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].     

Exact solution (within a double-zeta basis set) of the schrodinger electronic equation for water

Using recently developed theoretical techniques it has been possible to achieve an exact variational solution of the Schrödinger equation within a modest basis set or one-eleltron functions. The full configuration interaction for this system included a total of 256473 ¹A₁ spin-and space-adapted configurations. Comparison with many-body perturbation theory proves to be quite interesting.     

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.     

Single-run analysis of retinal isomers, retinol and photooxidation products by high-performance liquid chromatography

A high-performance liquid chromatographic (HPLC) procedure was developed to allow the rapid separation, in a single run, of a mixture of the main retinal isomers (all-trans, 13-cis, 9-cis), all-trans-retinol, and of the two major photooxygenated photoproducts (5,8-peroxyretinal and 5,6-epoxyretinal). The mixture was separated by HPLC on an octadecyl (ODS) column with 16% (v/v) diethyl ether in hexane as mobile phase and anthracene as the internal standard. A commercial type cosmetic formulation containing 0.05% all-trans-retinal was analyzed successfully for this analyte.