Rational functions with linear relations

We find all polynomials over a field such that and are linear and . We also solve the same problem for rational functions , in case the field is algebraically closed.

     

Analysis of brain lipids by directly coupled matrix-assisted laser desorption ionization time-of-flight mass spectrometry and high-performance thin-layer chromatography

Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF-MS) is a soft ionization MS technique providing only minor fragmentation of the analyte. Therefore, the method is basically suitable for mixture analysis, although the ion yields strongly depend on the basicity/acidity of the analyte in relation to the applied matrix. Accordingly, less sensitively detectable compounds may be suppressed by more sensitively detectable compounds. Thus, separation of the mixture into the individual compounds is normally indispensable. This paper demonstrates the capabilities and limitations of a direct, simple, and inexpensive MALDI-high-performance thin-layer chromatography (HPTLC) coupling for the analysis of a crude lipid extract from porcine brain. Brain lipids were chosen because they represent a rather complex mixture and are of currently significant research interest. It was found that normal-phase HPTLC-separated lipids can be easily characterized by direct MALDI-TOF-MS analysis with sufficient resolution to allow the assignment of virtually all lipid classes, even rather minor species such as phosphorylated phosphoinositides or complex glycolipids as gangliosides. Advantages and disadvantages of this approach are discussed.     

Preparation of Functionalized Ayous Sawdust-carbon Nanotubes Composite for the Electrochemical Determination of Carbendazim Pesticide

Fine particles of Ayous sawdust (AS) were successfully modified by maleic anhydride to increase their accumulation capability towards carbendazim (Cbz). For a more efficient use of the biosourced material as electrode modifier for electrochemical detection, the functionalized particles were mixed with carbon nanotubes to yield a conductive composite. After electrochemical characterization, the modified GCE was applied to Cbz detection. A sensitivity of (2.61±0.08) μA M⁻¹ and a detection limit of 0.04 μM were obtained under optimized experimental conditions. Moreover, the designed sensor was found efficient for Cbz determination in real samples (spring water and commercial pesticide product).     

An improved cryogen for plunge freezing

The use of an alkane mixture that remains liquid at 77 K to freeze specimens has advantages over the use of a pure alkane that is solid at 77 K. It was found that a mixture of methane and ethane did not give a cooling rate adequate to produce vitreous ice, but a mixture of propane and ethane did result in vitreous ice. Furthermore, the latter mixture produced less damage to specimens mounted on a very thin, fragile holey carbon substrate.     

LC‐MS/MS analysis of Δ9‐tetrahydrocannabinolic acid A in serum after protein precipitation using an in‐house synthesized deuterated internal standard

An assay based on liquid chromatography/tandem mass spectrometry is presented for the fast, precise and sensitive quantitation of Δ9‐tetrahydrocannabinolic acid A (THCA) in serum. THCA is the biogenetic precursor of Δ9‐tetrahydrocannabinol in cannabis and has aroused interest in the pharmacological and forensic field especially as a potential marker for recent cannabis use. After addition of deuterated THCA, synthesized from D₃‐THC as starting material, and protein precipitation, the analytes were separated using gradient elution on a Luna C18 column (150 × 2.0 mm × 5 µm) with 0.1% formic acid and acetonitrile/0.1% formic acid. Data acquisition was performed on a triple quadrupole linear ion trap mass spectrometer in multiple reaction monitoring mode with negative electrospray ionization. After optimization, the following sample preparation procedure was used: 200 μL serum was spiked with internal standard solution and methanol and then precipitated ‘in fractions’ with 500 μL ice‐cold acetonitrile. After storage and centrifugation, the supernatant was evaporated and the residue redissolved in mobile phase. The assay was fully validated according to international guidelines including, for the first time, the assessment of matrix effects and stability experiments. Limit of detection was 0.1 ng/mL, and limit of quantification was 1.0 ng/mL. The method was found to be selective and proved to be linear over a range of 1.0 to 100 ng/mL using a 1/x weighted calibration model with regression coefficients >0.9996. Accuracy and precision data were within the required limits (RSD ≤ 8.6%, bias: 2.4 to 11.4%), extractive yield was greater than 84%. The analytes were stable in serum samples after three freeze/thaw cycles and storage at ?20 °C for one month. Copyright © 2012 John Wiley & Sons, Ltd.     

Photoinduced electron transfer in a new Bis(C60)-phthalocyanine triad

[Structure: see text] A novel covalently linked bis([60]fullerene)-phthalocyanine triad is reported, exhibiting long-lived photoinduced charge separation both in solution and in the solid state. The first demonstration of a working solar cell using triad 1 as the active material is also presented.