Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier

Approximate analytical bound state solutions of the radial Schr?dinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where q?≥?1 and q?=?0. The energy eigenvalues and the corresponding normalized wave functions of the Manning–Rosen potential, the ‘standard’ Hulthén potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.     

Functions generating (m,M, $$\varvec{\Psi }$$ )-Schur-convex sums

Aequationes mathematicae - The notion of $$(m,M,\Psi )$$ -Schur-convexity is introduced and functions generating $$(m,M,\Psi )$$ -Schur-convex sums are investigated. An extension of the...     

Multiple Integral Inequalities for Schur Convex Functions on Symmetric and Convex Bodies

In this paper, by making use of Divergence theorem for multiple integrals, we establish some integral inequalities for Schur convex functions defined on bodies $B⊂\mathbb{R}^n$ that are symmetric, convex and have nonempty interiors. Examples for three dimensional balls are also provided.     

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.     

Fej\'{e}r type inequalities for Harmonically-convex functions with applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well.     

Absorption spectroscopy and binding constants for first-row transition metal complexes of a DOPA-containing peptide

A diverse array of biological systems incorporate 3,4-dihydroxyphenlyalanine (DOPA) into proteins and small molecules for cross-linking and material generation. Marine worm eggshells, sea squirt wound plugs, and marine mussel adhesives may all be formed by combining DOPA-containing molecules with high levels of metals. In order to provide model systems for characterizing these biomaterials, we carried out a study on metal binding to a DOPA-containing peptide. Ultraviolet-visible absorption spectra are presented for the AdopaTP peptide binding to Fe3+, V3+, VO2+, Mn3+, Ti4+, Cu2+, Co2+, and Ni2+ in mono, bis, and where applicable, tris coordination modes. Association constants were determined for selected metal ions binding to the peptide. In general, the spectroscopic and binding properties of this DOPA-containing peptide were found to be similar to those of catechol.     

Visible absorption spectra of metal-catecholate and metal-tironate complexes

Interactions between metals and catechol (1,2-dihydroxybenzene) or other ortho-dihydroxy moieties are being found in an increasing number of biological systems with functions ranging from metal ion internalization to biomaterial synthesis. Although metal-catecholate interactions have been studied in the past, we present the first systematic study of an array of these compounds, all prepared under identical conditions. We report the ultraviolet-visible absorption (UV-vis) spectra for catecholate and tironate complexes of the first row transition elements. Generation and identification of these species were accomplished by preparing aqueous solutions with varied ligand:metal ratios and subsequently titrating with base (NaOH). Controlled ligand deprotonation and metal binding resulted in sequential formation of complexes with one, two, and sometimes three catecholate or tironate ligands bound to a metal ion. We prepared the mono-, bis- and tris-catecholates and -tironates of Fe(3+), V(3+), V(4+)and Mn(3+), the mono- and bis-catecholates and -tironates of Cu(2+), Co(2+), Ni(2+), Zn(2+), Cr(2+) and Mn(2+), and several Ti(4+) and Cr(3+) species. The UV-vis spectra of each complex are described, some of which have not been reported previously. These data can now be applied to characterization of biological metal-catecholate systems.     

Approximation of the Stieltjes Integral and Applications in Numerical Integration

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.     

Functional inequalities and best approximation

We investigate the relationship between best approximations by elements of closed convex cones and the estimation of functionals on an inner product space (X, <⊙,⊙>) in terms of the inner product on X.     

Hilbert modular forms of weight 1/2 and theta functions

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result—under certain mild restrictions on the level and character—to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical difficulties which arise when we move out of Q.