Linear,non-homogeneous,symmetric patterns and prime power generators in numerical semigroups associated to combinatorial configurations

We prove that the numerical semigroups associated to the combinatorial configurations satisfy a family of linear, non-homogeneous, symmetric patterns. We use these patterns to prove an upper bound of the conductor and we also give an upper bound of the multiplicity. Also, we compare bounds of the conductor of numerical semigroups associated to balanced configurations, and to configurations with coprime parameters. The proof of the latter involves a bound of the conductor of prime power generated numerical semigroups.     

Detection of E. coli using a microfluidics-based antibody biochip detection system

This work demonstrates the detection of E. coli using a 2-dimensional photosensor array biochip which is efficiently equipped with a microfluidics sample/reagent delivery system for on-chip monitoring of bioassays. The biochip features a 4 × 4 array of independently operating photodiodes that are integrated along with amplifiers, discriminators and logic circuitry on a single platform. The microfluidics system includes a single 0.4 mL reaction chamber which houses a sampling platform that selectively captures detection probes from a sample through the use of immobilized bioreceptors. The independently operating photodiodes allow simultaneous monitoring of multiple samples. In this study the sampling platform is a cellulosic membrane that is exposed to E. coli organisms and subsequently analyzed using a sandwich immunoassay involving a Cy5-labeled antibody probe. The combined effectiveness of the integrated circuit (IC) biochip and the immunoassay is evaluated for assays performed both by conventional laboratory means followed by detection with the IC biochip, and through the use of the microfluidics system for on-chip detection. Highlights of the studies show that the biochip has a linear dynamic range of three orders of magnitude observed for conventional assays, and can detect 20 E. coli organisms. Selective detection of E. coli in a complex medium, milk diluent, is also reported for both off-chip and on-chip assays. Received: 13 October 2000 / Revised: 13 November 2000 / Accepted: 13 November 2000     

Phase behavior of SEBS triblock copolymer gels

Dynamic density functional theory calculations were performed for thermoplastic elastomer gels composed of an ABA triblock copolymer immersed in a B‐attractive solvent. The triblock copolymer model was parameterized for poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS), while the solvent model was parameterized for the hydrocarbon oil tetradecane. The effect of the solvent concentration and S‐EB interaction on the morphology was investigated, where complementary experimental data was used to validate results at χ_ABN ≈ 100. Agreement was observed at solvent volume fractions of 0.2, 0.4, and 0.6, which correspond to the cylindrical, spherical, and spherical phases, respectively. Qualitative agreement was observed for 0.8 volume fraction solvent, where a core‐shell spherical micelle morphology was found. For a 50/50 vol % mixture of polymer/solvent, the effect of solvent molecular weight on the morphology was considered, where a transition between micro and macrophase separation was predicted at a critical solvent molecular weight. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1479–1491, 2011     

Two-dimensional HPLC coupled to ICP-MS and electrospray ionisation (ESI)-MS/MS for investigating the bioavailability in vitro of arsenic species from edible seaweed

Edible seaweed consumption is a route of exposure to arsenic. However, little attention has been paid to estimate the bioaccessibility and/or bioavailability of arsenosugars in edible seaweed and their possible degradation products during gastrointestinal digestion. This work presents first use of combined inductively coupled plasma mass spectroscopy (ICP-MS) with electrospray ionization tandem mass spectrometry (ESI-MS/MS) with two-dimensional HPLC (size exclusion followed by anion exchange) to compare the qualitative and quantitative arsenosugars speciation of different edible seaweed with that of their bioavailable fraction as obtained using an in vitro gastrointestinal digestion procedure. Optimal extraction conditions for As species from four seaweed namely kombu, wakame, nori and sea lettuce were selected as a compromise between As extraction efficiency and preservation of compound identity. For most investigated samples, the use of ammonium acetate buffer as extractant and 1 h sonication in a water bath followed by HPLC-ICP-MS resulted in 40–61% of the total As to be found in the buffered aqueous extract, of which 86–110% was present as arsenosugars (glycerol sugar, phosphate sugar and sulfonate sugar for wakame and kombu and glycerol sugar and phosphate sugar for nori). The exception was sea lettuce, for which the arsenosugar fraction (glycerol sugar, phosphate sugar) only comprised 44% of the total extracted As. Interestingly, the ratio of arsenobetaine and dimethylarsinic acid to arsenosugars in sea lettuce extracts seemed higher than that for the rest of investigated samples. After in vitro gastrointestinal digestion, approximately 11–16% of the total As in the solid sample was found in the dialyzates with arsenosugars comprising 93–120% and 41% of the dialyzable As fraction for kombu, wakame, nori and sea lettuce, respectively. Moreover, the relative As species distribution in seaweed-buffered extracts and dialyzates was found to be very similar. Collection of specific fractions from the size-exclusion column to be analysed using anion-exchange HPLC-ESI-MS/MS enabled improved chromatographic selectivity, particularly for the less retained arsenosugar (glycerol sugar), facilitating confirmation of the presence of arsenosugars in seaweed extracts and dialyzates. Using this approach, the presence of arsenobetaine in sea lettuce samples was also confirmed.     

Using Electron Induced Dissociation (EID) on an LC Time-Scale to Characterize a Mixture of Analogous Small Organic Molecules

LC ESI FTICR MS of a sample of cediranib identified this pharmaceutical target molecule plus an additional 10 compounds of interest, all of which were less than 10% total ion current (TIC) peak intensity relative to cediranib. LC FTICR tandem mass spectrometry using electron induced dissociation (EID) has been achieved and has proven to be the best way to generate useful product ion information for all of these singly protonated molecules. Cediranib [M + H]⁺ fragmented by EID to give 29 product ions whereas QTOF-CID generated only one very intense product ion, and linear ion trap-CID, which generated 10 product ions, but all with poor S/N. Twenty-six of the EID product ions were unique to this fragmentation technique alone. By considering the complementary LC-EID and LC-CID data together, all 10 unknown compounds were structurally characterized and proven to be analogous to cediranib. Of particular importance, EID produced unique product ion information for one of the low level cediranib analogues that enabled full characterization of the molecule such that the presence of an extra propylpyrrolidine group was discovered and proven to be located on the pyrrolidine ring of cediranib, solving an analytical problem that could not be solved by collision induced dissociation (CID). Thus, it has been demonstrated that EID is in harmony with the chromatography duty-cycle and the dynamic concentration range of synthetic compounds containing trace impurities, providing crucial analytical information that cannot be obtained by more traditional methodologies.     

A quadruply-bonded [Cr2(guanidinate)4]4- tetraanion

The reaction of chromocene, Cp(2)Cr, with dilithiated 2,3-diphenylguanidine [(PhNH)(2)C=NH = L(2)H(3)] gives the novel, quadruply-bonded tetraanion [Cr(2)(L(2)H)(4)](4-).     

Capabilities of HPLC with APEX-Q nebulisation ICP-MS and ESI MS/MS to compare selenium uptake and speciation of non-malignant with different B cell lymphoma lines

The formation of intracellular dimethylselenide (DMSe) as a product of exposure of non-malignant (PBMCs) and lymphoma (RL and DHL-4) cell lines to methylseleninic acid (MSA) at clinical levels is suggested here for the first time. This was achieved by analysis of cell lysates by HPLC coupled to ICP-MS via APEX-Q nebulisation, enabling limits of detection for target methyl-Se species which are up to 12-fold lower than those obtained with conventional nebulisation. Methyl-Se-glutathione (CH₃Se-SG), although detected in lysates of cells exposed to MSA, was found to be a reaction product of MSA with glutathione. This was confirmed by HPLC-ESI MS (MS) analysis of lysates of control cells (unexposed to Se) spiked with MSA. The MS/MS data obtained by collision-induced dissociation fragmentation of the ion m/z 402 (for [M+H]^{+ 80}Se) were consistent with the presence of CH₃Se-SG. Formation of DMSe was not detected by HPLC-ICP-MS in these spiked lysates, and it was found to require live cells in cell media containing MSA. Interestingly, the ratio of DMSe to CH₃Se-SG was significantly higher in lymphoma cells exposed to MSA in comparison to non-malignant cells. Moreover, maximum Se uptake levels in lymphoma cell lines seemed to be reached much earlier (after 10 min of MSA exposure) than in non-malignant cells. Finally, the GC-TOF-MS speciation data obtained for cell headspace suggested that the major Se species (dimethyldiselenide) appeared to be present in lymphoma cell headspace at significantly higher concentrations than in non-malignant cell headspace after only 10 min of exposure to MSA. Evidence for the presence of dimethylselenidesulfide in lymphoma cell headspace is also provided for the first time.     

Axioms for function semigroups with agreement quasi-order

The agreement quasi-order on pairs of (partial) transformations on a set X is defined as follows: ${(f, g) \preceq (h, k)}$ if whenever f, g are defined and agree, so do h, k. We axiomatize function semigroups and monoids equipped with this quasi-order, thereby providing a generalisation of first projection quasi-ordered ${\cap}$ -semigroups of functions. As an application, axiomatizations are obtained for groups and inverse semigroups of injective functions equipped with the quasi-order of fix-set inclusion. All axiomatizations are finite.     

Partial Maps with Domain and Range: Extending Schein's Representation

Let A be a *-algebra. An additive mapping E : A → A is called a Jordan *-derivation if E(X²) = E(x)x^*+xE(x) holds, for all x 6 A. These mappings have been extensively studied in the last 6 years by Bresar, Semrl, Vukman and Zalar because they are closely connected with the problem of representability of quadratic functionals by sesquilinear forms. This study was, however, always in the setting of associative rings. In the present paper we study Jordan *-derivations on the Cayley-Dickson algebra of octonions, which is not associative. Our first main result is that every Jordan *-derivation on the octonion algebra is of the form E(x)=ax*-xa. In the terminology of earlier papers this means that every Jordan *-derivation on the octonion algebra is inner. This generalizes the known fact that Jordan *-derivations on complex and quaternion algebras are inner. Our second main result is a representation theorem for quadratic functionals on octonion modules. Its proof uses the result mentioned above on Jordan *-derivations.