Multivariate Analysis of MALDI Imaging Mass Spectrometry Data of Mixtures of Single Pollen Grains

Mixtures of pollen grains of three different species (Corylus avellana, Alnus cordata, and Pinus sylvestris) were investigated by matrix-assisted laser desorption/ionization time-of-flight imaging mass spectrometry (MALDI-TOF imaging MS). The amount of pollen grains was reduced stepwise from >?10 to single pollen grains. For sample pretreatment, we modified a previously applied approach, where any additional extraction steps were omitted. Our results show that characteristic pollen MALDI mass spectra can be obtained from a single pollen grain, which is the prerequisite for a reliable pollen classification in practical applications. MALDI imaging of laterally resolved pollen grains provides additional information by reducing the complexity of the MS spectra of mixtures, where frequently peak discrimination is observed. Combined with multivariate statistical analyses, such as principal component analysis (PCA), our approach offers the chance for a fast and reliable identification of individual pollen grains by mass spectrometry.

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Optimality of the quantified Ingham–Karamata theorem for operator semigroups with general resolvent growth

We prove that a general version of the quantified Ingham–Karamata theorem for $$C_0$$-semigroups is sharp under mild conditions on the resolvent growth, thus generalising the results contained in a recent paper by the same authors. It follows in particular that the well-known Batty–Duyckaerts theorem is optimal even for bounded $$C_0$$-semigroups whose generator has subpolynomial resolvent growth. Our proof is based on an elegant application of the open mapping theorem, which we complement by a crucial technical lemma allowing us to strengthen our earlier results.     

Rates of decay in the classical Katznelson-Tzafriri theorem

The Katznelson-Tzafriri Theorem states that, given a power-bounded operator T, ∥Tⁿ(I ? T)∥ → 0 as n → ∞ if and only if the spectrum σ(T) of T intersects the unit circle T in at most the point 1. This paper investigates the rate at which decay takes place when σ(T) ∩ T = {1}. The results obtained lead, in particular, to both upper and lower bounds on this rate of decay in terms of the growth of the resolvent operator R(e^iθ, T) as θ → 0. In the special case of polynomial resolvent growth, these bounds are then shown to be optimal for general Banach spaces but not in the Hilbert space case.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Periodic solutions of certain hybrid delay-differential equations and their corresponding difference equations

In this paper we use a method due to Carvalho (A method to investigate bifurcation of periodic solution in retarded differential equations, J. Differ. Equ. Appl. 4 (1998), pp. 17–27) to obtain conditions for the existence of nonconstant periodic solutions of certain systems of hybrid delay-differential equations. We first deal with a scalar equation of Lotka–Valterra type; then a system of two equations in two unknowns that could model the interactions of two identical neurons. It will be seen that such solutions are determined by solutions of corresponding difference equations. Another paper in which this method is used is by Cooke and Ladeira (Applying Carvalho's method to find periodic solutions of difference equations, J. Differ. Equ. Appl. 2 (1996), pp. 105–115).

We first state Carvalho's result.     

Current CONtrolled Transmit And Receive Coil Elements (C2ONTAR) for Parallel Acquisition and Parallel Excitation Techniques at High-Field MRI

A novel intrinsically decoupled transmit and receive radio-frequency coil element is presented for applications in parallel imaging and parallel excitation techniques in high-field magnetic resonance imaging. Decoupling is achieved by a twofold strategy: during transmission elements are driven by current sources, while during signal reception resonant elements are switched to a high input impedance preamplifier. To avoid B(0) distortions by magnetic impurities or DC currents a resonant transmission line is used to relocate electronic components from the vicinity of the imaged object. The performance of a four-element array for 3 T magnetic resonance tomograph is analyzed by means of simulation, measurements of electromagnetic fields and bench experiments. The feasibility of parallel acquisition and parallel excitation is demonstrated and compared to that of a conventional power source-driven array of equivalent geometry. Due to their intrinsic decoupling the current-controlled elements are ideal basic building blocks for multi-element transmit and receive arrays of flexible geometry.     

Trim-to-Coherence Fourier Transform

We introduce a discrete Fourier transform technique which extracts more spectral information from a given time series data set than conventional discrete Fourier transform (DFT). Valid information is obtained between the spectral bins of conventional DFT, scalloping error is greatly reduced, and amplitude and phase of Fourier components are more true to the process under study as with conventional DFT. We call the general idea Trim-to-Coherence Fourier Transform, and its particular embodiment ‘Phase-Rotation Fourier Transform’. Treatment of the raw data is minimally invasive; e.g. there is no zero padding.     

High Pressure — High Temperature — Synthesis and Properties of Chromium Kyanite, (Al,Cr)2SiO5

At pressures up to 30 kb and temperatures of 1000–1500°C up to 25% of the Al₃₊ in the Al₂SiO₂-polymorph kyanite could be replaced by Cr₃₊ (composition (Al_1.5Cr_0.5)SiO₅). The lattice constants a₀, b₀, c₀ increase by this substitution, whereas the triclinic angles α, β, γ remain virtually unaffected. Cr₃₊ substitutes for Al in the chains of (AlO₃₊)-octahedra parallel to c₀. The reflectance spectrum (240-1000 nm) exhibits the spin-forbidden ruby lines in addition to the spin-allowed transitions in Cr₃₊ in octahedral coordination. The half width (～3.8 kK), position, and shape of the 10 Dq band indicates a symmetry not higher than D_4h for the Cr₃₊-containing octahedra which is in accordance with structure refinement data for pure Kyanite (Burnham 1963).