Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

Theory and computation for multiple positive solutions of non-local problems at resonance

Resonance non-positone and non-isotone problems for first order differential systems subjected to non-local boundary conditions are reduced to the non-resonance positone and isotone case by changes of variables. This allows us to prove the existence of multiple positive solutions. The theory is illustrated by two examples for which three positive numerical solutions are obtained using the Mathematica shooting program.     

Vortex energy and 360° Néel walls in thin‐film micromagnetics

We study the vortex pattern in ultrathin ferromagnetic films of circular crosssection. The model is based on the following energy functional: for in‐plane magnetizations m: B² → S¹ in the unit disc . The avoidance of volume charges ? · m ≠ 0 in B² and surface charges m · ν ≠ 0 on δB² leads to the formation of a vortex in the limit ε → 0. At the level ε > 0 the vortex is regularized by the formation of a 360° Néel wall (a one‐dimensional transition layer with core of scale ε) concentrated along a radius of B². We derive the limiting energy of the vortex by matching upper and lower bounds. Our analysis on the lower bound is based on a dynamical system argument and an interpolation inequality with sharp leading‐order constant, while the upper bound uses the leading‐order energy for 360° Néel walls. © 2010 Wiley Periodicals, Inc.     

Pseudo-harmonic morphisms with low dimensional fibers

Harmonic morphisms with one-dimensional fibers are subject to various classification results [6], [13]. Motivated by this fact, we point out some particular phenomena which occur in the case ofpseudo-harmonic morphisms with one and two-dimensional fibers.     

Stable isotope study of precipitation and cave drip water in Florida (USA): implications for speleothem-based paleoclimate studies†

Stable isotopes of hydrogen and oxygen were used to examine how the isotopic signal of meteoric water is modified as it travels through soil and epikarst into two caves in Florida. Surface and cave water samples were collected every week from February 2006 until March 2007. The isotopic composition of precipitation at the investigated sites is highly variable and shows little seasonal control. The δ¹⁸O vs. δ²H plot shows a mixing line having a slope of 5.63, suggesting evaporation effects dominate the isotopic composition of most rainfall events of less than 8 cm/day, as indicated by their low d-excess values. The δ¹⁸O values of the drip water show little variability (<0.6‰), which is loosely tied to local variations in the seasonal amount of precipitation. This is only seen during wintertime at the Florida Caverns site.

The lag time of over two months and the lack of any relationship between rainfall amount and the increase in drip rate indicate a dominance of matrix flow relative to fracture/conduit flow at each site. The long residence time of the vadose seepage waters allows for an effective isotopic homogenisation of individual and seasonal rainfall events. We find no correlation between rainfall and drip water δ¹⁸O at any site. The isotopic composition of drip water in both caves consistently tends to resemble the amount-weighted monthly mean rainfall input. This implies that the δ¹⁸O of speleothems from these two caves in Florida cannot record seasonal cycle in rainfall δ¹⁸O, but are suitable for paleoclimate reconstructions at inter-annual time scales.? Revised version of a paper presented at the 9th, Symposium of the European Society for Isotope Research (ESIR), 23 to 28 June 2007, Cluj-Napoca, Romania.      

Hyperspectral Imaging in the Medical Field: Present and Future

Abstract

Hyperspectral imaging is an optical method that provides a large amount of information about the investigated object. Its medical applications are reviewed in this article, including tumor delimitation and identification, assessing tissue perfusion and its pathological conditions (including some complications like diabetic foot ulceration), making accurate surgical decisions, evaluating the health of dental structures, etc. Many of the articles show very promising results that required brief comments by the authors. It is clear that choosing the appropriate hyperspectral imaging system for each medical field, together with the most reliable hyperspectral image processing methods, are the main goals of future studies, before hyperspectral imaging becomes a widely applicable evaluation method in medicine. The authors try to answer some questions on this topic and set up some directions for future research.     

Mechanism of disease in early osteoarthritis: application of modern MR imaging techniques — a technical report

The application of biomolecular magnetic resonance imaging becomes increasingly important in the context of early cartilage changes in degenerative and inflammatory joint disease before gross morphological changes become apparent. In this limited technical report, we investigate the correlation of MRI T1, T2 and T1ρ relaxation times with quantitative biochemical measurements of proteoglycan and collagen contents of cartilage in close synopsis with histologic morphology. A recently developed MRI sequence, T1ρ, was able to detect early intracartilaginous degeneration quantitatively and also qualitatively by color mapping demonstrating a higher sensitivity than standard T2-weighted sequences. The results correlated highly with reduced proteoglycan content and disrupted collagen architecture as measured by biochemistry and histology. The findings lend support to a clinical implementation that allows rapid visual capturing of pathology on a local, millimeter level. Further information about articular cartilage quality otherwise not detectable in vivo, via normal inspection, is needed for orthopedic treatment decisions in the present and future.     

Influence of pitching on performance of VAWTs

Self- starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self-starting. To understand the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried out for the airfoil at various pitch angles, it was shown that the “dead band” phenomenon could be overcome, but only slightly. At the same time, to overcome the “dead band” with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75 to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine starting behavior and its influence parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady Flow and its Influence to Aerodynamic and Aeroacoustic of VAWT's

A study is reported of the influence of unsteady flow on the aerodynamics and aeroacoustics of vertical axis wind turbines by numerical simulation. The combination of aerodynamic predictions with a discrete vortex method and aeroacoustic predictions based on Ffowcs Williams-Hawkings equation is used to achieve this goal. The numerical results show that unsteady flow of the turbine has a significant influence on the turbine aerodynamics and can lead to a decrease in generated noise as compared to the conventional horizontal axis wind turbine at the similar aerodynamic performance. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)