Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295, 2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation

We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.     

Cytoprotective Mechanisms of DJ-1: Implications in Cardiac Pathophysiology

DJ-1 was originally identified as an oncogene product while mutations of the gene encoding DJ-1/PARK7 were later associated with a recessive form of Parkinson’s disease. Its ubiquitous expression and diversity of function suggest that DJ-1 is also involved in mechanisms outside the central nervous system. In the last decade, the contribution of DJ-1 to the protection from ischemia-reperfusion injury has been recognized and its involvement in the pathophysiology of cardiovascular disease is attracting increasing attention. This review describes the current and gaps in our knowledge of DJ-1, focusing on its role in regulating cardiovascular function. In parallel, we present original data showing an association between increased DJ-1 expression and antiapoptotic and anti-inflammatory markers following cardiac and vascular surgical procedures. Future studies should address DJ-1’s role as a plausible novel therapeutic target for cardiovascular disease.     

Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theoryof elasticity of hemitropic materials. We derive general representationformulae for the displacement and microrotation vectors by meansof six scalar metaharmonic functions. These formulae are veryconvenient and useful in many particular problems for domainswith concrete geometry. Here we consider two canonical transmissionproblems for piecewise homogeneous bodies with spherical interfacesand with the help of the representation formulae construct explicitsolutions in the form of absolutely and uniformly convergentseries. The representations can also be applied to multi-layeredbodies with spherical and cylindrical interfaces.     

A framework and algorithms for circular drawings of graphs

In this paper, we present a framework and two linear time algorithms for obtaining circular drawings of graphs. The first technique produces circular drawings of biconnected graphs and finds a zero crossing circular drawing if one exists. The second technique finds multiple embedding circle drawings. Techniques for the reduction of edge crossings are also discussed. Results of experimental studies are included.     

Improving the order and rates of convergence for the Super-Halley method in Banach spaces

In this study we are concerned with the problem of approximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4], [5], [8]. These results were not given in affine invariant form, and made use of a real quadratic majorizing polynomial. Here, we provide our results in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.     

Encapsulation of the corrosion inhibitor 8-hydroxyquinoline into ceria nanocontainers

Ceria nanocontainers were synthesized through a two-step process and then loaded with 8-hydroxyquinoline (8-HQ). The size of the containers was 110 nm as determined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). X-ray diffraction analysis (XRD) showed that the ceria nanocontainers were of the cerianite crystalline phase. The presence of 8-HQ in the nanocontainers was confirmed with Fourier-transform infrared spectroscopy (FT-IR). The loading of the inhibitor in the nanocontainers was estimated with differential thermal analysis (DTA) and thermogravimetric analysis (TGA). The loading amount of 8-HQ was 4.28% w/w. Based on the size of the nanocontainers and the assumption that they are not broken, we deduced that there were approximately 6.0 × 10⁵ molecules of 8-HQ per container. Furthermore, release of 8-HQ in a corrosive environment was studied by potentiodynamic measurements, showing that the inhibitor is released from the nanocontainers, suppressing the corrosion activities by a strong barrier effect. SEM and dynamic light scattering (DLS) measurements confirmed that the nanocontainers are not significantly agglomerated and maintain their shape after suspension in 0.5 M NaCl solution for more than 72 h.     

Acquisition times,relaxation rates and solvent and temperature effects as sensitivity parameters for quadrupolar nuclei

The relationship between the signal-to-noise ration and T₂ and, hence, the line width of a resonance for quadrupolar nuclei, with particular reference to ¹⁷O at natural abundance, is discussed. Emphasis is placed on the importance of choosing appropriate FID acquisition times related to the T₂ values or resonance widths of the quadrupolar nuclei. When this is feasible (i.e. when the principal resonances in a spectrum have similar widths) the signal-to-noise ratio attainable against a flat base line in a given time of spectral accumulation is independent of resonance line width. Although resolution improvements can be made by using appropriate solvents or elevated sample temperatures, the sensitivity has been to be strongly dependent on the acquisition parameters used.