Marcinkiewicz-Type Spectral Multipliers on Hardy and Lebesgue Spaces on Product Spaces of Homogeneous Type

Let \(X_1\) and \(X_2\) be metric spaces equipped with doubling measures and let \(L_1\) and \(L_2\) be nonnegative self-adjoint operators acting on \(L^2(X_1)\) and \(L^2(X_2)\) respectively. We study multivariable spectral multipliers \(F(L_1, L_2)\) acting on the Cartesian product of \(X_1\) and \(X_2\). Under the assumptions of the finite propagation speed property and Plancherel or Stein–Tomas restriction type estimates on the operators \(L_1\) and \(L_2\), we show that if a function F satisfies a Marcinkiewicz-type differential condition then the spectral multiplier operator \(F(L_1, L_2)\) is bounded from appropriate Hardy spaces to Lebesgue spaces on the product space \(X_1\times X_2\). We apply our results to the analysis of second-order elliptic operators in the product setting, specifically Riesz-transform-like operators and double Bochner–Riesz means.     

Structural investigation of hemicelluloses from Plantago ovata,Mimosa pudica and Lallemantia royleana by MALDI-ToF mass spectrometry

Abstract

This work concerns structural investigation of water-extractable hemicelluloses from seed husk of Plantago ovata and seeds of Mimosa pudica and Lallemantia royleana. The composition of the materials was determined by CHN elemental analysis, FT-IR spectrometry and monosaccharide analysis. The detailed structural analysis was carried out by MALDI-ToF mass spectrometry. The absence of nitrogen in the materials suggested that they were free from proteins. The isolated materials were found to be branched hemicelluloses. The mass spectrometric study showed presence of β-1,4-linked xylose with arabinose attached to main chain at β-1,3 positions (Plantago ovata), β-1,4-linked xylose with glucose attached to main chain at β-1,3 positions (Mimosa pudica), and β-1,2-linked rhamnose and β-1,3-linked arabinose units in the main chain with arabinose attached to the main chain through β-1,3-linkage (Lallemantia royleana).     

Marked point processes in discrete time

Queueing Systems - We develop a general framework for stationary marked point processes in discrete time. We start with a careful analysis of the sample paths. Our initial representation is a...     

Discovery and characterization of a cell-permeable, small-molecule c-Abl kinase activator that binds to the myristoyl binding site

c-Abl kinase activity is regulated by a unique mechanism involving the formation of an autoinhibited conformation in which the N-terminal myristoyl group binds intramolecularly to the myristoyl binding site on the kinase domain and induces the bending of the αI helix that creates a docking surface for the SH2 domain. Here, we report a small-molecule c-Abl activator, DPH, that displays potent enzymatic and cellular activity in stimulating c-Abl activation. Structural analyses indicate that DPH binds to the myristoyl binding site and prevents the formation of the bent conformation of the αI helix through steric hindrance, a mode of action distinct from the previously identified allosteric c-Abl inhibitor, GNF-2, that also binds to the myristoyl binding site. DPH represents the first cell-permeable, small-molecule tool compound for c-Abl activation.     

Merging the best of two worlds: artificial metalloenzymes for enantioselective catalysis

Artificial metalloenzymes result from combining a catalytically active organometallic moiety with a macromolecular host. The resulting hybrid catalysts combine attractive features of both homogeneous and enzymatic systems. Herein we summarize the recent progress in this emerging field and outline the challenges ahead.     

Characterizing the impact of thermal gels on isotachophoresis in microfluidic devices

Thermally reversible Pluronic gels have been employed as separation matrices in microfluidic devices in the analysis of biological macromolecules. The phase of these gels can be tuned between liquid and solid states using temperature to vary fluidic resistance and alter peak resolution. Although separations in thermal gels have been characterized, their effect on isotachophoresis has not. This study used fluorescein as a model analyte to evaluate isotachophoretic preconcentration as a function of thermal polymer concentration and temperature. Results demonstrated that increasing polymer concentration in microfluidic channels increased the apparent analyte concentration. A critical minimum of 10% (w/v) Pluronic was required to achieve efficient preconcentration with maximum focusing occurring in 20 and 25% polymer gels. Temperature of the thermal gel also impacted analyte focusing. Most efficient focusing was achieved at 25°C with diminishing analyte accumulation at higher and lower temperatures. Under optimal conditions, isotachophoretic preconcentration increased an additional threefold simply by including thermal gels in the system. This approach can be readily implemented in other applications to increase detection sensitivity and measure low-concentration analytes within simple microfluidic devices.     

Molecular motion in zinc hydrazone grid complexes

Four new grid forming hydrazone ligands substituted with methoxy and dimethylamino groups were synthesised. Combination of these ligands with zinc triflate in acetonitrile resulted in self-assembly to form grids as indicated by ¹H NMR and ES-MS. ¹H NMR also showed thermally induced rotation of the intercalated phenyl ring in both the new grids, and in three previously reported grid compounds. Of these seven, five were amenable to study by variable temperature ¹H NMR. Though the observed rates varied by more than an order of magnitude depending upon ligand structure and level of deprotonation, activation energies were similar (～60 kJ/mol) for all complexes studied. This suggests a model in which dissociation of the central pyrimidine ligand precedes phenyl group rotation with an enthalpy of dissociation near zero. The rate of rotation of the phenyl ring increases with an introduction of electron-donating substituents on the phenyl ring, possibly due to an increased repulsion between π systems.     

Quality-aware visual data analysis

The quality, certainty, or confidence of decisions made during the visual analytics process depends on many factors, including the completeness and reliability of the initial data, information loss due to filtering, sampling, and other transformations, and the accuracy and clarity of the visual presentation. Unfortunately, in most visualization tools the analyst is unaware of these and other forces that degrade the meaningfulness of their results. In this paper, we describe our efforts to design strategies for tackling the measurement, display, and utilization of quality aspects at all stages of the visualization pipeline. The goal is to help analysts maintain an awareness of the accuracy and completeness of the information conveyed in the images, and subsequently the patterns observed and decisions made based on the analysis. Quality measures can be used both to assist analysts in selecting, transforming, and mapping their data as well as to automatically refine processes to generate higher quality views. We have implemented several such techniques within XmdvTool, a public-domain package for visual analytics. We illustrate the quality-specific components of our tool with several case studies to show the usefulness of the approach. We also describe user studies that were performed to validate the accuracy of our quality measures.