The bidimensional interproximation problem and mixed splines

Interproximation methods for surfaces can be used to construct a smooth surface interpolating some data points and passing through specified regions. In this paper we study the use of mixed splines, that is smoothing splines with additional interpolation constraints, to solve the interproximation problem for surfaces in the case of scattered data. The solution is obtained by solving a linear system whose structure can be improved by using “bell-shaped” thin plate splines.     

Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction

We present an accurate investigation of the algebraic conditions that the symbols of a non-singular, univariate, binary, non-stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials. A subdivision scheme is said to possess the property of reproducing exponential polynomials if, for any initial data uniformly sampled from some exponential polynomial function, the scheme yields the same function in the limit. The importance of this property is due to the fact that several curves obtained by combinations of exponential polynomials (such as conic sections, spirals or special trigonometric and hyperbolic functions) are considered of interest in geometric modeling. Since the space of exponential polynomials trivially includes standard polynomials, this work extends the theory on polynomial reproduction to the non-stationary context. A significant application of the derived algebraic conditions on the subdivision symbols is the construction of new non-stationary subdivision schemes with specific reproduction properties.     

On Hyers— Ulam Stability of Hosszú’s Functional Equation

In this paper the Hyers-Ulam stability of the Hosszú functional equation is proved.     

Exceptional reduction of the diffusion constant in partially disordered photonic crystals

In real photonic crystals light is scattered by the imperfections of the periodic potential. We study experimentally the propagation of diffused light in silicon inverse opals and report an exceptionally reduced diffusion constant of 3.0+/-0.7 m(2)/s, in samples which are only partially disordered. Waves scattered both by the lattice planes and by their imperfections interfere and light is efficiently trapped in this hybrid scattering regime. Not only higher quality crystals, but also random materials present an order of magnitude bigger diffusion constant and hence weaker scattering.     

Dynamic reaction cell ICP-MS for determination of total As, Cr, Se and V in complex matrices: still a challenge? A review

Mass interferences, caused by atomic or polyatomic species and having the same mass/charge ratio of the analyte, can be a severe limit for a reliable assay of trace and ultratrace elements by ICP-MS. The DRC? technology uses a reaction gas to overcome these interferences. Reactions of charge exchange, atom transfer, adduct formation, condensation and analyte association/condensation are the main mechanisms. Interfering ions tend to react with the gas exothermally, while, the analyte reacts endothermally. Selecting the most appropriate reaction gas in DRC-ICP-MS is the very critical point for the determination of strongly interfered elements. A careful evaluation of the reaction mechanisms and the chemistry involved are required. The DRC allows the use of different gases, among them, ammonia (NH(3)), methane (CH(4)), hydrogen (H(2)) and oxygen (O(2)) are the most known, but there are other potentially useful gases like nitrous oxide (N(2)O), nitrogen oxide (NO), carbon dioxide (CO(2)), fluoromethane (CH(3)F), sulphur hexafluoride (SF(6)) and carbon disulfide (CS(2)). This paper provides a review on the analytical challenges for a reliable assay of As, Cr, Se and V by DRC-ICP-MS and illustrates different approaches and mechanisms involved in the analysis of polymers, biological fluids (serum, urine and whole blood), rock, soil and particulate matter.     

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection–diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations system is solved using a fractional time step procedure, splitting the convective components from the diffusive ones. In the case of existing scalar potential of the flow field, the convective components are solved using a finite volume marching in space and time (MAST) procedure; this solves a sequence of small systems of ordinary differential equations, one for each computational cell, according to the decreasing value of the scalar potential. In the case of variable-density groundwater transport problem, where a scalar potential of the flow field does not exist, a second MAST procedure has to be applied to solve again the ODEs according to the increasing value of a new function, called approximated potential. The diffusive components are solved using a standard Galerkin finite element method. The numerical scheme is validated using literature tests.     

A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines

This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The proposed approach is based on the analysis of certain polynomial identities in two variables and leads to interesting new interpolatory bivariate subdivision schemes.     

The Interplay between Strain,Sn Content,and Temperature on Spatially Dependent Bandgap in Ge1−x Sn x Microdisks

Germanium–tin (GeSn) microdisks are promising structures for complementary metal–oxide–semiconductor-compatible lasing. Their emission properties depend on Sn concentration, strain, and operating temperature. Critically, the band structure of the alloy varies along the disk due to different lattice deformations associated with mechanical constraints. An experimental and numerical study of Ge_1−x Sn _x microdisk with Sn concentration between 8.5 and 14 at% is reported. Combining finite element method calculations, micro-Raman and X-ray diffraction spectroscopy enables a comprehensive understanding of mechanical deformation, where computational predictions are experimentally validated, leading to a robust model and insight into the strain landscape. Through micro-photoluminescence experiments, the temperature dependence of the bandgap of Ge_1−x Sn _x is parametrized using the Varshni formula with respect to strain and Sn content. These results are the input for spatially dependent band structure calculations based on deformation potential theory. It is observed that Sn content and temperature have comparable effects on the bandgap, yielding a decrease of more than 20 meV for an increase of 1 at% or 100 K, respectively. The impact of the strain gradient is also analyzed. These findings correlate structural properties to emission wavelength and spectral width of microdisk lasers, thus demonstrating the importance of material-related consideration on the design of optoelectronic microstructures.