Subtleties in data analysis related to the size of critical region

We comment on the analysis of the critical behavior of a layered driven diffusive system recently done by Achahbar and Marro. We discuss why we believe their method of taking the thermodynamic limit and determining the order-parameter exponent leads to unreliable estimates.     

A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

On generalized quadratic equations in three prime variables

Leta ₁,a ₂ anda ₃ be any nonzero integers which are relatively prime and not all negative. In this paper, as a parallel problem of [11] for each integerk≥2, we consider the setE(X) of positive integersb≤X which satisfy the condition of congruent solubility and that the equation $$a_1 p_1^2 + a_2 p_2^2 + a_3 p_3^k = b$$ is insoluble in primesp _j. We obtain CardE(X)≤X ^1-ε. Our result extends the wellknown classical results (by Legendre and Gauss and byDavenport andHeilbronn [2]) on the equation $$x_1^2 + x_2^2 + x_3^k = b$$ in integral variablesx _j with the above bound for CardE(X) better than that in [2].     

Molecular sensing of 3-chloro-1,2-propanediol by molecular imprinting

A covalent interaction-based molecularly imprinted polymer (MIP) material for 3-chloro-1,2-propanediol (3-MCPD), a post-testicular anti-fertility agent and possible carcinogen and mutagen in food products containing acid-hydrolyzed vegetable proteins, has been successfully fabricated using 4-vinylphenylboronic acid as the functional monomer. Rebinding assay revealed that the binding constant, K_B, for the receptor sites and non-specific sites are 1.93±0.1×10⁴ and 2.74±0.7×10² M⁻¹, respectively. The estimated number of receptor site, B_max, imprinted is 123.3±3 μmol/g of MIP. The MIP material is able to act as a potentiometric chemosensor for 3-MCPD via increase in Lewis acidity of the receptor sites upon reaction of the arylboronic acid with 3-MCPD to form the more acidic arylboronic acid esters. A simple pH glass electrode is sufficient to monitor the analyte-specific rebinding. In unbuffered aqueous media, linear potentiometric response from 0 to 350 ppm of 3-MCPD can be achieved. The MIP-based chemosensing in a soya sauce matrix has also been attempted. It is found that the dynamic range of the potentiometric chemosensing response of the MIP material is much reduced, probably due to the blocking or deactivation of receptor sites by interferents in soya sauces. Nevertheless, the present work demonstrated the feasibility of using MIP-based chemosensors as semi-quantitative analytical tools for screening purposes in quality control of food products.     

Development of high-performance liquid chromatographic fingerprints for distinguishing Chinese Angelica from related umbelliferae herbs

A high-performance liquid chromatographic (HPLC) fingerprint of Chinese Angelica (CA) was developed basing on the consistent chromatograms of 40 CA samples (Angelica sinensis (Oliv.) Diels). The unique properties of this HPLC fingerprints were validated by analyzing 13 related herbs including 4 Japanese Angelicae Root samples (JA, A. acutiloba Kitagawa and A. acutiloba Kitagawa var. sugiyame Hikino), 6 Szechwan Lovage Rhizome samples (SL, Ligusticum chuanxiong Hort.) and 3 Cnidium Rhizome samples (CR, Cnidium officinale Makino). Both correlation coefficients of similarity in chromatograms and relative peak areas of characteristic compounds were calculated for quantitative expression of the HPLC fingerprints. The amount of senkyunolide A in CA was less than 30-fold of that in SL and CR samples, which was used as a chemical marker to distinguish them. JA was easily distinguished from CA, SL and CR based on either chromatographic patterns or the amount of coniferyl ferulate. No obvious difference between SL and CR chromatograms except the relative amount of some compounds, suggesting that SL and CR might have very close relationship in terms of chemotaxonomy. Ferulic acid and Z-ligustilide were unequivocally determined whilst senkyunolide I, senkyunolide H, coniferyl ferulate, senkyunolide A, butylphthalide, E-ligustilide, E-butylidenephthalide, Z-butylidenephthalide and levistolide A were tentatively identified in chromatograms based on their atmospheric pressure chemical ionization (APCI) MS data and the comparison of their UV spectra with those published in literatures.