Phase-shifting windowed Fourier ridges for determination of phase derivatives

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.     

Interaction between salinity intrusion and vegetation succession: A modeling approach

Predicting potential changes in groundwater salinity in low-lying coastal regions due to climate change is important, where coastal vegetation is abundant, succession competition between halophytes and glycophytes plays a significant role in the salinity budget. Sea level rise enhances salinity intrusion, contributing an additional dimension to vegetation competition. A new simulation model known as mangrove-hardwood hammock model coupled with saturated-unsaturated transport (MANTRA) has recently been developed by the authors to simulate groundwater salinity regimes in the presence of vegetation competition, subject to climate change. MANTRA is based upon linking two existing Unites States geological survey (USGS) simulation models known as mangrove-hardwood hammock model (MANHAM) and saturated-unsaturated transport (SUTRA). MANHAM simulates the evolution of vegetation succession subject to changing groundwater salinity. SUTRA simulates saturated and unsaturated transport of solutes and salinity in groundwater given sea salinity. MANTRA improves the simulation robustness to simultaneously simulate groundwater hydrology, salinity and coastal vegetation succession subject to sea level rise. Some simulation results will be presented to demonstrate the impact of sea level rise on coastal vegetation succession and groundwater salinity.     

Alternative charge stabilisation and a changing reactivity of 1,3,5-triazine based starburst compounds as studied by in situ ESR/UV–vis–NIR spectroelectrochemistry

The role of the chemical structure in an alternative charge stabilisation and a changing reactivity of star-shaped compounds with a central triazine ring linked to aryl groups like thiophene, furan or ethylenedioxythiophene synthesized by a Stille cross-coupling procedure, is followed by spectroelectrochemical measurements. While cathodic reduction leads to stable anion radicals with a delocalised spin on the central triazine moiety, dimerisation and oligomerisation occurs upon anodic oxidation. The stability of the charged states in the polymer film increased substantially using an EDOT (3,4-ethylenedioxythiophene) side group. The location of the charged states on the molecules has been proved by computations. These star-shaped molecules are excellent model structures for studies of the competition of dimerisation and oligomerisation processes based on the variation of the electron and spin distribution in the molecules.     

A new L-curve for ill-posed problems

The truncated singular value decomposition is a popular method for the solution of linear ill-posed problems. The method requires the choice of a truncation index, which affects the quality of the computed approximate solution. This paper proposes that an L-curve, which is determined by how well the given data (right-hand side) can be approximated by a linear combination of the first (few) left singular vectors (or functions), be used as an aid for determining the truncation index.     

Identification of complex,naturally occurring flavonoid glycosides in kale (Brassica oleracea var. sabellica) by high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry

Kale is a member of the Brassicaceae family and has a complex profile of flavonoid glycosides. Therefore, kale is a suitable matrix to discuss in a comprehensive study the different fragmentation patterns of flavonoid glycosides. The wide variety of glycosylation and acylation patterns determines the health‐promoting effects of these glycosides. The aim of this study is to investigate the naturally occurring flavonoids in kale. A total of 71 flavonoid glycosides of quercetin, kaempferol and isorhamnetin were identified using a high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry (HPLC‐DAD/ESI‐MSⁿ) method. Of these 71 flavonol glycosides, 27 were non‐acylated, 30 were monoacylated and 14 were diacylated. Non‐acylated flavonol glycosides were present as mono‐, di‐, tri‐ and tetraglycosides. This is the first time that the occurrence of four different fragmentation patterns of non‐acylated flavonol triglycosides has been reported in one matrix simultaneously. In addition, 44 flavonol glycosides were acylated with p‐coumaric, caffeic, ferulic, hydroxyferulic or sinapic acid. While monoacylated glycosides existed as di‐, tri‐ and tetraglycosides, diacylated glycosides occurred as tetra‐ and pentaglycosides. To the best of our knowledge, 28 compounds in kale are reported here for the first time. These include three acylated isorhamnetin glycosides (isorhamnetin‐3‐O‐sinapoyl‐sophoroside‐7‐O‐D‐glucoside, isorhamnetin‐3‐O‐feruloyl‐sophoroside‐7‐O‐diglucoside and isorhamnetin‐3‐O‐disinapoyl‐triglucoside‐7‐O‐diglucoside) and seven non‐acylated isorhamnetin glycosides. Copyright © 2010 John Wiley & Sons, Ltd.     

On the theory of convolution equations of the third kind, II

Existence results of Part I of the paper are generalized to two types of autoconvolution equations of the third kind having free terms with nonzero values at x=0 like the well-known Bernstein-Doetsch equation for the Jacobian theta zero functions. Also uniqueness results for the linear convolution equations in Part I of the paper are extended to more general function spaces. Further, a special class of integro-differential equations with autoconvolution integral and two classes of the linear singular Abel-Volterra equations are dealt with.     

Hexafluoroacetone as a Protecting and Activating Reagent. N- and O-Glycosylation of Isoserine and Isocysteine

Starting from HFA-protected malic and thiomalic acid a series of O- and N-glycoconjugates suitable for peptide and depsipeptide modification has been synthesized.     

A new zero-finder for Tikhonov regularization

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification (2000)  65F22, 65H05, 65R32     

The use of vector-valued martingales in risk theory

A completely dependent risk process with perturbation and phase-type distributed claim sizes is analyzed. Claim arrivals are modeled by a Markovian arrival process. Using a vector-valued martingale, the Laplace transform of the time to ruin is derived algorithmically. The conditional memoryless property of the phase-type distribution yields the distribution of the deficit at ruin as a corollary.