Commuting Traces of Biadditive Maps on Invertible Elements

Let R be a simple unital ring. Under a mild technical restriction on R, we will characterize biadditive mappings G: R² → R satisfying G(u, u)u = uG(u, u), and G(1, r) = G(r, 1) = r for all unit u ∈ R and r ∈ R, respectively. As an application, we describe bijective linear maps θ: R → R satisfying θ(xyx^?1y^?1) = θ(x)θ(y)θ(x)^?1θ(y)^?1 for all invertible x, y ∈ R. This solves an open problem of Herstein on multiplicative commutators. More precisely, we will show that θ is an isomorphism. Furthermore, we shall see the existence of a unital simple ring R′ without nontrivial idempotents, that admits a bijective linear map f: R′ → R′, preserving multiplicative commutators, that is not an isomorphism.     

Complex magnetic ordering as a driving mechanism of multifunctional properties of Heusler alloys from first principles

First-principles calculations are used to study the structural, electronic and magnetic properties of (Pd, Pt)-Mn-Ni-(Ga, In, Sn, Sb) alloys, which display multifunctional properties like the magnetic shape-memory, magnetocaloric and exchange bias effect. The ab initio calculations give a basic understanding of the underlying physics which is associated with the complex magnetic behavior arising from competing ferro- and antiferromagnetic interactions with increasing number of Mn excess atoms in the unit cell. This information allows to optimize, for example, the magnetocaloric effect by using the strong influence of compositional changes on the magnetic interactions. Thermodynamic properties can be calculated by using the ab initio magnetic exchange parameters in finite-temperature Monte Carlo simulations. We present guidelines of how to improve the functional properties. For Pt-Ni-Mn-Ga alloys, a shape memory effect with 14% strain can be achieved in an external magnetic field.     

On the normal subgroup lattice of a hypercentral p-group

We describe all hypercentral p-groups G whose lattice of normal subgroups n(G) is isomorphic to n(H) for a group H with hypercenwal derived subgroup and H not a pgroup.     

Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves

Meccanica - We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional...     

X-ray structural investigation of 1,3,6,8-tetramethyl-10-(4-m.xilenyl-2,6-pyridyl diketone) anthracene

The structure of the compound obtained by reaction of AlCl₃-promotedm-xilene with 2,6-pyridine dicarbonyldichloride in dichloromethane has been investigated by X-ray diffraction methods. The compound is monoclinic, space groupP2₁/c,a=13.907(2),b=17.247(3),c=12.042(2) Å,=109.75(4)°. The structure was solved by direct methods and refined by full matrix least-squares to a finalR=6.37 for 3718 independent observed reflections [I>2(I)]. The structure of the compound enables an understanding of the chemical pathway of the synthesis process.     

Simultaneous determination of atracurium and its metabolite laudanosine in post-mortem fluids by liquid chromatography/multiple-stage mass spectrometry on an ion trap

A method was developed to accurately quantify atracurium (a non-depolarizing skeletal muscle relaxant) and its metabolite laudanosine in post-mortem specimens. Analytes were isolated from blood and tissues by liquid/liquid extraction after adding vecuronium as an internal standard. Chromatographic separation was accomplished by gradient elution in a Synergy Max RP 150 x 2.1 mm column. Positive ion electrospray ionization and mass spectrometric analyses were carried out in an ion trap mass spectrometer under collision-induced dissociation conditions. The method proved selective and sensitive, and was validated in post-mortem blood, heart, lung and liver in the range of 1-2000 ng/mL (blood) and 5-5000 ng/g (tissues); the limits of quantification obtained were 1 ng/mL in blood and 5 ng/g in tissues.     

The interaction of EDTA with barium sulfate

Ethylenediaminetetraacetic acid (EDTA) is a known complexing agent that interacts with a host of cations. In this paper, various techniques are used to elucidate the mechanism of interaction between EDTA and barium sulfate surfaces. It is shown that complexation with metal ions is not sufficient to explain the inhibition of barite crystallization but that other processes such as chemisorption must also occur. EDTA is shown to always adsorb as the mono-protonated species - suggesting that the molecule is able to lose a proton when it adsorbs at lower pH. Molecular modelling shows that the interaction of the surface barium ions with the carboxylate group is an important one. Finally, in situ turbidity measurements provide information about the mechanism of nucleation/growth modification. It is found that the EDTA molecule inhibits barium sulfate nucleation and that this could be its primary means of inhibiting precipitation of barium sulfate.     

Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials

We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an indefinite weight. In particular we are interested in the case where such a weight is positive in a ball and negative outside, or in the reversed situation. We extend the approach to elliptic equations in presence of Hardy potentials, i.e. to

$$\begin{aligned} \varDelta u +\frac{h(|\text {x}|)}{|\text {x}|^2} u+ f(u, |\text {x}|)=0 \end{aligned}$$

where h is not necessarily constant. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.

     

On the Position of Chaotic Trajectories

The main purpose of this paper is to locate trajectories of a perturbed system, which is known to behave chaotically. The unperturbed system is assumed to have the origin as a hyperbolic fixed point, and to admit a trajectory homoclinic to the origin. This homocline is assumed to lie in a prescribed region having the origin in its border. Using a Mel’nikov type approach, we introduce natural conditions ensuring that all the chaotic trajectories of the perturbed system, given by classical results, lie in the same region. The applicability of our results is illustrated in two examples. In the first one, we find positive radial solutions for a class of P.D.E.’s, obtaining new results in the case of critical equations ruled by Laplacian with Hardy potentials. In the other one, we show that under certain conditions one of two weakly coupled pendula moves in one direction only.