Moments of the Mean of Dubins–Freedman Random Probability Distributions

Explicit formulas are given to recursively generate the moments of the mean M for Dubins–Freedman random distribution functions with arbitrary base measure . Using a standard inversion formula for moments of a distribution on the unit interval, the distribution of M is approximated for several natural choices of . The support of the mean is also considered. It is shown that the support of M is connected whenever is concentrated on the vertical bisector of the unit square S, but may have arbitrarily many gaps otherwise.     

A rheological and structural study of a discotic side chain polymer solution

The structural and dynamical properties of a physical network in a discotic side-chain polymer solution have been studied. For that purpose, use has been made of rheological measurements and a statistical network model for the crosslinking of polymer. The goal of the investigation was to gain more insight into processes playing important roles in the subtle interactions between discotic side-chain polymers. A relatively simple mechanical model is presented to describe the mechanical behaviour of the solutions. Moreover, results are shown for the specific dynamic as well as structural properties of the physical networks in these solutions.     

Preparation,physical properties,on-bead binding assay and spectroscopic reliability of 25 barcoded polystyrene-poly(ethylene glycol) graft copolymers

Here we describe the preparation of 25 beaded polystyrene-poly(ethylene glycol) graft copolymers from six spectroscopically active styrene monomers: styrene, 2,5-dimethylstyrene, 4-methylstyrene, 2,4-dimethylstyrene, 4-tert-butylstyrene, and 3-methylstyrene. These polymers were thoroughly characterized by Raman, infrared, and (1)H/(13)C NMR spectroscopies, and differential scanning calorimetry. Determination of the swelling properties, peptide synthesis, and on-bead streptavidin-alkaline phosphatase (SAP) binding assay further established that their physical and chemical properties where not significantly altered by the diversity of their encoded polystyrene core. Each of the 25 resins displayed a unique Raman and infrared vibrational fingerprint, which was converted into a "spectroscopic barcode". The position of each bar matches the peak wavenumber in the corresponding spectrum but is independent of its intensity. From this simplified representation similarity maps comparing 35 000 resin pairs were generated to establish the spectroscopic barcoding as a reliable encoding methodology. In effect, in 99% of the cases, the highest similarity coefficients were obtained for resin pairs prepared from the same styrene derivatives even after SAP binding assay. We have also shown that a small but unique combination of a resin's vibrations (30-40%) is sufficient for its identification. However, in rare cases where a resin's vibrational signature has been severely compromised, both the Raman and infrared barcodes were synergistically and reliably utilized to unequivocally identify its chemical make up.     

Rapid molecular assessment of the bioturbation extent in sandy soil horizons under pine using ester-bound lipids by on-line thermally assisted hydrolysis and methylation-gas chromatography/mass spectrometry

Each plant species has a unique chemical composition, and also within a given plant the various tissues differ from one another in their chemistry. These different compositions can be traced back after decay of the plant parts when they are transformed into soil organic matter (SOM). As a result, the composition of SOM reflects not only the plant origin, but also the various tissues, and the composition consequently provides an estimate of the contribution of above-ground vs. below-ground litter. From the latter distribution the extent of bioturbation (mixing of above-ground litter with the mineral soil) can be assessed.Application of thermally assisted hydrolysis and methylation (THM) using tetramethylammonium hydroxide (TMAH) and subsequent analysis by gas chromatography/mass spectrometry (GC/MS) releases all typical cutin- and suberin-derived aliphatic monomers (mono-, di- and trihydroxyalkanoic acids, alpha,omega-alkanedioic acids) as their methyl esters and/or ethers in a rapid manner. Using the distribution of omega-hydroxyalkanoic acids that are present in pine needle cutin (C(12) and C(14)) and not in root suberin, and those that are present in roots but not in needles (C(20) and C(22)), the extent of bioturbation (mixing of above-ground plant litter with the mineral soil) can be assessed. Similarly, the (9,16-dihydroxyhexadecanoic acid+9,10,18-trihydroxyoctadecanoic acid)/(C(20) + C(22) alpha,omega-alkanedioic acids) ratio reflects the degree of bioturbation. Three mineral soil profiles under Corsican pine with an A horizon that exhibited extensive bioturbation phenomena, and underlying C horizons with hardly any or no bioturbation, were investigated in order to examine the applicability of such an approach. It appeared that the A horizons contained all four mentioned omega-hydroxyalkanoic acids, while the C horizons contained virtually only the C(20) and C(22) members. The results not only suggest that bioturbation occurs in the A horizons, but also that possible illuviation or other transport mechanisms of omega-hydroxyalkanoic acids seem hardly ever or never to occur, which is a prerequisite for applying this biomarker approach in assessing degrees of bioturbation.     

Crosslinking index,molar mass distribution and rubber equilibrium shear modulus during polyfunctional crosslinking: Part II: Application to real systems

In a previous paper a theory was presented concerning gels formed by polyfunctional crosslinks in a polydisperse primary polymer. The equilibrium shear modulus as well as the crosslinking index were obtained as functions of the functionality of the crosslinks and of the sol fraction. In this paper the theory is applied to gelatin gels (known functionality of crosslinks) and to poly(vinyl chloride) gels (known number of crosslinks).     

An inequality for sums of binary digits, with application to Takagi functions

Let ?(x)=2inf{|x−n|:n∈Z}, and define for α>0 the function

     

Lelek?s problem is not a metric problem

We show that Lelek?s problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.     

Level sets of signed Takagi functions

This paper examines level sets of functions of the form $$ f(x)=\sum_{n=0}^\infty \frac{r_n}{2^n}\phi(2^n x), $$ where $\phi(x)=\operatorname{dist}\, (x,\mathbb {Z})$ , the distance from x to the nearest integer, and r _n =±1 for each n. Such functions are referred to as signed Takagi functions. The case when r _n =1 for all n is the classical Takagi function, a well-known example of a continuous but nowhere differentiable function. For f of the above form, the maximum and minimum values of f are expressed in terms of the sequence {r _n }. It is then shown that almost all level sets of f are finite (with respect to Lebesgue measure on the range of f), but the set of ordinates y with an uncountably large level set is residual in the range of f. The concept of a local level set of the Takagi function, due to Lagarias and Maddock, is extended to arbitrary signed Takagi functions. It is shown that the average number of local level sets contained in a level set of f is the reciprocal of the height of the graph of f, and consequently, this average lies between 3/2 and 2. These results generalize recent findings by Buczolich [8], Lagarias and Maddock [14], and Allaart [3].     

Describing the soil physical characteristics of soil samples with cubical splines

The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations’ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interaction between the soil moisture retention and the hydraulic conductivity relationship, some data sets yield a fit that seems not to be optimal. So the search for alternatives started. We ended with the cubical spline approximation of the soil physical characteristics. Software was developed to fit the spline-based curves to sets of measured data. Five different objective functions are tested and their results are compared for four different data sets. It is shown that the well-known least-square approximation does not always perform best. The distance between the measured points and the fitted curve, as can be evaluated numerically in a simple way, appears to yield good fits when applied as a criterion in the optimization procedure. Despite an increase in computational effort, this method is recommended over the least square method.     

Hyperfine structure and \user1{g} factor measurements on Ba+ and Eu+ isotopes

Paul and Penning ion traps have been used to determine hyperfine structure coupling constants as well as nuclear $\user1{g} $ factors of Ba⁺ ions with great precision. Attempts are under way to measure both quantities for a long chain of Eu isotopes in order to determine differential hyperfine anomalies for a better understanding of the Bohr–Weisskopf effect.