Micrometric single crystal germanates obtained using a double‐spherical mirror furnace

Micro‐crystals of two new compounds EuMnGe₂O₇ and SmMnGe₂O₇ were grown performing the flux method in a double‐spherical mirror furnace. One valuable advantage of this system was that the heating profile could be modified easily adjusting lamp positions and orientation as well. The micrometric crystals were observed and analyzed for chemical composition by scanning electron microscopy and energy dispersive spectroscopy. This furnace is perfectly suitable to grow at low price, low temperature and short time new materials as a single crystal for basic research or to obtain raw material. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Presentations for subsemigroups of finitely generated commutative semigroups

We introduce the concept of presentation for subsemigroups of finitely generated commutative semigroups, which extends the concept of presentation for finitely generated commutative semigroups. We show that for every subsemigroup of a finitely generated commutative semigroup there are special presentations which solve the word problem in the given subsemigroup. Some properties like being cancellative, reduced and/or torsion free are studied under this new point of view. This paper was supported by the project DGES PB96-1424.     

The arithmetic extensions of a numerical semigroup

Abstract

In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained.     

Symmetric numerical semigroups with arbitrary multiplicity and embedding dimension

We construct symmetric numerical semigroups for every minimal number of generators and multiplicity , . Furthermore we show that the set of their defining congruence is minimally generated by elements.

     

Two‐Photon Imaging of a Cellular Line Using Organic Fluorescent Nanoparticles Synthesized by Laser Ablation

A comparative study of the optical properties of organic fluorescent nanoparticles fabricated by laser ablation (NPs‐LA), reprecipitation (NPs‐RP), and microemulsion (NPs‐ME) methods is presented. These nanoparticles contain a fluorene‐based p‐conjugated molecule (BT2). Distinctive electronic transitions are observed in samples due to the specific way in which the molecule BT2 is assembled in each type of nanoparticles; for instance, transitions involved in absorption and emission spectra of NPs‐LA result in blueshifting with respect to the molecular solution of BT2, whereas redshifting is observed in NPs‐RP and NPs‐ME. Further, the results show that under infrared excitation, the aqueous suspensions of NPs‐LA exhibit the highest fluorescence induced by two‐photon absorption (≈790 GM at 740 nm), as well as the best photostability, compared with aqueous suspensions of NPs‐RP and NPs‐ME. The nanoparticles synthetized by the three aforementioned methods are employed as exogenous agents for the visualization of human cervical cancer cell line (HeLa) using confocal and two‐photon microscopy. Under similar experimental conditions, it is found that microscopy images of the best quality are obtained with NPs‐LA. These results show that laser ablation is a suitable technique for the fabrication of organic fluorescent nanoparticles used as contrast agents for in vitro fluorescence microscopy.     

Influence of Majorana Bound States in Quantum Rings

A quantum ring coupled to a 1D topological superconductor hosting Majorana bound states (MBSs) is investigated. The MBSs effects over the spectrum and persistent current along the quantum ring are studied. The spectra of the system are obtained by an exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian in the Majorana representation. In addition, Green's function formalism is implemented for analytical calculations and obtained a switching condition in the MBSs fermionic parity. Three different patterns that could be obtained for the spatial separation of the MBSs, named: bowtie, diamond, and asymmetric, are reported here, which are present only in odd parity in the quantum ring, while only a single pattern (bowtie) is obtained for even parity. Those patterns are subject strictly to the switching condition for the MBSs. Besides, quantum ring with the presence of a Majorana zero mode presents gapped/gapless spectra in odd/even parity showing in the even case a subtle signature in the persistent current.     

An efficient method for the incompressible Navier–Stokes equations on irregular domains with no-slip boundary conditions,high order up to the boundary

Common efficient schemes for the incompressible Navier–Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier–Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, including semi-implicit treatments of viscosity, and in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy in the L^∞ norm, for both the velocity and the pressure. The scheme has a natural extension to 3-D.     

Exact Solutions of Some Nonlinear Evolution Equations

A different approach to finding solutions of certain diffusive-dispersive nonlinear evolution equations is introduced. The method consists of a straightforward iteration procedure, which is carried to all terms, followed by a summation of the resulting infinite series. Sometimes this is done directly and other times in terms of inverses of operators in an appropriate space. We first illustrate the method with Burgers's and Thomas's equations, and show how it quickly leads to the Cole-Hopf and Thomas transformations which linearize these equations. The method is described in detail with the Korteweg-de Vries equation and then applied to the modified KdV, sine-Gordon, nonlinear (cubic) Schrödinger, complex modified KdV and Boussinesq equations. In all these cases the multisoliton solutions are easily obtained, and new expressions for some of them follow. More generally, the Mar?enko integral equations, together with the inverse problem that originates them, follow naturally from the approach. A method for modifying known solutions (in a way different from the known Backlund transformations) is also developed. Thus, for example, formulas for the interaction of solitons with an arbitrary given solution are obtained. Other equations tractable by this approach are presented. These include the vector-valued cubic Schrödinger equation and a two-dimensional nonlinear Schrödinger equation. Higher-order and matrix-valued equations with nonscalar dispersion functions are also included.