Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on L₁(\mathbbR)L_{1}({\mathbb{R}}), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.     

Interlaboratory study of the Charm ROSA Safe Level Aflatoxin M1 Quantitative lateral flow test for raw bovine milk

An interlaboratory study of 21 public health, state agriculture, and industry laboratories in the United States tested raw commingled bovine milk containing aflatoxin M1 using the Charm Rapid One Step Assay (ROSA) Safe Level Aflatoxin M1 Quantitative lateral flow method. Blind coded sample pairs were fortified with 0, 300, 350, 400, 450, 500, and 550 parts per trillion (ppt) aflatoxin M1. A ROSA reader quantitatively interpreted test strips with ppt readings. Readings < or = 400 ppt were interpreted as negative, and readings >400 ppt were interpreted as positive. Initial positive samples were subsequently assayed 2 additional times. If both retest results were >400 ppt, the sample was called positive/ actionable relative to U.S. and Codex levels, 500 ppt. The concentration of 400 ppt was chosen for the positive/negative interpretation to provide 90% sensitivity with 95% confidence at the 500 ppt legislative level. The combined false negative rate was <5% (4 of 83) for samples at 500 and 550 ppt. The false violatives at 0, 300, 350, 400, and 450 ppt (n = 42 at each level) were 0, 0, 21, 14, and 93%, respectively. The 90% positive concentration with 95% confidence was 503 ppt by probit analysis. The average intralaboratory repeatability was 11% and average interlaboratory reproducibility was 13% for the fortified sample pairs. High-performance liquid chromatography analysis of the study samples by 5 laboratories showed 38% false negatives with the 500 and 550 ppt samples, and a 0% false-violative rate with samples less than the 500 ppt action level.     

Observation of Light Non-Aqueous Phase Liquid Migration in Aggregated Soil Using Image Analysis

Physical model experiments were conducted to observe the migration of light non-aqueous phase liquids (LNAPL) in a double-porosity soil medium. The double-porosity characteristics of the soil were simulated through aggregation of kaolin which resulted in well-defined intra-aggregate and inter-aggregate pores. Digital images were collected to monitor LNAPL (modeled by toluene) migration. A special experimental setup was developed to enable the instantaneous capture of the LNAPL migration around the whole soil column using a single digital camera. An image processing module was applied to the captured images and the results plotted using a surface mapping programme. Events observed during the duration of the experiments were discussed. It was found that the LNAPL flowed much faster in the aggregated soil as compared to a single-porosity soil. The wettability of the fluid and the capillary pressure characteristics were demonstrated to be influential factors in immiscible fluids migration when the soil fabric showed highly contrasting porosity values.     

Application of proteomics to hordein screening in the malting process

This study was undertaken to investigate the effect of the malting process on hordein composition. For this purpose, combination of sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE), matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) and the method of isotopic peptides labeling iTRAQ was used. Barley proteins are essential components determining the quality of both malt and beer. Since hordeins represent the most abundant proteins accounting for about 40-50% of total protein fraction of mature barley grain, our research was focused on them. In this respect, the proteins of interest were extracted from milled samples of barley grain, germinated barley grain (samples collected at different time intervals), green malt and malt, respectively. Particular hordein extracts were firstly fractionated via SDS- PAGE, which was used as a relatively rapid and reliable technique providing information about hordein profile of analyzed samples. Then, separated proteins were in-gel digested and resulting peptides were measured by mass spectrometry. In addition, the chosen proteins, after in-gel digestion, were subjected to the iTRAQ method and the screening of proteins during malting process was evaluated. Our results have revealed that most of the hordein components present in the barley grain can be found in all stages of the malting process as well as in the final malt. The amount of hordeins decreases during the malting process; in the case of C hordein, the protein decrease is approximately 65%. On the other hand, significant degradation of D hordein was detected. The suggested procedure can be used to follow the development of the hordein profile during germination, which is of great technological importance in beer production.     

Ghost circles in lattice Aubry–Mather theory

Monotone lattice recurrence relations such as the Frenkel–Kontorova lattice, arise in Hamiltonian lattice mechanics, as models for ferromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multi-dimensional counterpart of monotone twist maps.Such recurrence relations often admit a variational structure, so that the solutions $x:{\mathbb{Z}}^d\to \mathbb{R}$ are the stationary points of a formal action function $W(x)$. Given any rotation vector $\omega \in {\mathbb{R}}^d$, classical Aubry–Mather theory establishes the existence of a large collection of solutions of $\mathrm{?}W(x)=0$ of rotation vector ω. For irrational ω, this is the well-known Aubry–Mather set. It consists of global minimizers and it may have gaps.In this paper, we study the parabolic gradient flow $\frac{dx}{dt}=?\mathrm{?}W(x)$ and we will prove that every Aubry–Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called ‘ghost circle’. The existence of these ghost circles is known in dimension $d=1$, for rational rotation vectors and Morse action functions. The main technical result of this paper is therefore a compactness theorem for lattice ghost circles, based on a parabolic Harnack inequality for the gradient flow. This implies the existence of lattice ghost circles of arbitrary rotation vectors and for arbitrary actions.As a consequence, we can give a simple proof of the fact that when an Aubry–Mather set has a gap, then this gap must be filled with minimizers, or contain a non-minimizing solution.     

Sedimentation equilibria of ferrofluids: II. Experimental osmotic equations of state of magnetite colloids

The first experimental osmotic equation of state is reported for well-defined magnetic colloids that interact via a dipolar hard-sphere potential. The osmotic pressures are determined from the sedimentation equilibrium concentration profiles in ultrathin capillaries using a low-velocity analytical centrifuge, which is the subject of the accompanying paper I. The pressures of the magnetic colloids, measured accurately to values as low as a few pascals, obey Van 't Hoff's law at low concentrations, whereas at increasing colloid densities non-ideality appears in the form of a negative second virial coefficient. This virial coefficient corresponds to a dipolar coupling constant that agrees with the coupling constant obtained via independent magnetization measurements. The coupling constant manifests an attractive potential of mean force that is significant but yet not quite strong enough to induce dipolar chain formation. Our results disprove van der Waals-like phase behavior of dipolar particles for reasons that are explained.     

Application of the R-functions method to the solution of elliptic PDEs (Poster Presentation)

In the current work, the basics of the theory of R-functions have been presented. Applications of this theory were shown on two model problems – Poisson equation and biharmonic equation – in complex two-dimensional domains both with homogeneous Dirichlet boundary conditions. The solution is performed in conjunction with the Bubnov-Galerkin method. As the basis for approximation tensor products of monomials were taken. The convergence study includes the comparison of current results with the standard finite element solution and the dependence of the number of coordinate functions on the relative error in the maximum-norm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Causal Categories: Relativistically Interacting Processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.     

Reduction of nitric oxide,nitrous acid and nitrogen dioxide at platinum electrodes in acidic solutions: Review and new voltammetric results

The literature concerning the chemical and electrochemical reactions of nitric oxide, nitrous acid and nitrogen dioxide in aqueous solutions is reviewed briefly, with emphasis on electrochemical reductions at platinum electrodes in acidic solutions. The voltammetric behavior of NO and NO₂ at a Pt electrode in perchloric acid is virtually identical to that for HNO₂ and this is explained on the basis of a common electroactive precursor concluded to be NO⁺. Three cathodic waves are obtained for acidic solutions of NO, HNO₂ and NO₂. The first two waves correspond to reduction of NO⁺ to NO and N₂O₃ to NO, respectively. The presence of N₂O₃ results from decomposition of the parent compounds. The presence of Br^- or Cl^- in acidic solutions of the title compounds promotes the voltammetric reductions at lower H⁺ concentrations. This probably results from formation of electroactive nitrosyl halides.     

A study of the mechanism of response of liquid ion exchanger calcium selective electrodes: Part III. Membrane behaviour under non-zero current conditions

The I-E response of the liquid membrane of the calcium selective electrode is studied under constant or linearly varying current and voltage. An increase in the membrane resistance, recorded when an electrical current crosses the membrane, is due to the outflow of Cl^? ions initially present in the membrane. When calcium ions are replaced by alkaline ions inside the membrane at constant current, the decrease of the membrane resistance due to an ion exchange is in agreement with the conductivity measurements (Part II). When the applied voltage is imposed besides the ion exchange one must take into account the interfacial overpotential to explain the important rectification effect observed. The interfacial transfer constant rate of alkaline ions seems greater than that of Ca²⁺ ion.