Interpretation of Lagrange multipliers in nonlinear pricing problem

We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization problem more efficiently. We also find that the multipliers satisfy a conservation law for each node in the digraph, and the non-uniqueness of the multipliers are connected to the stability of the solution structure.     

Proton conducting polymers containing 1H‐1,2,3‐triazole moieties

Polyacrylates containing a different number of 1H‐1,2,3‐triazole groups per repeat unit have been synthesized via conventional free radical polymerization. These polymers were characterized by nuclear magnetic resonance spectroscopy (NMR), gel permeation chromatography (GPC), thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC). Proton conductivity measurements were made using impedance spectroscopy. Introduction of more than one triazole per repeat unit did not result in an increase in conductivity as there was an accompanying increase in glass transition temperature (T_g). A maximum conductivity of 17.5 μS/cm was obtained at 200 °C under anhydrous condition. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 188–196, 2009     

Nanostructured block-random copolymers with tunable magnetic properties

It was recently shown that block copolymers (BCPs) produced room-temperature ferromagnetic materials (RTFMs) due to their nanoscopic ordering and the cylindrical phase yielded the highest coercivity. Here, a series of metal-containing block-random copolymers composed of an alkyl-functionalized homo block (C(16)) and a random block of cobalt complex- (Co) and ferrocene-functionalized (Fe) units was synthesized via ring-opening metathesis polymerization. Taking advantage of the block-random architecture, the influence of dipolar interactions on the magnetic properties of these nanostructured BCP materials was studied by varying the molar ratio of the Co units to the Fe units, while maintaining the cylindrical phase-separated morphology. DC magnetic measurements, including magnetization versus field, zero-field-cooled, and field-cooled, as well as AC susceptibility measurements showed that the magnetic properties of the nanostructured BCP materials could be easily tuned by diluting the cobalt density with Fe units in the cylindrical domains. Decreasing the cobalt density weakened the dipolar interactions of the cobalt nanoparticles, leading to the transition from a room temperature ferromagnetic (RTF) to a superparamagnetic material. These results confirmed that dipolar interactions of the cobalt nanoparticles within the phase-separated domains were responsible for the RTF properties of the nanostructured BCP materials.     

Liquid chromatography tandem mass spectrometry determination of total budesonide levels in dog plasma after inhalation exposure

A sensitive and selective method to quantify budesonide in dog plasma samples was developed and fully validated. Liquid–liquid extraction was followed by solid-phase extraction and liquid chromatography–tandem mass spectrometry with electrospray ionization. After reconstitution of the analytes in the mobile phase, samples were analysed by reversed-phase liquid chromatography with isocratic elution. d8-Budesonide was used as an internal standard, and characteristic transitions of d8-budesonide and budesonide were used for quantification. The method was validated with respect to selectivity, specificity, linearity, recovery, repeatability, reproducibility and limits of detection and quantification. The validated method was successfully applied to monitor the plasma levels of budesonide in dogs exposed to clinical doses of inhaled and intravenous drug.     

Anhydrous proton conductivities of squaric acid derivatives

In this communication, we introduce squaric acid derivatives as anhydrous proton conductors. We report the synthesis, characterization and proton conductivities of four squaric acid derivatives. The anhydrous proton conductivity of one of the derivatives was 2.3 × 10(-3) S cm(-1) at 110 °C, comparable to the conductivity of molten 1H-1,2,3-triazole or 1H-imidazole.     

Dense Packing of Patterns in a Permutation

We study the length L _k of the shortest permutation containing all patterns of length k. We establish the bounds e ⁻² k ² < L _k ≤ (2/3 + o(1))k ². We also prove that as k → ∞, there are permutations of length (1/4 + o(1))k ² containing almost all patterns of length k. Received January 2, 2007     

Dark Supersymmetry

We propose a model of Dark Supersymmetry, where a supersymmetric dark sector is coupled to the classically scale invariant non-supersymmetric Standard Model through the Higgs portal. The dark sector contains a mass scale that is protected against radiative corrections by supersymmetry, and the portal coupling mediates this scale to the Standard Model, resulting in a vacuum expectation value for the Higgs field and the usual electroweak symmetry breaking mechanism. The supersymmetric dark sector contains dark matter candidates, and we show that the observed dark matter abundance is generated for a natural choice of parameters, while avoiding the current experimental bounds on direct detection. Future experiments can probe this scenario if the dark sector mass scale is not too high.     

Isotope dilution high-resolution gas chromatography/high-resolution mass spectrometry method for analysis of selected acidic herbicides in surface water

In this work, an isotope dilution method for determination of selected acidic herbicides by high-resolution gas chromatography/high-resolution mass spectrometry (HRGC/HRMS) was developed for surface water samples. Average percent recoveries of native analytes were observed to be between 70.8 and 93.5% and average recoveries of labeled quantification standards [(13)C(6)]2,4-D and [(13)C(6)]2,4,5-T were 85.5 and 101%, respectively. Using this method, detection limits of 0.05 ng/L for dicamba, MCPA, MCPP, and triclopyr, and 0.5 ng/L for 2,4-D were routinely achieved. The method was applied to measuring the concentration of these analytes in surface water samples collected from five sampling locations in the Lower Fraser Valley region of British Columbia, Canada. All of the herbicides monitored were detected at varying levels in the surface water samples collected. The highest concentrations detected for each analyte were 345 ng/L for 2,4-D, 317 ng/L for MCPA, 271 ng/L for MCPP, 15.7 ng/L for dicamba, and 2.18 ng/L for triclopyr. Average detection frequencies of the herbicides were 95% for MCPA, 80% for MCPP, 70% for dicamba, 65% for 2,4-D, and 46% for triclopyr. Seasonal variations of herbicide levels are also discussed.