Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Optimal linear estimators of the unknown mean of a random field observed on a cross

Explicit formulas of minimum-variance linear unbiased estimators of the unknown mean are derived for homogeneous random fields with correlation functions observed on the set (a cross).Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 116–121, 1988.     

A sequential multielement separation scheme for determination of As,Mn, Mo,Cu and Zn in human milk by neutron activation analysis

A simple separation scheme for the analysis of As, Mn, Mo, Cu and Zn using neutron activation is described. It has been checked using three standard reference materials, A-11 milk powder (IAEA) and bovine liver and orchard leaves (USNBS) and found to give acceptable results. This scheme was applied for determination of these trace elements in mature human milk samples. The concentrations of As, Mn, Mo, Cu in samples obtained from two socio-economic groups—low and middle incomes—were not significantly different. However, Zn levels in samples obtained from the poor income group were significantly lower than in those obtained from the other group. Work carried out under Research Contract No. 2598/RB of International Atomic Energy, Vienna. Health Physics Division. Analytical Chemistry Division.     

含茂钛低聚物的制备与光谱

文中报道两种新的含茂钛低钛物Cp_2Ti(Cl)-O-[-Ti(Cp)(O_2CCH_4CH-O)-O-]n-H(Ⅰ)与Cp_2Ti(Cl)-O-[-Ti(Cp)(O_2CCH_2CH)-O-]_u-H(Ⅰ)的制备并用元素分析和光谱(IR,1~H NMR,MS)对它们进行了鉴定。     

Austauscher mit cyclischen Polyethern als Ankergruppen—II: Anwendungen

Exchangers with cyclic polyethers as anchor groups have a large range of applications such as separations of cations with a common anion, of anions with a common cation, and of neutral organic compounds, and the determination of water by elution chromatography. Some crown ether monomers, especially 4- and 4,4′-alkyl-substituted benzo-derivatives are suitable for extractions and their adducts with heteropoly acids are used as liquid ion-exchangers. The exchangers are also applied in thin-layer chromatography and thin-layer electrophoresis. Furthermore the exchangers are successfully used in preparative chemistry, e.g., in salt conversions in order to isolate salts which are difficult to prepare by other means, in isolation and purification of organic compounds, and for anion activation in organic reactions.     

Simple Approximate Expressions for Electrical Double-Layer Interaction at Constant Moderate Potentials

Simple yet accurate expressions for the electrical double-layer interaction force and energy between the particles that hold for a wide range of surface potential is required in the modeling, simulation, and optimization of many processes employed in industry. In this paper, simple approximate expressions for the interaction are obtained based on the asymptotic results and the numerical solution to the Poisson-Boltzmann equation for identical parallel plates with constant surface potential up to 180/z(i) mV at 25 degrees C, and the Derjaguin approximation. Within the moderate surface potential range, the semianalytical expressions agree well with the exact numerical results and are convenient to use for the purpose of process modeling and simulation. Copyright 2000 Academic Press.     

An annulation toward fused bicyclolactones

The combination of Lewis and Bronsted acids catalyzed the addition of beta-ketoesters to cyclic diene. Lactonization occurs in situ to afford fused bicyclic lactones directly. The catalysis provides an expedient route to bicylic lactones via a zip-process.     

Self-assembly of flexible supramolecular metallacyclic ensembles: structures and adsorption properties of their nanoporous crystalline frameworks

The syntheses, structures, and N2 adsorption properties of six new supramolecular metallacycles are reported. Flexible ditopic linkers, 1-4, with systematically varied lengths and conformational degrees of freedom were synthesized utilizing ester linkages. They were used in combination with (dppp)M(OTf)2, where M = Pt(II) and Pd(II), and cis-(Me3P)2Pt(OTf)2 to form flexible supramolecular metallacycles 5-10 in 88-98% isolated yields. Their structures were characterized via multinuclear NMR and X-ray crystallography. The metallacycles stack to form porous structures in the crystalline state. The pore dimensions depend on both the phosphorus ligands attached to the metals and the flexible linkers. Adsorption studies on the porous materials show that 5a, 6, 8, and 9 held 11.7, 16.5, 5.7, and 6.8 cm3/g STP of N2 at 77 K, respectively. A guest-exchange study with nitromethane and toluene reveals that the nanopore in 5 is flexible, a property which was transferred from the linker to the supramolecular structure in the solid state.     

First observation of aS C * -S A-TGBA multicritical point in a pure compound

High pressure experiments have been performed by thermobarometric analysis on two homologous (n=10 and 11) of the [3-fluoro-4((R) or (S)-methylheptyloxy) 4′-(4″-alkoxy-3″-fluorobenzoyloxy) tolans series, which both exhibit the TΓB_A phase. The character (first or/and second order) of the transitions involving the TGB_A phase are determined from thermobarograms. The pressure-temperature phase diagrams show that the TGB_A phase is stabilized under high pressure for the two compounds. Forn=11 an inducedS _A phase is observed under high pressures leading to the first experimental observation, on pressure-temperature phase diagram of pure compounds, of aS _C ^* -S _A-TGB_A multicritical point, previously predicted by the Renn-Lubensky theory.