On matrices with operator entries

In this paper we consider certain matrix equations in the field of Mikusiński operators, and construct a method for obtaining an approximate solution which allows working with numerical constants instead of operators. The theory of diagonally dominant matrices is applied for the analysis, existence and character of the obtained solutions. We introduce a method for determining approximate solutions of a discrete analogue for operational differential equations and give conditions for their existence. The error of the approximation is estimated.     

Anion and Additive Effects on the Structure of Mercury(II) Halides Complexes with Tripodal Ligand

The metal complexes [Hg₂(tbim)₂Br₄]·2DMF ( 1 ) and [Hg₂(tbim)I₄]·1.5DMF ( 2 ) were prepared by reactions of 1,3,5‐tris(benzimidazol‐1‐ylmethyl)‐2,4,6‐trimethylbenzene (tbim) with HgBr₂, HgI₂, respectively, and [Hg₂(tbim)I₄]·0.5(FeCp₂)·H₂O ( 3 ) was obtained by the same method with addition of ferrocene (FeCp₂) as additive. Their structures were determined by X‐ray crystallographic analyses. Complex 1 has a macrocyclic binuclear structure with one benzimidazole arm of the ligand free of coordination and the binuclear units are further connected by C‐H···N hydrogen bonds to give an infinite zigzag chain. Complexes 2 and 3 have a 2D network structure in which tbim serves as a tridentate ligand. The results showed that the halides of bromide and iodide have remarkable impact on the structure of the complexes. The FeCp₂ molecules are trapped in the voids of framework 3 .     

Synthesis of Benzopyran-4-Amides Potassium Channel Openers Via Palladium-Catalyzed Amidation

The novel potassium channel openers benzopyran-4-amides have been synthesized via palladium-catalyzed amidation of 4-bromobenzopyrans under an atmoshere in the presence of an equivalent of potassium iodide.     

Construction of Helically Stacked π‐Electron Systems in Poly(quinolylene‐2,3‐methylene) Stabilized by Intramolecular Hydrogen Bonds

π‐Stacked polymers, which consist of layered π‐electron systems in a polymer, can be expected to be used in molecular electronic devices. However, the construction of a stable π‐stacked structure in a polymer is considerably challenging because it requires sophisticated designs and precise synthetic methods. Herein, we present a novel π‐stacked architecture based on poly(quinolylene‐2,3‐methylene) bearing alanine derivatives as the side chain, obtained through the living cyclo‐copolymerization of an o‐allenylaryl isocyanide. In the resulting polymer, the neighboring quinoline rings of the main chain form a layered structure with π–π interactions, which is stabilized by intramolecular hydrogen bonds. The vicinal quinoline units form two independent helices and the whole molecule is a twisted‐tape structure. This structure is established on the basis of UV/CD spectra, theoretical calculations, and atomic‐force microscopy.     

On the character of operational solutions of the time-fractional diffusion equation

The nonhomogeneous time-fractional diffusion equation is analyzed in the frames of the Mikusiński calculus. The exact and the approximate solution of the considered problem are constructed and their character is analyzed.     

Structures and bonding situation of Pb2X2 (X?=?H, F, Cl, Br and I)

Quantum chemical calculations using DFT (BP86) and ab initio methods (MP2, MP4 and CCSD(T)) have been carried out for the title compounds. The nature of the Pb?CPb interactions has been investigated with an energy decomposition analysis. The energy minimum structures of the halogen substituted Pb₂X₂ molecules possess a doubly bridged butterfly geometry A like the parent system Pb₂H₂. The unusual geometry can be explained with the interactions between PbX fragments in the X ²?? ground state which leads to one Pb?CPb electron-sharing ?? bond and two donor?Cacceptor bonds between the Pb?CX bonds as donor and vacant p(??) AOs of Pb. The energy difference between the equilibrium form A and the linear structure XPb??PbX (E) which is a second-order saddle point is much higher when X is a halogen atom than for X?=?H. This is because the a ⁴??^?????X ²?? excitation energies of PbX (X?=?F?CI) are higher than for PbH. The structural isomers B, D1, D2, E, F1, F2 and G of Pb₂X₂ are no minima on the potential energy surface.