A continuous family of partition statistics equidistributed with length

This article investigates a remarkable generalization of the generating function that enumerates partitions by area and number of parts. This generating function is given by the infinite product _∏i?11/(1−tqi). We give uncountably many new combinatorial interpretations of this infinite product involving partition statistics that arose originally in the context of Hilbert schemes. We construct explicit bijections proving that all of these statistics are equidistributed with the length statistic on partitions of n. Our bijections employ various combinatorial constructions involving cylindrical lattice paths, Eulerian tours on directed multigraphs, and oriented trees.     

Protein labeling with red squarylium dyes for analysis by capillary electrophoresis with laser-induced fluorescence detection

Two new red luminescent asymmetric squarylium dyes (designated "Red-1c and Red-3") have been shown to exhibit absorbance shifts to longer wavelengths upon the addition of protein, along with a concomitant increase in fluorescence emission. Specifically, the absorbance maxima for Red-1c and Red-3 dyes are 607 and 622 nm, respectively, in the absence of HSA, and 642 and 640 nm in the presence of HSA, making the excitation of their protein complexes feasible with inexpensive and robust diode lasers. Fluorescence emission maxima, in the presence of HSA, are 656 and 644 nm for Red-1c and Red-3, respectively. Because of the inherently low fluorescence of the dyes in their free state, Red-1c and Red-3 were used as on-column labels (that is, with the dye incorporated into the separation buffer), thus eliminating the need for sample derivatization prior to injection and separation. A comparison of precolumn and on-column labeling of proteins with these squarylium dyes revealed higher efficiencies and greater sensitivities for on-column labeling, which, when conducted with a basic, high-salt content buffer, permitted baseline resolution of a mixture of five model proteins. LOD for model proteins, such as transferrin, alpha-lactalbumin, BSA, and beta-lactoglobulin A and B, labeled with these dyes and analyzed by CE with LIF detection (CE-LIF) were found to be dependent upon dye concentration and solution pH, and are as low as 5 nM for BSA. Satisfactory linear relationships between peak height (or peak area) and protein concentration were obtained by CE-LIF for this on-column labeling method with Red-3 and Red-1c.     

Evaluation of a tungsten coil atomization-laser-induced fluorescence detection approach for trace elemental analysis

The analytical utility of a tungsten (W)-coil atomization-laser-induced fluorescence (LIF) approach has been evaluated for trace level measurements of elemental chromium (Cr), arsenic (As), selenium (Se), antimony (Sb), lead (Pb), tin (Sn), copper (Cu), thallium (Tl), indium (In), cadmium (Cd), zinc (Zn) and mercury (Hg). Measurements of As, Cr, In, Se, Sb, Pb, Tl, and Sn were performed by laser-induced fluorescence using a single dye laser operating near 460 nm whose output was converted by frequency doubling and stimulated Raman scattering to wavelengths ranging from 196 to 286 nm for atomic excitation. Absolute limits of detection (LODs) of 1, 0.3, 0.3, 0.2, 1, 6, 1, 0.2 and 0.8 pg and concentration LODs of 100, 30, 30, 20, 100, 600, 100, 20, and 80 pg/mL were achieved for As, Se, Sb, Sn, In, Cu, Cr, Pb and Tl, respectively. Determinations of Hg, Pb, Zn and Cd were performed using two-color excitation approaches and resulted in absolute LODs of 2, 30, 5 and 0.6 pg, respectively, and concentration LODs of 200, 3000, 500 and 60 pg/mL, respectively. The sensitivities achieved by the W-coil LIF approaches compare well with those reported by W-coil atomic absorption spectrometry, graphite furnace atomic absorption spectrometry, and graphite furnace electrothermal atomization-LIF approaches. The accuracy of the approach was verified through the analysis of a multielement reference solution containing Sb, Pb and Tl which each had certified performance acceptance limits of 19.6-20.4 μg/mL. The determined concentrations were 20.05 ± 2.60, 20.70 ± 2.27 and 20.60 ± 2.46 μg/mL, for Sb, Pb and Tl, respectively. The results demonstrate that W-coil LIF provides good analytical performance for trace analyses due to its high sensitivity, linearity, and capability to measure multiple elements using a single tunable laser and suggest that the development of portable W-coil LIF instrumentation using compact, solid-state lasers is feasible.     

Existence of multiple positive solutions of singular nonlinear boundary value problems

For a given positive integer N, we provide conditions on the nonlinear function f which guarantee that the boundary value problem

     

Strongly n-Trivial Knots

The authors prove in this paper that, given any knot k of genusg,k fails to be strongly n-trivial for all n with n 6g –3. 2000 Mathematics Subject Classification 57M99.     

Determination of phycobiliproteins by capillary electrophoresis with laser-induced fluorescence detection

Phycobiliproteins are derived from the photosynthetic apparatus of cyanobacteria and eukaryotic algae. They are composed of a protein backbone to which linear tetrapyrrole chromophores are covalently bound. Furthermore, they are water-soluble highly fluorescent, and relatively stable at room temperature and neutral pH. For this reason, capillary electrophoresis-laser induced fluorescence (CE-LIF) seems the idea method for determination of these important proteins. The effects of buffer additives such as sodium dodecyl sulfate (SDS)and putrescine on the separation of the three major phycobiliprotein types, namely allophycocyanin, phycocyanin, and phycoerythrin, with excitation and emission maxima at 652/660, 615/647, and 565(494)/575 nm, respectively, are considered. Detection limits for these proteins by CE-LIF are some 60-500 times better than by absorbance detection. The development of a fast and sensitive CE-LIF assay such as this is of potential significance to our understand ing of chemical and biological oceanographic processes.     

Combining approaches for evaluating auditing populations: A simulation study

This research explores ways of combining four distinct bounds for the mean error in an auditing population. Two competing objectives for a bound are to be close to the true mean being estimated and to be reliable: not less than the true mean in more than 5% of estimations. The optimal combination should provide the best balance of these competing objectives. Estimating the mean error by a single approach is difficult because typically most accounts have no error and the distribution of the errors among those that do is discontinuous and highly skewed. This study reveals that the weights in the optimal combination are not constant but depend on the characteristic of the population being estimated. The optimally combined bound is only 7% smaller overall than the best of the constituents. However, while the best of the constituents fails in 50% of most challenging populations, the optimal combination never fails.     

Dissimilarity between metallic-like transport in the dielectric spin density wave and field-induced spin density wave states in (TMTSF)<Subscript>2</Subscript>PF<Subscript>6</Subscript>

We report similarities and differences of the transport features in the spin density wave (SDW) and in the field-induced SDW (FISDW) phases of the quasi-one-dimensional compound (TMTSF)₂PF₆. As temperature decreases below ≈2 K, the resistance in both phases exhibits a maximum and a subsequent strong drop. However, the characteristic temperature of the R(T) maximum and its scaling behavior in different magnetic fields B are evidence that the nonmonotonic R(T) dependences have different origin in SDW and FISDW regions of the phase diagram. We also found that the borderline T₀(B, P) which divides the FISDW region of the P-B-T phase diagram into the hysteresis and nonhysteresis domains terminates in the N=1 subphase; the borderline thus has no extension to the SDW N=0 phase.     

Surface magnetic anisotropy in glass-coated amorphous microwires as determined from ferromagnetic resonance measurements

The ferromagnetic resonance frequency of different Co base glass-coated amorphous magnetic microwires about 3.5 μm in diameter with negative, vanishing and positive magnetostriction has been investigated from power absorption measurements in the microwave frequency range. The experimental technique employed here involves the replacement of the dielectric of a coaxial transmission line by the sample to be measured. From the evolution of the resonance frequency with DC applied magnetic field, the surface magnetic anisotropy field of the microwires has been quantitatively obtained and, as expected, found to depend on the sign and strength of the magnetostriction. Similar values for the surface anisotropy are obtained in comparison with bulk anisotropy as determined from quasi-static hysteresis loops measurements.