Signal broadening in potential modulation differentiation

A method is developed for handling the effect of a finite amplitude on the results of potential modulation differentiation. The procedure is applied to harmonic modulation and allows to extrapolate measured Fourier coefficients to zero modulation amplitude. It is therefore possible to use modulation amplitudes as dictated by signal-to-noise considerations avoiding dynamical broadening of the detected signal. The formalism can be easily extended to combine with dynamic background subtraction. Examples are given for soft x-ray appearance potential measurements.     

An application of isoperimetric inequalities to the transmission of scalar waves through small apertures

Isoperimetric inequalities bound the exact solution of complicated boundaryvalue problems through the use of certain simple geometric quantities. As an example of this concept, we propose bounds on the scalar (acoustic) transmission coeficient which characterizes a small aperture of arbitrary shape. These bounds depend solely on the area and perimeter of the aperture. The plausibility of the bounds is demonstrated through the evaluation of several known solutions. Results are noted for apertures in both flexible and rigid screens and these results are compared and contrasted with those of the corresponding vector (electromagnetic) problem.     

Simple and extractionless high-performance liquid chromatographic determination of rosiglitazone in human plasma and application to pharmacokinetics in humans

A simple and extractionless HPLC method using fluorescence detection was developed for the determination of rosiglitazone in human plasma. After deproteinization using perchloric acid the plasma samples were directly injected onto the HPLC system. The mobile phase was composed of acetonitrile (52%) and 20 mm ammonium acetate (48%, pH 7.5), and analysis was run at a flow rate of 0.2 mL/min with the detector operating at 247 nm for excitation wavelength and at 367 nm for emission wavelength, respectively. The method has a mean recovery of 97%, while the intra-day and inter-day precisions were all less than 7%. This method is simple, specific, sensitive and requires only a small plasma volume with short analytical time, and is suitable for the determination of plasma rosiglitazone in routine measurements for pharmacokinetic studies.     

An HPLC assay of hydroxyl radicals by the hydroxylation reaction of terephthalic acid

An HPLC assay for hydroxyl radicals is described. The hydroxyl radical was trapped by terephthalic acid (non-fluorescent), and 2-hydroxyl terephthalic acid (fluorescent) was quantitated by HPLC-fluorescence detection. At a terephthalic acid concentration of 4.25 mmol/L, the hydroxyl radical formed in the Fenton reaction was successfully assayed in the concentration range of hydrogen peroxide of 2.5-50 micro mol/L, where the concentration of Fe(II) was 50 micro mol/L. The fluorescence of 2-hydroxy terephthalate was stable at 24 h, and its detection limit by this method was 5 nmol/L (100 fmol).     

A sharp bound for the degree of proper monomial mappings between balls

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.     

Another Look at the Erdős–Hajnal–Pósa Results on Partitioning Edges of the Rado Graph

Dedicated to the memory of Paul Erdős Erdős, Hajnal and Pósa exhibited in [1] a partition (U,D) of the edges of the Rado graph which is a counterexample to . They also obtained that if every vertex of a graph has either in or in the complement of finite degree then . We will characterize all graphs so that . Received October 29, 1999 RID="†" ID="†" Supported by NSERC of Canada Grant #691325.     

The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that 02511543_f1.jpg" alt="MediaObjects/41_2006_BF02511543_f1.jpg"> if 0<p<1, 0<q<1, ℝ, while 02511543_f2.jpg" alt="MediaObjects/41_2006_BF02511543_f2.jpg"> if 0<p<1, 1≤q<+∞, ∝, and 02511543_f3.jpg" alt="MediaObjects/41_2006_BF02511543_f3.jpg"> if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.