A fast linearized numerical method for nonlinear time-fractional diffusion equations

Numerical Algorithms - In this paper, we study a fast linearized numerical method for solving nonlinear time-fractional diffusion equations. A new weighted method is proposed to construct...     

Regioselective synthesis of the bridged tricyclic core of Garcinia natural products via intramolecular aryl acrylate cycloadditions

[reaction: see text] Two different routes to the tricyclic core of Garcinia-derived natural products are described. The first approach is based on a tandem Claisen/Diels-Alder rearrangement and delivers the desired lactone 14. The second approach, employing a Wessely oxidation/Diels-Alder protocol, leads to the same caged heterocycle, albeit with modified constitution.     

Chemical Modification of Silica Gels

Highly porous pure and polyethyleneglycol (PEG)-doped silica gels have been prepared from tetraethyl orthosilicate (TEOS) in ethanol using NH₄OH base-catalysis. Addition of PEG to the SiO₂-system increases the average particle size and most frequent pore diameter of the resultant gels while their total surface area decreases. The viscosity of the sol increases with PEG concentration and passes through a maximum with increasing molecular weight at PEG 200. Results obtained indicate a definite interaction of the polymer with SiO₂ and that this interaction is not as a result of direct formation of Si– O– C linkage, but is more likely to be due to hydrogen bonding between the hydrated PEG and the Si– O– Si network. Structure-process correlations are considered.     

On a generalization of Aczél’s inequality

In this paper, we prove a generalization of Aczél’s inequality. The obtained inequalities extend some results established recently. We also give some comments on a recent result concerning the refinements of the generalized Aczél–Popoviciu’s inequality.     

Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations

Two fully discrete methods are investigated for simulating the distributed-order sub-diffusion equation in Caputo’s form. The fractional Caputo derivative is approximated by the Caputo’s BDF1 (called L1 early) and BDF2 (or L1-2 when it was first introduced) approximations, which are constructed by piecewise linear and quadratic interpolating polynomials, respectively. It is shown that the first scheme, using the BDF1 formula, possesses the discrete minimum-maximum principle and nonnegativity preservation property such that it is stable and convergent in the maximum norm. The method using the BDF2 formula is shown to be stable and convergent in the discrete H ¹ norm by using the discrete energy method. For problems of distributed order within a certain region, the method is also proven to preserve the discrete maximum principle and nonnegativity property. Extensive numerical experiments are provided to show the effectiveness of numerical schemes, and to examine the initial singularity of the solution. The applicability of our numerical algorithms to a problem with solution which lacks the smoothness near the initial time is examined by employing a class of power-type nonuniform meshes.     

High‐order compact schemes for fractional differential equations with mixed derivatives

In this article, we consider two‐dimensional fractional subdiffusion equations with mixed derivatives. A high‐order compact scheme is proposed to solve the problem. We establish a sufficient condition and show that the scheme converges with fourth order in space and second order in time under this condition.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2141–2158, 2017     

Columnar/smectic metallomesogens derived from heterocyclic benzoxazoles

The synthesis, mesomorphic behavior, and optical properties of two new series of metal complexes 1a,b-M (M=Pd, Cu, Zn) derived from benzoxazoles 2a,b are reported. The crystal and molecular structures of mesogenic 5-decyloxy-2-(6-decyloxybenzooxazol-2-yl)phenol and nonmesogenic bis[5-octyloxy-2-(6-octyloxybenzooxazol-2-yl) phenol]Pd(II) were determined by means of X-ray structural analysis. Two benzoxazoles 2a exhibited monotropic SmA phases, and all benzoxazoles 2b were nonmesogenic. On the other hand, metal complexes 1a-M exhibited distinctly different mesomorphism from complexes 1b-M. Complexes 1a-Pd formed SmC phases; complexes 1a-Cu and 1a-Zn formed crystal phases. In contrast, complexes 1b-Zn exhibited columnar phases, and complexes 1b-Cu and 1b-Pd were nonmesogenic. The difference of the mesomorphism in 1a-M and 1b-M was probably attributed to the geometry and/or the overall molecular shape created by 2a and 2b. The electronic configuration of metal ion might play an important role in forming the mesophases. The fluorescent properties of these compounds were also examined.     

High-temperature, high-pressure hydrothermal synthesis and characterization of an open-framework uranyl silicate with nine-ring channels: Cs2UO2Si10O22

A new uranium(VI) silicate, Cs(2)UO(2)Si(10)O(22), has been synthesized by a high-temperature, high-pressure hydrothermal method and characterized by single-crystal X-ray diffraction, luminescence, and solid state NMR spectroscopy. It crystallizes in the monoclinic space group P2(1)/c (No. 14) with a = 12.2506(4) ?, b = 8.0518(3) ?, c = 23.3796(8) ?, β = 90.011(2)°, and Z = 4. Its structure consists of silicate double layers in the ab plane which are connected by UO(6) tetragonal bipyramids via four equatorial oxygen atoms to form a 3D framework with nine-ring channels parallel to the b axis where the Cs(+) cations are located. The photoluminescence emission spectrum at room temperature consists of one broad structured band which is typical of uranyl. The (29)Si MAS NMR spectrum is consistent with the crystal structure as determined from X-ray diffraction, and the resonances in the spectrum are assigned. A comparison of related uranyl silicate structures is made.     

Cs8U(IV)(U(VI)O2)3(Ge3O9)3·3H2O: a mixed-valence uranium germanate with 9-ring channels

A mixed-valence uranium(IV,VI) germanate has been synthesized under high-temperature, high-pressure hydrothermal conditions. The structure contains discrete U(IV)O(6) octahedra and U(VI)O(6) tetragonal bipyramids, which are connected by three-membered single-ring Ge(3)O(9)(6-) anions to form a three-dimensional framework with 9-ring channels. The U 4f X-ray photoelectron spectroscopy spectrum was measured to identify the valence states of the uranium.     

Functional Hydride Transfer by a Thiolate‐Containing Model of Mono‐Iron Hydrogenase featuring an Anthracene Scaffold

We report the synthesis, X‐ray structure and functional biomimetic activity of a model complex of mono‐iron hydrogenase (Hmd). To achieve the desired biomimetic fac‐CNS(thiolate) ligation motif, an anthracene framework is used to provide the requisite donors in a single chelate. A bulky aryl thiolate (ortho dimethylphenyl) is included to achieve mononuclearity. In addition to exhibiting structural (X‐ray) and spectroscopic (NMR, IR) similarity to the enzyme, the complex is competent for H₂ activation (heterolysis) and hydride transfer to a model substrate—mimicking the functional behavior of the enzyme in a biomimetic CNS coordination sphere for the first time.