Lanthanide Contraction within a Series of Asymmetric Dinuclear [Ln2] Complexes

A complete isostructural series of dinuclear asymmetric lanthanide complexes has been synthesized by using the ligand 6‐[3‐oxo‐3‐(2‐hydroxyphenyl)propionyl]pyridine‐2‐carboxylic acid (H₃ L ). All complexes have the formula [Ln₂(H L )₂(H₂ L )(NO₃)(py)(H₂O)] (Ln=La ( 1 ), Ce ( 2 ), Pr ( 3 ), Nd ( 4 ), Sm ( 5 ), Eu ( 6 ), Gd ( 7 ), Tb ( 8 ), Dy ( 9 ), Ho ( 10 ), Er ( 11 ), Tm ( 12 ), Yb ( 13 ), Lu ( 14 ), Y ( 15 ); py=pyridine). Complexes of La to Yb and Y have been crystallographically characterized to reveal that the two metal ions are encapsulated within two distinct coordination environments of differing size. Whereas one site maintains the coordination number (nine) through the whole series, the other one increases from nine to ten owing to a change in the coordination mode of an NO₃^? ligand. This series offers a unique opportunity to study in detail the lanthanide contraction within complexes of more than one metal. This analysis shows that various representative parameters proportional to this contraction follow a quadratic decay as a function of the number n of f electrons. Slater’s model for the atomic radii has been used to extract, from these decays, the shielding constant of 4f electrons. The average of O???O distances within the coordination polyhedra shared by both metals and of the Ln???Ln separations follow also a quadratic decay, therefore showing that such dependence holds also for parameters that receive the contribution of two lanthanide ions simultaneously. The magnetic behavior has been studied for all nondiamagnetic complexes. It reveals the effect of the spin–orbit coupling and a weak antiferromagnetic interaction between both metals. Photoluminescent studies of all the complexes in the series reveal a single broad emission band in the visible region, which is related to the coordinated ligand. On the other hand, the Nd, Er, and Yb complexes show features in the near‐IR region due to metal‐based transitions.     

A Simple Method to Prepare Alkyl 3,5-Dioxohexanoates

A simple and efficient method to prepare alkyl 3,5-dioxohexanoates by alcoholysis of isopropylidene (1-hydroxy-3-oxo-butylidene) malonate is described.     

Large eddy simulation of a confined square cavity with natural convection based on compressible flow equations

Large eddy simulation of natural convection in a confined square cavity is described. The use of a complex compressible code with an artificial acoustic stiffness correction method, allows the use of higher time steps for a faster time and statistical convergence. We consider a broadly studied experimental case, consisting of a natural convective flow in a confined square cavity, with vertical walls heated at different rates (active walls), set at Ra = 1.58 × 10⁹. Turbulent boundary layers developing on the active walls and a vertical stable stratification characterize the mean flow. It is shown here that the results of this study match the experimental results reported in literature; for instance, mean velocity results. Although results for rms velocity fluctuations are barely over-predicted, the peak region is properly represented, while the greatest disagreements are found in the turbulent heat flow rate (velocity–temperature correlations). Turbulent structures were identified using different visualization methods and statistical studies. The authors found that the boundary layers on the active walls almost reach the fully turbulent regime, tending toward the laminar regime along the horizontal walls.     

Conditions for selective photocatalytic degradation of naphthalene in triton X‐100 water solutions

Naphthalene is degraded selectively in surfactant Triton X‐100 water solutions when treated with disperse TiO₂ catalyst and UV‐B simulated solar light. After complete degradation of the naphthalene, degradation of the Triton X‐100 commences. The pseudo‐first‐order k_obs values obtained for both naphthalene and Triton X‐100 decrease with increasing Triton X‐100 concentration. Experimental rate values fit the Langmuir–Hinshelwood equations. An apparent rate constant for naphthalene degradation k_N = 17.3 ppm min^?1 and an adsorption equilibrium constant k_N = 0.009 ppm^?1 are obtained from a plot of 1/k_obs vs. naphthalene concentration. An apparent rate constant for Triton X‐100 degradation k_T, calculated from a 1/k_obs vs. Triton X‐100 concentration plot of 1.1 ppm/min, was obtained. Therefore, the selectivity observed in naphthalene vs. Triton X‐100 degradation is then due to the favorable naphthalene rate constant degradation that more than balances its unfavorable adsorption equilibrium on the TiO₂ surface. This result is quite important to establish actual experimental conditions for treatment of sites contaminated with polyaromatic hydrocarbons (PAH). © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 414–419, 2005     

Slot-waveguide biochemical sensor

We report an experimental demonstration of an integrated biochemical sensor based on a slot-waveguide microring resonator. The microresonator is fabricated on a Si3N4-SiO2 platform and operates at a wavelength of 1.3 microm. The transmission spectrum of the sensor is measured with different ambient refractive indices ranging from n=1.33 to 1.42. A linear shift of the resonant wavelength with increasing ambient refractive index of 212 nm/refractive index units (RIU) is observed. The sensor detects a minimal refractive index variation of 2x10(-4) RIU.     

Synthesis and characterization of SBA-3, SBA-15, and SBA-1 nanostructured catalytic materials

A highly ordered large pore mesoporous silica molecular sieve SBA-3, SBA-15, Al-SBA-15, and SBA-1, were developed and characterized by XRD, BET, FTIR, SEM, and NMR-MAS. The catalytic materials were synthesized using different raw materials and operation conditions. These materials contain a regular arrangement of uniform channels with diameters between 1.8 and 10 nm, high specific surface area and high specific pore volume. The designed methods were effective for the synthesis, presenting each mesostructured materials, patterns of XRD and other characteristics corresponding to the reported ones in literature. The new route employed to synthesize Al-SBA-15, generates a catalyst with only aluminum in tetrahedral form, according to the data of (27)Al NMR-MAS. However, several reports indicated that the coordination of the Al atoms changes below the Si/Al ratio of 45, presenting peaks corresponding to penta and hexa-coordinated aluminum, which are absent in our samples (Si/Al = 50 and 33).     

Ratio Asymptotics for Polynomials Orthogonal on Arcs of the Unit Circle

Ratio asymptotics for orthogonal polynomials on the unit circle is characterized in terms of the existence of lim _n |Φ _n (0)| and {lim _n [ Φ _n+1 (0)/ Φ _n (0)] , where denotes the sequence of reflection coefficients. The limit periodic case, that is, when these limits exist for n = j mod k , j = 1, . . ., k , is also considered. December 27, 1996. Date revised: October 14, 1997. Date accepted: December 22, 1997.     

An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses

In this paper, we provide a priori and a posteriori error analyses of an augmented mixed finite element method with Lagrange multipliers applied to elliptic equations in divergence form with mixed boundary conditions. The augmented scheme is obtained by including the Galerkin least-squares terms arising from the constitutive and equilibrium equations. We use the classical Babuška–Brezzi theory to show that the resulting dual-mixed variational formulation and its Galerkin scheme defined with Raviart–Thomas spaces are well posed, and also to derive the corresponding a priori error estimates and rates of convergence. Then, we develop a reliable and efficient residual-based a posteriori error estimate and a reliable and quasi-efficient Ritz projection-based one, as well. Finally, several numerical results illustrating the performance of the augmented scheme and the associated adaptive algorithms are reported.     

A Widder’s Type Theorem for the Heat Equation with Nonlocal Diffusion

The main goal of this work is to prove that every non-negative strong solution u(x, t) to the problem $$u_t + (-\Delta)^{\alpha/2}{u} = 0 \,\, {\rm for} (x, t) \in {\mathbb{R}^n} \times (0, T ), \, 0 < \alpha < 2,$$ can be written as $$u(x, t) = \int_{\mathbb{R}^n} P_t (x - y)u(y, 0) dy,$$ where $$P_t (x) = \frac{1}{t^{n/ \alpha}}P \left(\frac{x}{t^{1/ \alpha}}\right),$$ and $$P(x) := \int_{\mathbb{R}^n} e^{i x\cdot\xi-|\xi |^\alpha} d\xi.$$ This result shows uniqueness in the setting of non-negative solutions and extends some classical results for the heat equation by Widder in [15] to the nonlocal diffusion framework.