A Brief Account on Lagrange’s Algebraic Identity

In Indiscrete Thoughts [18], G.-C. Rota remarked, ??The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.?? Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.     

New measurements of high-momentum nucleons and short-range structures in nuclei

We present new measurements of electron scattering from high-momentum nucleons in nuclei. These data allow an improved determination of the strength of two-nucleon correlations for several nuclei, including light nuclei where clustering effects can, for the first time, be examined. The data also include the kinematic region where three-nucleon correlations are expected to dominate.     

Laser dressed donor impurities in free-standing GaAs films under an electric field

The laser-field dependence of the shallow donor states in a free-standing thin GaAs film under an external static field is studied within the effective mass approximation. The laser dressing effects are considered for the confinement potential of the well as well as for the impurity Coulomb interaction distorted by the dielectric mismatch at interfaces. We found that (i) the increase of the laser intensity dramatically modifies the electron potential energy, which establishes the quantum confinement; (ii) the ground state subband energy is significantly enhanced by the electrostatic self-energy arising from the interaction between the electron and its images; (iii) the impurity binding is much larger than those of the dielectrically homogenous case and it becomes stronger sensitive to the laser intensity variation; (iv) under an electric field parallel to the growth direction, the inversion symmetry with respect to the quantum well center is broken and a red/blue-shift of the binding energy, depending on the impurity position along the field direction, occurs. Therefore, the shallow donor energy levels in the free-standing thin films can be tuned in a wide range by proper tailoring of the structure parameters (well size, impurity position) as well as by varying the external applied fields.     

Off‐center shallow donors in a spherical Si quantum dot with dielectric border

Within the effective mass approximation and using a finite element method, the ground state energy and electron cloud localization of the shallow donors in a Si quantum dot (QD) with dielectric border are calculated. Simultaneous effects of dielectric mismatch (DM) at the core–shell interface, the impurity radial position, and the external electric field on the electronic properties are investigated. We found that (i) for a freestanding QD, the binding energy is strongly enhanced due to the additional interactions of the electron with the polarization charges; (ii) the electron cloud distribution can be easily modulated by varying the impurity position; (iii) the electric field‐induced shift in energy levels increases with the DM. Therefore, the electronic energy levels of the nanocrystal could be tuned by properly tailoring the heterostructure parameters (DM with the surrounding matrix, impurity location) as well as by varying the electric field strength. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Thermal analysis of Romanian ancient ceramics

The present work is focused on thermoanalytical investigations as thermogravimetric analysis (TG) and derivative thermal analysis (DTG), applied for the characterization of some samples collected from archaeological sites (Brasov and Trofeum Traiani) located in different regions of Romania. New informations derived about ceramic technologies concerning raw materials and binding materials (mineralogical components) have been obtained. All these experimental results have been correlated with related techniques as X-ray diffraction (XRD), energy-dispersive X-ray fluorescence (EDXRF) and inductively coupled plasma—atomic emission spectrometry (ICP-AES). By progressive heating in static air atmosphere and in the temperature range of 20–800 °C, all investigated materials exhibit three main successive processes, associated with the dehydration and thermo-oxidative degradations. The rate of the first thermooxidative process, temperatures corresponding to the maximum rate of the second thermooxidative process and shrinkage temperature were associated with the damage of the investigated materials due to environmental impact. Heating also affects the contact between the fine-sized clay matrix and mineral clast fragments, appearing in reaction rims, sometimes showing newly formed phases. The temperature at which ancient ceramics and pottery were fired varies over a wide range (600–800 °C) depending on the type of clay used, although firing temperatures not above 30–400 °C have also been suggested. Clay minerals, as the main material for production of ceramics and pottery, show some characteristic reactions (dehydroxylation, decomposition, transformation) in the course of firing (heating effects) and several thermoanalytical criteria can be used for reconstruction of former production conditions.     

Dielectric enhancement of the exciton energies in laser-dressed near-surface quantum wells

A theoretical study of the intense high-frequency laser field effect on the interband transitions and on the ground (1S-like) and excited (2S-like) exciton states in InGaAs/GaAs near-surface quantum wells is performed within the effective mass approximation. The carrier confinement potentials and image charge contributions to the Coulomb interaction can significantly be modified and controlled by the capped layer thickness and laser field intensity. We found that: (i) the interband and exciton transition energies monotonically enhance with the laser amplitude; (ii) for small capped layers the splitting between the 2S and 1S exciton lines are more sensitive to the dressing laser parameter, and (iii) for high enough laser intensities the dressing effects on both confining potential and Coulomb interactions can yield entirely different exciton emission spectra depending on the cap layer thickness. Our results are compared with the theoretical and experimental data obtained in the absence of the laser field and a good agreement is reached.     

The Hermite-Hadamard inequality for convex functions on a global NPC space

We prove an extension of Choquet's theorem to the framework of compact metric spaces with a global nonpositive curvature. Together with Sturm's extension [K.T. Sturm, Probability measures on metric spaces of nonpositive curvature, in: Pascal Auscher, et al. (Eds.), Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces, Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs April 16-July 13, 2002, Paris, France, in: Contemp. Math., vol. 338, Amer. Math. Soc., Providence, RI, 2003, pp. 357-390] of Jensen's inequality, this provides a full analogue of the Hermite-Hadamard inequality for the convex functions defined on such spaces.