A novel methodological approach for δ18O analysis of sugars using gas chromatography-pyrolysis-isotope ratio mass spectrometry

Although the instrumental coupling of gas chromatography-pyrolysis-isotope ratio mass spectrometry (GC-Py-IRMS) for compound-specific δ¹⁸O analysis has been commercially available for more than a decade, this method has been hardly applied so far. Here we present the first GC-Py-IRMS δ¹⁸O results for trimethylsilyl-derivatives of plant sap-relevant sugars and a polyalcohol (glucose, fructose, sucrose, raffinose and pinitol). Particularly, we focus on sucrose, which is assimilated in leaves and which is the most important transport sugar in plants and hence of utmost relevance in plant physiology and paleoclimate studies. Replication measurements of sucrose standards and concentration series indicate that the GC-Py-IRMS δ¹⁸O measurements are not stable over time and that they are amount (area) dependent. We, therefore, suggest running sample batch replication measurements in alternation with standard concentration series of reference material. This allows for carrying out (i) a drift correction, (ii) a calibration against reference material and (iii) an amount (area) correction. Tests with ¹⁸O-enriched water do not provide any evidence for oxygen isotope exchange reactions affecting sucrose and raffinose. We present the first application of GC-Py-IRMS δ¹⁸O analysis for sucrose from needle extract (soluble carbohydrate) samples. The obtained δ¹⁸O_{sucrose/ Vienna Standard Mean Ocean Water (VSMOW)} values are more positive and vary in a wider range (32.1–40.1 ‰) than the δ¹⁸O_{bulk/ VSMOW} values (24.6–27.2 ‰). Furthermore, they are shown to depend on the climate parameters maximum day temperature, relative air humidity and cloud cover. These findings suggest that δ¹⁸O_sucrose of the investigated needles very sensitively reflects the climatically controlled evaporative ¹⁸O enrichment of leaf water and thus highlights the great potential of GC-Py-IRMS δ¹⁸O_sucrose analysis for plant physiology and paleoclimate studies.     

Spectrum of the Cesàro operator in ℓ p

We present a novel proof of the fact that the spectrum of the Cesàro operator acting in ? ^p , for 1 < p < ∞, consists of the closed disc centered at q/2 and with radius q/2, where q is the conjugate index of p.     

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F^{\prime }(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss–Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to $0$ both for an a priori stopping rule and for a Lepski?-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback–Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performance of the proposed method for these problems is illustrated in numerical examples.     

Weak convergence of approximate solutions of random equations

Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions.     

Variable Resolution Bivariate Plots

Abstract

Scatterplots are the method of choice for displaying the distribution of points in two dimensions. They are used to discover patterns such as holes, outliers, modes, and association between the two variables. A common problem is overstriking—the overlap on the plotting surface of glyphs representing individual observations. Overstriking can create a misleading impression of the data distribution. The variable resolution bivariate plots (Varebi plots) proposed in this article deal with the problem of overstriking by mixing display of a density estimate and display of individual observations. The idea is to determine the display format by analyzing the actual amount of overstriking on the screen. Thus, the display format will depend on the sample size, the distribution of the observations, the size and shape of individual icons, and the size of the window. It may change automatically when the window is resized. Varebi plots reveal detail wherever possible, and show the overall trend when displaying detail is not feasible.     

Computational singular perturbation with non-parametric tabulation of slow manifolds for time integration of stiff chemical kinetics

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H₂–air and CH₄–air ignition, over a range of initial conditions. For CH₄–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy.     

The Robin problem for the scalar Oseen equation

We study the Robin problem for the scalar Oseen equation in an open n‐dimensional set with compact Ljapunov boundary. We prescribe two types of Robin boundary conditions, and prove the unique solvability of these problems as well as a representation formula for the solution in form of a scalar Oseen single layer potential. Moreover, we prove the maximum principle for the solution to the Robin problem of the scalar Oseen equation. Copyright © 2013 John Wiley & Sons, Ltd.