On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

Hermite interpolation with symmetric polynomials

We study the Hermite interpolation problem on the spaces of symmetric bivariate polynomials. We show that the multipoint Berzolari-Radon sets solve the problem. We also give a Newton formula for the interpolation polynomial and use it to prove a continuity property of the interpolation polynomial with respect to the interpolation points.     

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f ^nm (z)f ^nd (qz + c))^(k) for meromorphic functions in a non-Archimedean field.     

Electronic Structure of N-Bridged High-Valent Diiron-Oxo

Density functional theory (DFT) and an advanced ab initio technique based on density matrix renormalization group (DMRG-CASPT2) were employed to investigate a reactive N-bridged high-valent diiron-oxo species involved in H-abstraction reactions. We studied in detail two important doublet states, the ground state with two iron(IV) centers and a mixed valence Fe^V-Fe^IV excited state. We found that the latter state is low-lying. Furthermore, its electronic structure and spin density imply that it has significantly higher H-abstraction reactivity than the ground state. This low-lying excited state might be the reason behind the high oxidation reactivity of this diiron-oxo species towards methane.     

Oliveridepsidones A–D,antioxidant depsidones from Garcinia oliveri

Four new prenylated depsidones, oliveridepsidones A–D, were isolated from the bark of Garcinia oliveri collected in Vietnam. Their structures were elucidated using mainly NMR techniques (¹H and ¹³C NMR, HMQC, HMBC and NOE experiments). Copyright © 2012 John Wiley & Sons, Ltd.     

Organic Positive Materials for Magnesium Batteries: A Review

Magnesium batteries, like lithium-ion batteries, with higher abundance and similar efficiency, have drawn great interest for large-scale applications such as electric vehicles, grid energy storage and many more. On the other hand, the use of organic electrode materials allows high energy-performance, metal-free, environmentally friendly, versatile, lightweight, and economically efficient magnesium storage devices. In particular, the structural diversity and the simple activity of organic molecules make redox properties, and hence battery efficiency, easy to monitor. While organic magnesium batteries still in their infancy, this field becomes more and more promising because significant results were reported. To summarize the achievements in studies on organic cathodes for magnesium systems, their synthesis is discussed, combined with electrode design to provide the basis for controlling the electrochemical properties. Moreover, the techniques to synthesize organic materials with high-yield are mentioned. Finally, potential problems and prospects are explored to further improve organic cathodes.     

Hopf bifurcation control via a dynamic state-feedback control

To relocate two Hopf bifurcation points, simultaneously, to any desired locations in n-dimensional nonlinear systems, a novel dynamic state-feedback control law is proposed. Analytical schemes to determine the control gains according to the conditions for the emergence of Hopf bifurcation are derived. To verify the effectiveness of the proposed control law, numerical examples are provided.     

Synthesis and Transformation of 4-(1-Chloro-1-nitroethyl)-6,7-dimethoxy-2-methylquinazoline: Spectral Characterization and Anti-cancer Properties of some Novel Quinazoline Derivatives

An efficient and simple method has been reported for the synthesis of 4-(1-Chloro-1-nitroethyl)-6,7-dimethoxy-2-methylquinazoline ( 2 ) as a key compound for further transformation to other novel 6,7-dimethoxy-2-methyl-4-substituted quinazolines. The structure of the synthesized compounds was characterized by spectroscopic methods. The pathway of some unprecedented reactions was proposed. (E)-1-(6,7-dimethoxy-2-methylquinazolin-4-yl)-3-(4-nitrophenyl)prop-2-en-1-one (11) exhibits high in vitro cytotoxicity on three cell lines, Hepatocellular carcinoma (Hep-G2), Human lung carcinoma (LU-1), and Human breast carcinoma (MCF-7) with IC₅₀ of 2.1, 11.6 and 2.2 μM, respectively.