Strukturelle Untersuchungen einiger neutraler Komplexe des zweiwertigen Molybdäns

Unit cell parameters have been calculated from x-ray powder diffraction data of Mo₂Br₄ Py ₄ (A), Mo₂I₄ Py ₄ (B), Mo₂I₄ Pic ₄ (C), Mo₂(SCN)₄ Py ₄ (D) and Mo₂(SCN)₄ Pic ₄ (E), A, B and C crystallize tetragonal. A witha=9,4₂,c=15,O₂ Å; B witha=9,4₆,c=14,9₈ Å and C witha=9,6₆ andc=15,7₂ Å D and E crystallize orthorhombic. D witha=10,0₉,b=9,1₄,c=15,0₈ Å; E witha=10,2₂,b=9,4₁ andc=15,1₅ Å.Py=pyridine,Pic=4-methylpyridine.

     

Approximate chemical analysis of volcanic glasses using Raman spectroscopy

The effect of chemical composition on the Raman spectra of a series of natural calcalkaline silicate glasses has been quantified by performing electron microprobe analyses and obtaining Raman spectra on glassy filaments (~450 µm) derived from a magma mingling experiment. The results provide a robust compositionally‐dependent database for the Raman spectra of natural silicate glasses along the calcalkaline series. An empirical model based on both the acquired Raman spectra and an ideal mixing equation between calcalkaline basaltic and rhyolitic end‐members is constructed enabling the estimation of the chemical composition and degree of polymerization of silicate glasses using Raman spectra. The model is relatively insensitive to acquisition conditions and has been validated using the MPI‐DING geochemical standard glasses 1 as well as further samples. The methods and model developed here offer several advantages compared with other analytical and spectroscopic methods such as infrared spectroscopy, X‐ray fluorescence spectroscopy, electron and ion microprobe analyses, inasmuch as Raman spectroscopy can be performed with a high spatial resolution (1 µm²) without the need for any sample preparation as a nondestructive technique. This study represents an advance in efforts to provide the first database of Raman spectra for natural silicate glasses and yields a new approach for the treatment of Raman spectra, which allows us to extract approximate information about the chemical composition of natural silicate glasses using Raman spectroscopy. We anticipate its application in handheld in situ terrestrial field studies of silicate glasses under extreme conditions (e.g. extraterrestrial and submarine environments). © 2015 The Authors Journal of Raman Spectroscopy Published by John Wiley & Sons Ltd     

Applications of Approximation Theory to thermographic images in earthquake engineering

In this paper we show some new applications of the approximation theory, by means of the multivariate sampling Kantorovich operators, to thermographic images in seismic engineering. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluating the potential of vaccine-induced type replacement for high-risk human papillomaviruses

Persistent infection with human papillomavirus (HPV) is the main cause of cervical cancer. Current HPV vaccines protect against both HPV-16 and -18, which are known to cause approximately 70% of cervical cancer cases worldwide. These vaccines have shown to be highly effective in preventing infection by their targeted types. However, there is a broad diversity of HPV types not targeted by the vaccines, and there is controversy about a possible increase in the prevalence of these non-targeted types after a vaccination program. Here, we propose a within-host metapopulation model to study the possibility of vaccine-induced type replacement for oncogenic types. It is generally believed that the theoretical possibility of type replacement strongly depends on the existence of natural type competition mechanisms. Nevertheless, our results suggest that type replacement is viable at the within-host level if the degree of cross-protection induced by the vaccine is low, even if there is no underlying competition among HPV types. Consequently, the impact of current HPV vaccines at both the immunological and epidemiological levels rely upon the level of cross-protection.     

Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

In this article, we study a nonlinear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to image processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L ^?(? ⁿ ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L ^p (? ⁿ )-spaces, L ^αlog ^β L(? ⁿ )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included.     

On the divisor function in short intervals

Let d(n) denote the number of positive divisors of the natural number n. The aim of this paper is to investigate the validity of the asymptotic formula

$\begin{array}{lll}\sum \limits_{x < n \leq x+h(x)}d(n)\sim h(x)\log x\end{array}$

for \({x \to + \infty,}\) assuming a hypothetical estimate on the mean

$\begin{array}{lll} \int \limits_X^{X+Y}(\Delta(x+h(x))-\Delta (x))^2\,{d}x, \end{array}$

which is a weakened form of a conjecture of M. Jutila.

     

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces

In this paper, we study the theory of a Kantorovich version of the multivariate neural network operators. Such operators, are activated by suitable kernels generated by sigmoidal functions. In particular, the main result here proved is a modular convergence theorem in Orlicz spaces. As special cases, convergence theorem in \(L^p\)-spaces, interpolation spaces, and exponential-type spaces can be deduced. In general, multivariate approximations by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of activation functions of sigmoidal-type for which the above theory holds have been described.     

Interpolation by neural network operators activated by ramp functions

In this paper, a family of interpolation neural network operators are introduced. Here, ramp functions as well as sigmoidal functions generated by central B-splines are considered as activation functions. The interpolation properties of these operators are proved, together with a uniform approximation theorem with order, for continuous functions defined on bounded intervals. The relations with the theory of neural networks and with the theory of the generalized sampling operators are discussed.