On the Nilpotency Class of a Generalized 3-Abelian Group

A group G is called 3-abelian if the map ${x \mapsto x^{3}}$ is an endomorphism of G and it is called generalized 3-abelian, if there exist elements ${c_{1}, c_{2}, c_{3} \in G}$ such that the map ${\varphi : x \longmapsto {x^{c_{1}} x^{c_{2}} x^{c_{3}}}}$ is an endomorphism of G. Abdollahi, Daoud and Endimioni have proved that a generalized 3-abelian group G is nilpotent of class at most 10. Here, we improve the bound to 3 and we show that the exponent of its derived subgoup is finite and divides 9. We also prove that G is 3-Levi, 9-central, 9-abelian and 3-nilpotent of class at most 2.     

LIMIT CYCLES OF THIRD-ORDER DIFFERENTIAL EQUATION

In this paper, we investigate a third-order differential equation. Based on the averaging theory, we obtain sufficient conditions for the existence of periodic solutions to the equation.     

Comparison of Some Classical Topologies on Hyperspaces within the Framework of Point Spaces

S. Dolecki, G. Greco and A. Lechicki call a space X consonant if the co-compact topology and the upper Kuratowski topology on the set of closed subsets of X coincide. We call a space X hyperconsonant if Fell's topology and the (Kuratowski) convergence topology coincide. Recently, we proved that a first countable, locally paracompact, T ₃-space is hyperconsonant if and only if the space possesses at most one point without a compact neighbourhood, extending the same result of D. Fremlin obtained for metrizable spaces. In this paper, we pursue the study of hyperconsonance within the framework of point spaces (countable T ₁-spaces with exactly one accumulation point) and we compare consonance and hyperconsonance in such spaces. In particular, we answer a question of T. Nogura and D. Shakhmatov: does there exist a nonconsonant point space? We provide a Fréchet, -point space which is not consonant. Moreover, this example proves that the consonance is not preserved by continuous closed compact-covering maps of separable complete metrizable spaces onto Hausdorff spaces.     

A Characterization of b‐Perfect Graphs

A b‐coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b‐chromatic number of a graph G is the largest integer k such that G admits a b‐coloring with k colors. A graph is b‐perfect if the b‐chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is b‐perfect if and only if it does not contain as an induced subgraph a member of a certain list of 22 graphs. This entails the existence of a polynomial‐time recognition algorithm and of a polynomial‐time algorithm for coloring exactly the vertices of every b‐perfect graph. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:95–122, 2012     

Highly cross-linked polymers containing N,N',N' '-chelate ligands for the Cu(II)-mediated hydrolysis of phosphoesters

Three immobilized Cu(II) complexes were generated by the following: (a) homopolymerization of the N,N',N' '-chelate ligand tris[2-(1-vinylimidazolyl)]phosphine (1) and subsequent metalation with CuCl2; (b) copolymerization of 1 with ethyleneglycol dimethacrylate (EGDMA) und subsequent metalation with CuCl2; or (c) molecular imprinting with the organometallic Mo-complex [Mo(eta3-C4H7)(CO)2(1)](TsO) (5) and EGDMA and subsequent replacement of Mo(II) by Cu(II). All three polymeric Cu complexes were found to efficiently promote the hydrolysis of activated phosphoesters with the relative activity being dependent on the nature of the polymer and the substrate.     

Computational parametric analysis of fuel cells: Application to PEMFC and SOFC

This study presents a numerical investigation on the proton exchange membrane fuel cell (PEMFC) and the solid oxide fuel cell (SOFC), using the aerothermal and electrochemistry equations to describe all phenomena included in both types of the fuel cells. The computational process is based on the implementation of the mathematical fuel cells models in FLUENT computational fluid dynamics code. This is in order to evaluate the temperature field, the production of the electricity, and the distribution of the water mass fraction in different region of the fuel cells. The obtained results show that the simulation is able to evaluate the physical and chemical parameters to explain the main phenomena in the fuel cells.     

DFT investigation of homotrinuclear and heterotrinuclear [M3(Phz)2], [MM′2(Phz)2], [M3(CO)2(Phz)2], [MM′2(CO)2(Phz)2] sandwich complexes (M = Ti,Cr, Fe and Ni; M′ = V and Mn,Phz = C12H8N2): predicted models and electronic structures

Structural Chemistry - The results described in this work report a DFT/BP86 (using the TZ2P basis) study concerning the molecular and electronic structures of homotrinuclear and heterotrinuclear...     

Bis(Tetramethylselenophosphoramidoyl) Methylamine Complexes of Cd(Ii) and Zn(Ii): Synthesis and Multinuclear (31P, 77Se,and 113Cd) Nmr Characterization in Solution

Abstract

Five new complexes ZnL₂(ClO₄)₂ (1), CdL₂(ClO₄)₂ (2), CdL₂(BF₄)₂ (3), CdLCl₂ (4), and CdL(NO₃)₂ (5) [L = ((Me₂N)₂PSe)₂NMe] have been synthesized and characterized by elemental analysis, infrared (IR) and multinuclear (³¹P, ⁷⁷Se, and ¹¹³Cd), and nuclear magnetic resonance (NMR) spectroscopy. The ³¹P and ⁷⁷Se NMR data showed that the title ligand is coordinated in a bidentate fashion to the metal center via its both P=Se groups. The solution structure of the cadmium complexes was further confirmed by its ¹¹³Cd NMR spectra, which displayed a quintuplet for the perchlorate complex and a triplet for each of the nitrate and chloride complexes, respectively due to coupling with four (two ligands) and two (one ligand) equivalent phosphorus nuclei, consistent with a four-coordinate tetrahedral geometry for the cadmium center. The results are discussed and compared with the corresponding oxo and thio analogues.