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.     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

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     

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.     

Determination of iron-porphyrin-like complexes at nanomolar levels in seawater

A new method for the non-specific determination of iron-porphyrin-like complexes in natural waters has been developed. It is based on the chemiluminescent oxidation of the luminol in the presence of dioxygen (O₂) at pH 13. The method has been implemented in a FIA manifold that allowed the direct injection of seawater. The limit of detection is 0.11 nM of equivalent hemin (Fe-protoporphyrin IX). Fe²⁺, Fe³⁺, H₂O₂, siderophore (deferoxamin mesylate), humic acid and phytic acid did not interfere when they were present at the concentrations expected in seawater. Metal free porphyrin and Mg, Cu, Co porphyrin complexes did not induce a significant chemiluminescent signal. Poisoned unfiltered samples could be stored for several weeks before analyses. The new method was successfully applied to the determination of the Fe-porphyrin complexes contained in cultured phytoplankton and in natural samples.     

Anti-Hyperglycemic Effects of Refined Fractions from Cyclocarya paliurus Leaves on Streptozotocin-Induced Diabetic Mice

To identify the chemical components responsible for the anti-hyperglycemic effect of Cyclocarya paliurus (Batal.) Iljinsk (Juglandaceae) leaves, an ethanol extract (CPE) and a water extract (CPW) of C. paliurus leaves, as well as their total flavonoids (CPF), triterpenoids (CPT) and crude polysaccharides (CPP), were prepared and assessed on streptozotocin (STZ)-induced diabetic mice. After being orally administrated once a day for 24 days, CPF (300 mg/kg), CPP (180 mg/kg), or CPF+CPP (300 mg/kg CPF + 180 mg/kg CPP) treatment reversed STZ-induced body weight and muscle mass losses. The glucose tolerance tests and insulin tolerance tests suggested that CPF, CPP, and CPF+CPP showed anti-hyperglycemic effect in STZ-induced diabetic mice. Furthermore, CPF enhances glucose-stimulated insulin secretion in MIN6 cells and insulin-stimulated glucose uptake in C2C12 myotubes. CPF and CPP suppressed inflammatory cytokine levels in STZ-induced diabetic mice. Additionally, CPF and CPP improved STZ-induced diabetic nephropathy assessed by H&E staining, blood urea nitrogen content, and urine creatinine level. The molecular networking and Emperor analysis results indicated that CPF showed potential anti-hyperglycemic effects, and HPLC–MS/MS analysis indicated that CPF contains 3 phenolic acids and 9 flavonoids. In contrast, CPT (650 mg/kg) and CPC (300 mg/kg CPF + 180 mg/kg CPP + 650 mg/kg CPT) did not show anti-hyperglycemic effect. Taken together, polysaccharides and flavonoids are responsible for the anti-hyperglycemic effect of C. paliurus leaves, and the clinical application of C. paliurus need to be refined.