Division point measures resulting from triangle subdivisions

When dividing a 1- or 2-dimensional region according to a specified scheme, division points are continually created as the process continues. A measure results from assigning weights to each of these points. In the 1-dimensional setting, results concerning the distribution of division points are well known, and suggest how to study analogous processes in two dimensions. We explore two different division schemes on a triangular region and three different measures based on each subdivision, finding the limiting measures in each case.     

Regularity of fractional maximal functions through Fourier multipliers

We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n\ge 2$. We also show that the spherical fractional maximal function maps $L^p$ into a first order Sobolev space in dimensions $n\ge 5$.     

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

Journal of Fourier Analysis and Applications - We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition...     

Superhydrophobic and superoleophobic nanocellulose aerogel membranes as bioinspired cargo carriers on water and oil

We demonstrate that superhydrophobic and superoleophobic nanocellulose aerogels, consisting of fibrillar networks and aggregates with structures at different length scales, support considerable load on a water surface and also on oils as inspired by floatation of insects on water due to their superhydrophobic legs. The aerogel is capable of supporting a weight nearly 3 orders of magnitude larger than the weight of the aerogel itself. The load support is achieved by surface tension acting at different length scales: at the macroscopic scale along the perimeter of the carrier, and at the microscopic scale along the cellulose nanofibers by preventing soaking of the aerogel thus ensuring buoyancy. Furthermore, we demonstrate high-adhesive pinning of water and oil droplets, gas permeability, light reflection at the plastron in water and oil, and viscous drag reduction of the fluorinated aerogel in contact with oil. We foresee applications including buoyant, gas permeable, dirt-repellent coatings for miniature sensors and other devices floating on generic liquid surfaces.     

Matrix effect in the analysis of drugs of abuse from urine with desorption atmospheric pressure photoionization-mass spectrometry (DAPPI-MS) and desorption electrospray ionization-mass spectrometry (DESI-MS)

We have studied the matrix effect within direct analysis of benzodiazepines and opioids from urine with desorption electrospray ionization-mass spectrometry (DESI-MS) and desorption atmospheric pressure photoionization-mass spectrometry (DAPPI-MS). The urine matrix was found to affect the ionization mechanism of the opioids in DAPPI-MS favoring proton transfer over charge exchange reaction. The sensitivity for the drugs in solvent matrix was at the same level with DESI-MS and DAPPI-MS (LODs 0.05–6 μg mL⁻¹) but the decrease in sensitivity due to the urine matrix was higher with DESI (typically 20–160-fold) than with DAPPI (typically 2–15-fold) indicating better matrix tolerance of DAPPI over DESI. Also in MS/MS mode, DAPPI provided better sensitivity than DESI for the drugs in urine. The feasibility of DAPPI-MS/MS was then studied in screening the same drugs from five authentic, forensic post mortem urine samples. A reference measurement with gas chromatography-mass spectrometry (GC–MS) (including pretreatment) revealed 16 findings from the samples, whereas with DAPPI-MS/MS after sample pretreatment, 15 findings were made. Sample pretreatment was found necessary, since only eight findings were made from the same samples untreated.     

The offline combination of thin-layer chromatography and high-performance liquid chromatography with diode array detection and micrOTOF-Q mass spectrometry for the separation and identification of spinochromes from sea urchin (Strongylocentrotus droebachiensis) shells

Thin-layer chromatography (TLC) with off-line high-performance liquid chromatography coupled to diode array detection and micrOTOF-Q mass spectrometry (HPLC-DAD-MS) resulted in the successful fractionation, separation and identification of spinochrome pigments from sea urchin (Strongylocentrotus droebachiensis) shells. Two fractions of pigments were separated by TLC and eluted with methanol using a TLC-MS interface. HPLC-DAD-MS analysis of the fractions indicated the presence of six sea urchin pigments: spinochrome monomers B and D, three spinochrome dimers (anhydroethylidene-6,6'-bis(2,3,7-trihydroxynaphthazarin) and its isomer and ethylidene-6,6'-bis(2,3,7-trihydroxynaphthazarin)), and one pigment that was preliminary identified as a spinochrome dimer with the structural formula C(22)H(16)O(16).     

Sobolev space properties of superharmonic functions on metric spaces

Our objective is to study regularity of superharmonic functions of a nonlinear potential theory on metric measure spaces. In particular, we are interested in the local integrability properties of a superharmonic function and its derivative. We show that every superharmonic function has a weak upper gradient and provide sharp local integrability estimates. In addition, we study absolute continuity of a superharmonic function.