Global stability of a rational symmetric difference equation

Motivated by ideas from papers: C. Cinar, I. Yalçinkaya, S. Stević, A note on global asymptotic stability of a family of rational equations, Rostock. Math. Kolloq. 59 (2004), 41–49, and S. Stević, Global stability and asymptotics of some classes of rational difference equations, J. Math. Anal. Appl. 316 (2006), 60–68, here we confirm a conjecture on a rational symmetric difference equation from the paper: K. Berenhaut, J. Foley, S. Stević, The global attractivity of the rational difference equation , Appl. Math. Lett. 20 (2007), 54–58.     

Effect of stochastic resonance on bone loss in osteopenic conditions

We investigate the effect of noise on the remodelling process of the inner spongy part of the trabecular bone. Recently, a new noise-induced phenomenon in bone formation has been reported experimentally. We propose the first conceptual model for this finding, explained by the stochastic resonance effect, and provide a theoretical basis for the development of new countermeasures for bone degeneration in long space flights, which currently has dramatic consequences on return to standard gravity. These results may also be applicable on Earth for patients under osteopenic conditions.     

Comment on “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” by Rohde et al. [Physica D 237 (2008) 619-629]

In the recent article “Stochastic analysis of recurrence plots with applications to the detection of deterministic signals” (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.Nevertheless, we also clearly assert that an uncritical application of RQA may lead to wrong conclusions.     

Complex networks in climate dynamics

Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.     

Bindungsverhältnisse in molekülen vom typ R3X-CY (R = H,CH3; X = C,Si; Y = N,CH)

Starting with the experimental results for the X-C bond lengths in this series of compounds, an attempt was made to explain the effect of the substituents R and Y on this bond length in the single molecules. Using the results of CNDO/2 calculations it can be shown why only the substituent Y has a dominant effect on the Si-C bond length in the silicon compounds, while the substituent R has a dominant effect on the C-C bond length in the carbon analogues.     

Quantitative Raman and ESCA characterization of titania supported tungsten catalysts

Summary The distribution of supported species in a series of W/TiO₂ catalysts (1.8 – 28 wt% WO₃) has been determined by Raman and X-ray photoelectron spectroscopy (XPS, ESCA). The results show that three tungsten species are present on oxidic W/TiO₂ catalysts. A tungsten interaction species is formed almost exclusively for catalysts with W loadings lower or equal to 6.7 wt% WO₃. WO₃ is observed above 6.7 wt% WO₃. For W loadings higher than 10 wt%, a disordered W species W_DS is also present. The amounts of W_DS and WO₃ increase with increasing W content above 10 wt% WO₃.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

An electron diffraction study of the molecular structure of gaseous cyclobutylgermane

The molecular structure and conformation of cyclobutylgermane have been determined by gas-phase electron diffraction. Like its counterpart cyclobutylsilane (CBS) it possesses quasi-equatorial and quasi-axial conformers. The most interesting aspect of the structure of CBG is the influence of the germyl group on the ratio of equatorial to axial conformers. The predominance of the quasi-equatorial conformer (ΔG = 3.1(1) kJ mol⁻¹), the near equality of the skeleton C---C bond lengths (C---C = 1.557(3)A) (r_a value) and the values of the puckering angles for the equatorial angles form and the axial one of 25.3(3.1)° and −20.4(3.6)° respectively, all support the predictions made by Jonvik and Boggs concerning the correlation between electronegativity and structural parameters in four-membered rings. From a consideration of these predictions, a comparison of the most prominent structural factors in CBG and cyclobutylsilane indicates that the germanium atom is more electronegative than silicon. This result could be considered as the first structural evidence for the previously postulated inversion of the electronegativity order within group IV.     

Nearfield binaural synthesis and ambisonics

Ambisonic encodings can be rendered binaurally, as well as for speaker arrays. This process is developed for general high-order Ambisonic encodings of soundfields containing near as well as far sources. For sufficently near sources an error is identified, resulting from the limited field of validity of the freefield harmonic expansion. A modified expansion is derived that can render such sources correctly.     

A New and Elegant Approach for Solving $$\varvec{n \times n}$$-Order Linear Fractional Differential Equations

The application of fractional differential equations (FDEs) in the fields of science and engineering are gradually increasing day by day during the last two decades. The solutions of linear systems of FDEs are of great importance. Several investigations are carried out on such systems using eigenvalue analysis or Laplace transform method. But both the methods have limitations, and as of now there are no methods for solving \(n \times n\)-order linear FDEs. In the present investigation, the issues of such difficulties are addressed, and the exact solutions of linear \(2 \times 2\)-order linear FDEs are presented by Laplace transform. We are unable to provide the exact solutions of such system of order \(n \times n\) by Laplace transform. To overcome this, we provide a new and elegant approach to find the approximate solutions of \(n \times n\)-order linear FDEs with the help of residual power series (RPS) method. The results thus obtained are verified by providing numerous examples.