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].     

The monitoring of fluoride in ambient air by fluoridation rate candles

The determination of fluoridation rate provides a relatively inexpensive time-average surveillance method for monitoring atmospheric fluorides in specific areas. The fluoride is collected by the reaction with calcium oxide coating on a filter paper strip during the exposure of the candle to ambient air. The collected fluorides are then extracted from the exposed filter paper into a buffer solution and subsequently determined by ion selective electrode.     

Polyvinyl pyridines as flocculating agents

Summary High molecular weight poly 2- and 4-vinyl pyridines were synthesized by ionic polymerisation and their flocculation efficiency tested against kaolin and silica dispersions at pH 3. Low additions of the polymers, around 3 parts per 10₃ parts solid, destabilize the dispersions and clarify silica dispersions to a remarkable extent; however, over-addition of polymer leads to partial restabilization. The flocculation efficiency improves with increase of solids content, especially with clay dispersions. Flocculation efficiency increases with polymer molecular weight, especially over the lower part of the range covered, but is relatively independent of pH in the range 2–4. Quaternization of poly(4-vinyl pyridine) with bromobutane produces a good flocculant for aqueous silica dispersions in which the degree of restabilization on over-dosing depends on the KCI content. TheN-oxide derivatives of the vinyl pyridine polymers do not affect the colloidal stability of silica dispersions. The observations are interpreted in terms of bridging flocculation by the cationic polymer molecules between anionic surface sites on the solid particles.     

Seawater—A test of multicomponent electrolyte solution theories. II. Enthalpy of mixing and dilution of the major sea salts

In a continuing effort to predict the physicochemical properties of seawater from the properties of single aqueous electrolyte solutions, the pairwise heats of mixing at constant molal ionic strength,I=1.0 ional, have been determined for the six possible pairs of salts from the set (NaCl, Na₂SO₄, MgCl₂, MgSO₄) at 30°C. In addition, heats of dilution for two aqueous solutions formed from these salts and havingI=1.0 ional have been determined at 30°C. In order to present the most thermodynamically consistent results, it was found necessary to apply a correction term to the relative apparent equivalent enthalpies given in the literature at 30°C. These correction terms derived from a consideration of published results on heats of dilution at very low concentrations. Further, in order to make predictions for seawater at 25°C, it was deemed desirable to refit existing heat-capacity data. The heats relative apparent equivalent enthalpies for the two mixtures mentioned as well as for seawater. The estimates are based on the theoretical equation of Reilly and Wood for charge-asymmetric mixtures which derives from the work of Friedman. In the most applicable cases, the estimates agree with experimental relative apparent equivalent enthalpies to within 5%. In general, the results substantiate the theoretical equation.Taken in part from the Ph.D. dissertation of W. H. Leung, University of Miami, Miami, Florida 33149.     

The enthalpy of formation of magnesium sulfate ion pairs

The enthalpies of dilution of lithium, sodium, potassium, and magnesium chloride and sulfate solutions in the range 0.1 to 1.0 m have been measured at 30°C with a microcalorimeter. The relative apparent enthalpies φ_L of these solutions have been determined with the aid of an extended form of the Debye-Hückel limiting law $$\phi _L = S_H I^{1/2} [1/(1 + I^{1/2} ) - (\sigma /3)] + {\rm B}{\rm I} + CI^{3/2} $$ whereS _H is the limiting-law slope, σ = 3/I^3/2 × [(1+I^1/2 ? 1/(1+I^1/2 ? 2 ln (2+I^1/2)], andB andC are empirical constants. This equation fits the experimental results to within a standard deviation of 2 cal-mole^?1 for all the salts. The measured φ_L for the MgSO₄ solutions were compared to those calculated using the additivity principle, φ_L(MgCl₂) + φ_L(Na₂SO₄) ? 2φ_L(NaCl), and the extended Debye-Hückel equation. The results of this comparison have been used to calculate the ΔH _A ^o for the formation of MgSO ₄ ⁰ . A value of ΔH _A ^o = 1.15 to 1.36 was obtained, depending upon the φ_L estimates for the free ions Mg²⁺ and SO ₄ ^2? . The results are briefly discussed and compared to the results obtained by other workers.     

Reaction of Tetracopper(I)-Phosphonitocavitand with PhSeSiMe3: Synthesis and Structure of a Polyanionic Cluster [pyH]6[(CuCl)9(μ3-SePh)5(μ4-SePh)]

Treatment of tetracopper(I)-phosphonitocavitand [1·Cu₄(μ-Cl)₄(μ₄-Cl)] (2) (1 = tetraphosphonitocavitand [rccc-2,8,14,20-tetrakis-(iso-butyl)-phosphonitocavitand (C₄₄H₄₈O₈P₄Ph₄)]) with PhSeSiMe₃ in THF at low temperature afforded a novel polyanionic cluster [pyH]₆[(CuCl)₉(μ₃-SePh)₅(μ₄-SePh)] (4) as a major product along with a new tetracopper(I)-phosphonitocavitand (3) with a centered μ₃-Cl. Molecular structure of anionic cluster in 4 consists of six PhSe⁻ bridging ligands containing five μ₃-SePh and one exceptional μ₄-SePh bridging nine copper atoms, of which eight copper atoms have trigonal coordination geometry and the other has distorted tetrahedral geometry. Dedicated to Professor Han-Qin Liu on the occasion of his 70th birthday.     

Oxidation of guanosine derivatives by a platinum(IV) complex: internal electron transfer through cyclization

Many transition-metal complexes mediate DNA oxidation in the presence of oxidizing radiation, photosensitizers, or oxidants. The DNA oxidation products depend on the nature of the metal complex and the structure of the DNA. Earlier we reported trans-d,l-1,2-diaminocyclohexanetetrachloroplatinum (trans-Pt(d,l)(1,2-(NH(2))(2)C(6)H(10))Cl(4), [Pt(IV)Cl(4)(dach)]; dach = diaminocyclohexane) oxidizes 2'-deoxyguanosine 5'-monophosphate (5'-dGMP) to 7,8-dihydro-8-oxo-2'-deoxyguanosine 5'-monophosphate (8-oxo-5'-dGMP) stoichiometrically. In this paper we report that [Pt(IV)Cl(4)(dach)] also oxidizes 2'-deoxyguanosine 3'-monophosphate (3'-dGMP) stoichiometrically. The final oxidation product is not 8-oxo-3'-dGMP, but cyclic (5'-O-C8)-3'-dGMP. The reaction was studied by high-performance liquid chromatography, (1)H and (31)P nuclear magnetic resonance, and matrix-assisted laser desorption ionization time-of-flight mass spectrometry. The proposed mechanism involves Pt(IV) binding to N7 of 3'-dGMP followed by nucleophilic attack of a 5'-hydroxyl oxygen to C8 of G and an inner-sphere, 2e(-) transfer to produce cyclic (5'-O-C8)-3'-dGMP and [Pt(II)Cl(2)(dach)]. The same mechanism applies to 5'-d[GTTTT]-3', where the 5'-dG is oxidized to cyclic (5'-O-C8)-dG. The Pt(IV) complex binds to N7 of guanine in cGMP, 9-Mxan, 5'-d[TTGTT]-3', and 5'-d[TTTTG]-3', but no subsequent transfer of electrons occurs in these. The results indicate that a good nucleophilic group at the 5' position is required for the redox reaction between guanosine and the Pt(IV) complex.     

Electron energy loss studies of room-temperature co adsorption on Cu(100) induced by electron or ion irradiation

A custom-built multi-technique portable spectrometer was used to study the vibrational (and electronic) excitations associated with the “anomalous” CO adsorption recently observed on clean and oxidized Cu(100) surfaces at room temperature. Results from the electron energy loss (and thermal desorption) experiments have provided strong evidence for in-situ CO production induced by low-energy electron or ion irradiation of CO or C₂H₄ on Cu(100). In particular, the C-O vibrational stretch frequency for the room-temperature CO adsorption was found to be red-shifted by 9 meV from its nominal position (259 meV) and could be observed even at temperature as high as 420 K. Several plausible mechanisms involving coadsorbate interactions with CO on metal surfaces have been discussed. A direct interaction model involving partial bonding between CO, adsorbed on an atop site, and a coadsorbed O atom in a four-fold hollow site was found to be adequate in explaining the observed red shift and the apparent stabilization of CO on Cu(100) at room temperature.