Ferromagnetic transition metal implanted ZnO: a diluted magnetic semiconductor?

Recently theoretical works predict that some semiconductors (e.g. ZnO) doped with magnetic ions are diluted magnetic semiconductors (DMS). In DMS magnetic ions substitute cation sites of the host semiconductor and are coupled by free carriers resulting in ferromagnetism. One of the main obstacles in creating DMS materials is the formation of secondary phases because of the solid-solubility limit of magnetic ions in semiconductor host. In our study transition metal ions were implanted into ZnO single crystals with the peak concentrations of 0.5-10 at.%. We established a correlation between structural and magnetic properties. By synchrotron radiation X-ray diffraction (XRD) secondary phases (Fe, Ni, Co and ferrite nanocrystals) were observed and have been identified as the source for ferromagnetism. Due to their different crystallographic orientation with respect to the host crystal these nanocrystals in some cases are very difficult to be detected by a simple Bragg-Brentano scan. This results in the pitfall of using XRD to exclude secondary phase formation in DMS materials. For comparison, the solubility of Co diluted in ZnO films ranges between 10 and 40 at.% using different growth conditions pulsed laser deposition. Such diluted, Co-doped ZnO films show paramagnetic behaviour. However, only the magnetoresistance of Co-doped ZnO films reveals possible s-d exchange interaction as compared to Co-implanted ZnO single crystals.Comment: 27 pages, 8 figure

Complexity and integrability in 4D bi-rational maps with two invariants

In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

A multiple scales approach to maximal superintegrability

In this paper we present a simple, algorithmic test to establish if a Hamiltonian system is maximally superintegrable or not. This test is based on a very simple corollary of a theorem due to Nekhoroshev and on a perturbative technique called multiple scales method. If the outcome is positive, this test can be used to suggest maximal superintegrability, whereas when the outcome is negative it can be used to disprove it. This method can be regarded as a finite dimensional analog of the multiple scales method as a way to produce soliton equations. We use this technique to show that the real counterpart of a mechanical system found by Jules Drach in 1935 is, in general, not maximally superintegrable. We give some hints on how this approach could be applied to classify maximally superintegrable systems by presenting a direct proof of the well-known Bertrand's theorem.Comment: 30 pages, 4 figur

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.Comment: 27 page

Darboux integrability of trapezoidal H4H^{4} and H6H^{6} families of lattice equations I: First integrals

In this paper we prove that the trapezoidal $H^{4}$ and the $H^{6}$ families of quad-equations are Darboux integrable systems. This result sheds light on the fact that such equations are linearizable as it was proved using the Algebraic Entropy test [G. Gubbiotti, C. Scimiterna and D. Levi, Algebraic entropy, symmetries and linearization for quad equations consistent on the cube, \emph{J. Nonlinear Math. Phys.}, 23(4):507543, 2016]. We conclude with some suggestions on how first integrals can be used to obtain general solutions.Comment: 34 page

Ungaliophis, U. continentalis, U. panamensis

Number of Pages: 4Integrative BiologyGeological Science

A generalized Cartan decomposition for the double coset space U(n_1) x U(n_2) x U(n_3)) U(n) / U(p) x U(q)

Motivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups $L$, $G'$ and $H$ surjects a Lie group $G$ in the setting that $G/H$ carries a complex structure and contains $G'/G' \cap H$ as a totally real submanifold. Particularly important cases are when $G/L$ and $G/H$ are generalized flag varieties, and we classify pairs of Levi subgroups $(L, H)$ such that $L G' H = G$, or equivalently, the real generalized flag variety $G'/H \cap G'$ meets every $L$-orbit on the complex generalized flag variety $G/H$ in the setting that $(G, G') = (U(n), O(n))$. For such pairs $(L, H)$, we introduce a \textit{herringbone stitch} method to find a generalized Cartan decomposition for the double coset space $L \backslash G/H$, for which there has been no general theory in the non-symmetric case. Our geometric results provides a unified proof of various multiplicity-free theorems in representation theory of general linear groups

Multi P2P Energy Trading Market, Integrating Energy Storage Systems and Used for Optimal Scheduling

The increasing use of renewable energy and storage systems by end users has changed the paradigm of electricity markets, with consumers changing their role from passive to active players, the so-called prosumers. Different countries have encouraged the aggregation of these prosumers in energy communities. In these communities, it is essential to create a market to manage energy exchanges between neighbors, who can sell surpluses or buy energy to reduce their bills. This paper presents the framework definition of a multi-peer-to-peer market. As contributions, it defines how storage systems can participate in the market and multiple exchanges between prosumers are possible. This market can be integrated in an optimization process to perform optimal scheduling in the community by setting an objective. All this has been tested in a community with 5 prosumers with generation and storage, where the effect of multiple exchanges and valuation of assets is observed, achieving as a result higher bill reductions