Design, synthesis and characterization of a Pt-Gd metal-organic framework containing potentially catalytically active sites

The heterobimetallic metal-organic framework {[(BPDC)PtCl(2)](3)(Gd(H(2)O)(3))(2)}.5H(2)O (BPDC = 2,2'-bipyridine-5,5'-dicarboxylate) has been designed and synthesized by hydrothermal methods. The new coordination polymer contains subunits of (BPDC)PtCl(2) (1) where both N atoms of the BPDC ligand are attached to a square-planar Pt(II) center. The two remaining cis coordination sites at Pt(II) are occupied by chloride ions. The final structure (2) of the polymeric network is obtained when Gd(III) ions link together the (BPDC)PtCl(2) units, which are organized in sheets, into larger blocks. These blocks are stacked along the crystallographic [010] direction and are held together by a hydrogen bonding scheme that involves carboxylate oxygen atoms and water molecules in the coordination sphere of Gd. The coordination polymer 2 can be obtained in a single-step reaction or in a two-step synthesis where the corresponding Pt complex (1) was first synthesized followed by reacting 1 with Gd(NO(3))(3).6H(2)O. In situ high temperature powder X-ray diffraction shows that the crystalline coordination polymer transforms into an anhydrous modification at 100 degrees C. This modification is stable to 350 degrees C, at which temperature the structure starts to decompose. The coordination sphere around platinum in the polymer closely resembles organometallic Pt complexes that have been previously found to catalytically or stoichiometrically activate and functionalize hydrocarbon C-H bonds in homogeneous systems.     

Synthesis of 1-hydroxy-substituted pyrazolo[3,4-c]- and pyrazolo[4, 3-c]quinolines and -isoquinolines from 4- and 5-aryl-substituted 1-benzyloxypyrazoles

1-Hydroxypyrazolo[3,4-c]quinoline (22), 1-hydroxypyrazolo[4, 3-c]quinoline (21), 1-hydroxypyrazolo[3,4-c]isoquinoline (20), and 1-hydroxypyrazolo[4,3-c]isoquinoline (19) were prepared from 1-benzyloxypyrazole (6), establishing the pyridine B-ring in the terminal step. The pyridine ring of pyrazoloquinolines 14 and 18 was formed via cyclization of a formyl group at C-4 or C-5 and an amino group of a 2-aminophenyl substituent at C-5 or C-4 in 1-benzyloxypyrazole. The pyridine ring of pyrazoloisoquinolines 5 and 9 was created via cyclization of a formyl group in a 2-formylphenyl substituent at C-4 or C-5 with an iminophosphorane group installed at C-5 or C-4 of 1-benzyloxypyrazole by lithiation followed by reaction with tosyl azide and then with tributylphoshine utilizing the Staudinger/aza-Wittig protocol. The 2-aminophenyl and the 2-formylphenyl substituent were introduced at C-5 or C-4 by regioselective metalation followed by transmetalation to the pyrazolylzinc halide and subsequent palladium-catalyzed cross-coupling with 2-iodoaniline or 2-bromobenzaldehyde. The order of reactions and use of protecting groups in the individual sequences have been optimized. The 1-benzyloxy-substituted pyrazoloquinolines and isoquinolines thus obtained were debenzylated by strong acid to the corresponding 1-hydroxy-substituted pyrazoloquinolines and isoquinolines 19-22.     

Continuous dependence results for non-linear Neumann type boundary value problems

We obtain estimates on the continuous dependence on the coefficient for second-order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et al., Jakobsen and Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation.     

Gamma-ray spectroscopy with relativistic exotic heavy-ions

Feasibility of gamma-ray spectroscopy at relativistic energies with exotic heavy-ions and new generation of germanium detectors (segmented Clover) is discussed. An experiment with such detector array and radioactive is discussed.     

A method for estimating the orientation of a directional sound source from source directivity and multi-microphone recordings: principles and application

Taking into account directivity of real sound sources makes it possible to try solving an interesting and biologically relevant problem: estimating the orientation in three-dimensional space of a directional sound source. The source, of known directivity, produces a broadband signal (in the ultrasonic range, in this application) that is recorded by microphones whose position with respect to source is known. An analytical method to process the recorded signals and estimate source orientation is developed in this paper. Experiments testing method performance in estimating source orientation were performed both in a laboratory environment with a Polaroid transducer as source and in a flight room with a Myotis daubentonii bat. In the first case, results showed the estimation method to be accurate and pointed out its limitations. The latter case is significant as an example biological application of the method for extracting behavioral features from bats; results are compared with alternative calculations based on microphone root-mean-square (rms)-pressure values.     

Continuous dependence estimates for viscosity solutions of integro-PDEs

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods.     

Least-squares spectral method for solving advective population balance problems

The combined CFD-PBE (population balance models) are computationally intensive requiring efficient numerical methods for solving practical problems. In this paper, a high order method is presented based on the least-squares method (LSM) for the solution of a spatial-dependent population balance equation which includes advective processes. Numerical experiments are performed in order to study the behavior of the proposed method for one-dimensional cases using model problems with analytical solutions.     

On distributional solutions of local and nonlocal problems of porous medium type

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of

(0.1)${?}_{t}u?{\mathfrak{L}}^{\sigma ,\mu }[\phi (u)]=g(x,t)\text{in}{\mathbb{R}}^N\times (0,T),$

where φ is merely continuous and nondecreasing, and ${\mathfrak{L}}^{\sigma ,\mu }$ is the generator of a general symmetric Lévy process. This means that ${\mathfrak{L}}^{\sigma ,\mu }$ can have both local and nonlocal parts like, e.g., ${\mathfrak{L}}^{\sigma ,\mu }=\mathrm{\Delta }?{(?\mathrm{\Delta })}^{\frac{1}{2}}$. New uniqueness results for bounded distributional solutions to this problem and the corresponding elliptic equation are presented and proven. A key role is played by a new Liouville type result for ${\mathfrak{L}}^{\sigma ,\mu }$. Existence and a priori estimates are deduced from a numerical approximation, and energy-type estimates are also obtained.