On the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f₁,₂, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f₁),λ(f₂)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f₁, f₂ each with λ(f_i) ≤ 1.     

Amino substituted 1-oxa-3-azabutatrienium salts: preparation, structure and reaction with carbonyl compounds

N,N-Dimethylformamide ($\text{4a}$) and N,N-dimethylpivalamide ($\text{4b}$) react with carbonyl chloride isocyanate ($\text{5}$) in the presence of antimony pentachloride to afford the amino substituted 1-oxa-3-azabutatrienium hexachloroantimonates $\text{6a}$,$\text{b}$. An X-ray diffraction analysis of $\text{6a}$ confirms the proposed structure. The heterocumulenes $\text{6a}$,$\text{b}$ react with aldehydes, ketones and tertiary carboxamides to give the amino substituted 2-azaallenium salts $\text{13a}$-$\text{O}$ in high yields.     

Particle-stabilized emulsions comprised of solid droplets

We kinetically stabilize oil-in-water emulsions comprising paraffin crystals by adsorbing solid particles (silica) of colloidal size at the oil/water interface. We obtain a set of emulsions that are quiescently stable for a long period of time (months), while the same emulsions are destabilized after only a few hours in the presence of surfactant molecules alone. The emulsions are submitted to a shear stress in order to probe their stability under flow conditions. Partial coalescence and gelation occur when the shear is applied for a sufficiently long period of time. The experiments reveal the existence of a critical droplet mass fraction, phi*, that defines a sharp transition between slow and fast gelation. The process of gelation is rather slow for phi < phi*, occurring at the scale of hours, and becomes almost instantaneous above phi*.     

Smart materials based on self-assembled hydrogen-bonded comb-shaped supramolecules

Block copolymer self-assembly and supramolecular chemistry can be combined most naturally to prepare smart polymer nanomaterials. An attractive route is based on comb-shaped supramolecules, obtained by attaching side chains to (co)polymers by physical (non-covalent) interactions. Hydrogen bonding is a key element of our approach. It combines an ease of synthesis with other important approach-specific elements, such as hierarchical self-assembly, strongly enhanced processability, swelling, and cleaving. Functional properties discussed include anisotropic proton conductivity, switching proton conductivity, electronically conducting nanowires, polarized luminance, dielectric stacks (optical reflectivity), functional membranes, and nano objects.     

On applicability of PCA,voxel-wise variance normalization and dimensionality assumptions for sliding temporal window sICA in resting-state fMRI

Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤ 0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations.     

Isolation and Characterization of Cellulosic Pulp Fines and Their Interactions with Cationic Polyacrylamides

Four different types of cellulosic fines were isolated from refiner mechanical and kraft pulp samples to characterize their chemical and physical properties. The pulp fines were flocculated using four different types of cationically modified polyacrylamides. The extent of flocculation was observed with multiple light scattering apparatus. The maximum adsorption of the polyelectrolytes on the pulp fines was determined by polyelectrolyte titration. It was concluded that it is the combination of the molar mass and the charge density of a polyelectrolyte, as well as the origins and characteristics of the fines which define the adsorption and flocculation behavior. None of these properties alone could fully describe these phenomena, but the molar mass of the polyelectrolyte was the predominant factor. The most important fines characteristics were the charge properties and the microstructure.     

Spectroscopic imaging with volume selection by unpaired adiabatic pi pulses: theory and application

In NMR spectroscopy, volume selection can be advantageously achieved using adiabatic pi pulses, which enable high bandwidth and B(1) insensitivity. In order to avoid the generation of non-linear phase profiles and the subsequent signal loss caused by incoherent averaging, adiabatic pi pulses are usually used in pairs for volume selection in each spatial dimension. Alternatively, when performing spectroscopic imaging (SI), a high enough spatial resolution results in negligible phase dispersion within each pixel. This allows using only one pulse per selected spatial dimension, resulting in a reduced echo-time and reduced power deposition. In this work, the feasibility of such an approach is explored theoretically and numerically, allowing the derivation of explicit conditions to obtain SI images without artifact. Adequate spatial and spectral post-processing procedures are described to compensate for the effect of non-linear phase profiles. These developments are applied to SI in the rat brain at 9.4 T, using a new adiabatic sequence named Pseudo-LASER.