with the following biharmonic problem: to find a biharmonic function V(x,y) in the domain D when boundary values of its partial derivatives ?V/?x, ?V/?y are given on the boundary ?D. Using a hypercomplex analog of the Cauchy‐type integral, we reduce the mentioned Schwarz‐type boundary value problem to a system of integral equations on the real axes and establish sufficient conditions under which this system has the Fredholm property. Copyright © 2015 John Wiley & Sons, Ltd.     

Homogenization in the Theory of Viscoplasticity

We study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of 4-polyfluoroalkyl-1,3-dithiolanes via [3+2] cycloaddition of thiocarbonyl ylide to polyfluoroalkanethioamides

Chemistry of Heterocyclic Compounds - New 4-polyfluoroalkyl-1,3-dithiolanes were synthesized by reaction of polyfluoroalkanethioamides with thiocarbonyl ylide that was generated in situ by...     

Sulfonimidamides and Imidosulfuric Diamides: Compounds from an Underexplored Part of Biologically Relevant Chemical Space

Two novel solid reagents—1-sulfonimidoyl- and 1-sulfamimidoyl-3-methylimidazolium derivatives—for the synthesis of sulfonimidamides and imidosulfuric diamides, respectively, were developed. It is shown that these reagents are very effective in substitution reactions with various N- and O-nucleophiles; therefore, they significantly extend the accessibility to the chemical space covered by organosulfur(VI) compounds with S=N bonds. In addition, previously unknown imidosulfuric diamides with free imino nitrogen groups were prepared, and their physical and chemical properties were characterized (including molecular geometry, pK_a, Log P, microsomal stability, and reactivity towards typical electrophiles). Similar to other organosulfur(VI) derivatives with S=N bonds, these compounds can be considered as promising bioisosteres of amides, ureas, or sulfonamides.     

X-ray structure analysis and the intervalent electron transfer in organic mixed-valence crystals with bridged aromatic cation radicals

X-ray crystallography identifies the aromatic donor group D = 2,5-dimethoxy-4-methylphenyl to be a suitable redox center for the construction of organic mixed-valence crystals owing to its large structural change attendant upon 1e oxidation to the cation-radical (D*(+)). The combination of cyclic voltammetry, dynamic ESR line broadening, and electronic (NIR) spectroscopy allows the intervalence electron transfer between the redox centers in the mixed-valence system D-br-D*(+) [where br can be an aliphatic trimethylene or an aromatic (poly)phenylene bridge] to be probed quantitatively. Independent measures of the electronic coupling matrix element (H) for D/D*(+) electron exchange via Mulliken-Hush theory accord with the X-ray crystallographic data-both sufficient to consistently identify the various D-br-D*(+) according to the Robin-Day classification. Thus, the directly coupled biaryl D-D*(+) is a completely delocalized cation in class III with the charge distributed equally over both redox centers. The trimethylene- and biphenylene-bridged cations D(CH(2))(3)D*(+) and D(ph)(2)D*(+) with highly localized charge distributions are prototypical class II systems involving moderately coupled redox centers with H approximately equal to 400 cm(-1). The borderline region between class II/III is occupied by the phenylene-bridged cation D(ph)D*(+); and the X-ray, CV, and NIR analyses yield ambivalent H values (which we believe to be) largely a result of an unusually asymmetric (20/80) charge distribution that is polarized between the D/D*(+) redox centers.     

One- and two-dimensional coordination networks of the tetracyanoethylene anion-radicals with potassium counter-ions

Potassium-mirror reduction of tetracyanoethylene (TCNE) acceptor in tetrahydrofuran affords K(THF)₂ TCNE salt (1) showing double TCNE/K chains assembled via unusual μ₃-TCNE-bridging of potassium cations. These parallel ladder-type chains are further tethered by pairs of THF bridges between potassium centers and by intermolecular π-bonding in (TCNE)₂^2? dimers, and this results in formation of quasi-2-D coordination networks. In the presence of crown-ether ligand, the same potassium-mirror reduction lead to formation of [K(18-crown-6)(THF)₂]TCNE salt (2) in which monomeric tetracyanoethylene anion-radicals are positioned between bulky [K⁺(18-crown-6)(THF)₂] counter-ions. In comparison, crystallization of tetracyanoethylene anion-radicals with K⁺(18-crown-6) counter-ions in dichloromethane affords K(18-crown-6)TCNE salt (3) consisting of 1-D chains with 1,2-(N,N’)-TCNE bindings of potassium cations (nested in the crown-ether cavities). Temperature-dependent magnetic susceptibility study revealed essentially isolated tetracyanoethylene anion-radicals (S = 1/2) in this 1-D coordination polymer.