Magnetism in multivacancy graphene systems

Ab initio calculations using density functional theory (DFT) have been performed in order to study defects in graphene. The structural distortions that can be observed when multi-atom vacancies are created in graphene and the net magnetic moment that can eventually appear are characterized for a variety of vacancy sizes and shapes. We conclude that the configuration arising in the construction of multivacancies in graphene can unambiguously indicate whether a magnetic response of the defected system is to be expected. Making use of the shape of the complementary figure-i.e.?the geometric figure of the atomic arrangement that is extracted from graphene when the multivacancy is created-it is possible to construct a set of rules by means of which the optimized structural and magnetic behavior can be predicted. The validity of the rules is determined through DFT calculations.     

Bis(2‐amino‐1H‐benzimidazol‐3‐ium) tetrakis(μ‐but‐2‐enoato)‐κ4O:O′;κ3O,O′:O;κ3O:O,O′‐bis[bis(but‐2‐enoato‐κ2O,O′)holmium(III)]

The title ionic compound, (C₇H₈N₃)₂[Ho₂(C₄H₅O₂)₈], is constructed from two almost identical independent centrosymmetric anionic dimers balanced by two independent 2‐amino‐1H‐benzimidazol‐3‐ium (Habim⁺) cations. The asymmetric part of each dimer is made up of one Ho^III cation and four crotonate (crot or but‐2‐enoate) anions, two of them acting in a simple η²‐chelating mode and the remaining two acting in two different μ₂:η² fashions, viz. purely bridging and bridging–chelating. Symmetry‐related Ho^III cations are linked by two Ho—O—Ho and two Ho—O—C—O—Ho bridges which lead to rather short intracationic Ho...Ho distances [3.8418 (3) and 3.8246 (3) Å]. In addition to the obvious Coulombic interactions linking the cations and anions, the isolated [Ho₂(crot)₈]²⁻ and Habim⁺ ions are linked by a number of N—H...O hydrogen bonds, in which all N—H groups of the cation are involved as donors and all (simple chelating) crot O atoms are involved as acceptors. These interactions result in compact two‐dimensional structures parallel to (110), which are linked to each other by weaker π–π contacts between Habim⁺ benzene groups.     

Bis(4‐methylphenylsulfonyl)amino 4‐methylbenzenesulfonate: a new member of the (RSO2)ON(SO2R)2 family

The title compound, C₂₁H₂₁NO₇S₃, consists of an SO₂ON(SO₂)₂ central fragment and three terminal 4‐methylphenyl groups each attached at a sulfonyl S atom. The most obvious characteristic is the presence of two nearly face‐to‐face benzene rings, with their centroids separated by a rather short distance [3.7808 (18) Å], but with a rather slanted relative orientation [dihedral angle = 20.63 (13)°] so as to preclude a strong intramolecular π–π interaction. The third benzene ring is nearly perpendicular to the other two [dihedral angles = 71.62 (14) and 70.4 (13)°]. The packing of the structure is directed by two C—H...O hydrogen bonds involving aromatic H atoms (methyl H atoms are strictly non‐interacting), which define chains running in the [100] direction. These one‐dimensional chains evolve parallel to each other and exhibit no significant lateral interactions.     

Fractional variational problems depending on indefinite integrals

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and natural boundary conditions, which provide a generalization of the previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and depending on higher-order Caputo derivatives, as well as fractional Lagrange problems, are considered.     

The tractability index of memristive circuits: branch‐oriented and tree‐based models

The memory‐resistor or memristor is a new electrical element characterized by a nonlinear charge‐flux relation. This device poses many challenging problems, in particular from the circuit modeling point of view. In this paper, we address the index analysis of certain differential‐algebraic models of memristive circuits; specifically, our attention is focused on so‐called branch‐oriented models, which include in particular tree‐based formulations of the circuit equations. Our approach combines results coming from differential‐algebraic equation theory, matrix analysis and theory of digraphs. This framework should be useful in future studies of dynamical aspects of memristive circuits. Copyright © 2012 John Wiley & Sons, Ltd.     

Spherically symmetric solution in a space–time with torsion

By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein–Cartan equations of motion, corresponding to a space–time threaded with a three-form Kalb–Ramond field strength. The solution describes in its more generic form, a space–time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution and to a exact solution with a localized scalar field and a torsion kink, already reported in literature. In the process we have found evidence towards the construction of more new solutions.     

Synthesis of 1,8–Naphthyridines and Their Application in the Development of Anionic Fluorogenic Chemosensors

Two 1,8-naphthyridines were synthesized and found to be fluorescent in solution. These compounds were studied in the presence of Cu(+) and Cu(2+) ions and it was verified that the metal causes the quenching of their fluorescence emission, due to the formation of complexes between the naphthyridine and the metal. A displacement assay was carried out in a DMSO-water mixture with the addition of various anions to the solutions of the complexes, and it was observed that these systems have a high capacity to selectively detect cyanide.     

Modelling the Spread of HIV/AIDS Epidemic

In this paper, a deterministic mathematical model for the spread of HIV/AIDS in a variable size population through horizontal transmission is considered. The existence of a threshold parameter, the basic reproduction number, is established, and the stability of both the disease-free equilibrium and the endemic equilibrium is discussed in terms of $R_0$.     

Alternative evaluation of statistical indicators in atoms: The non-relativistic and relativistic cases

In this work, the calculation of a statistical measure of complexity and the Fisher-Shannon information is performed for all the atoms in the periodic table. Non-relativistic and relativistic cases are considered. We follow the method suggested in [C.P. Panos, N.S. Nikolaidis, K.Ch. Chatzisavvas, C.C. Tsouros, arXiv:0812.3963v1] that uses the fractional occupation probabilities of electrons in atomic orbitals, instead of the continuous electronic wave functions. For the order of shell filling in the relativistic case, we take into account the effect due to electronic spin-orbit interaction. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the atomic number Z is observed. The shell structure and the irregular shell filling is well displayed by the Fisher-Shannon information in the relativistic case.